Appunti Integrativi, Complementi E Problemi

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Alessandro Petrolini October 12, 2011 Dipartimento di Fisica dell’Universit` a di Genova and INFN Sezione di Genova - ITALY [email protected] Appunti Integrativi, Complementi e Problemi su alcuni argomenti dei corsi di: Fisica Generale Avvertenze Importanti Questi appunti non vogliono essere, non possono essere e non sono un trattato su argomenti di Fisica Generale, argomento sul quale esistono molti ottimi testi, il cui uso `e indispensabile per uno studio approfondito e completo. Questi appunti sono solo un sommario sintetico e una referenza per alcuni degli argomenti trattati nel Corso di Fisica Generale, da usarsi come integrazione alle lezioni e ai testi tradizionali di Fisica Generale e dopo lo studio delle lezioni e dei testi tradizionali. Queste note sono solo un semplice sommario/traccia di alcuni degli argomenti svolti durante il corso, con l’aggiunta di alcuni argomenti non svolti. Non hanno pretesa di completezza, non sostituiscono in nessun modo la frequenza alle lezioni (che `e indispensabile), non sostituiscono in nessun modo lo studio dei testi raccomandati (che `e indispensabile), e non esonerano in nessun modo dallo svolgimento di un adeguato numero di problemi. Questi appunti, che nascono durante la preparazione delle lezioni, sono soggetti a frequenti e continui aggiornamenti, e non hanno certamente la completezza n`e l’organicit` a che deve avere un libro sull’argomento. In ogni caso l’apprendimento e la comprensione degli argomenti trattati nel corso richiede necessariamente numerosi e vasti approfondimenti e la consultazione di testi, come quelli riportati nella bibliografia di queste note, `e assolutamente indispensabile. Queste note non sono di pubblico dominio ma sono strettamente riservate agli studenti dei Corsi di Fisica Generale del Corso di Studi in Fisica dell’Universit` a degli Studi di Genova. Queste note non coprono tutto il programma di insegnamento, per il quale si rimanda agli appropriati documenti ufficiali. Lo scopo principale `e fornire un sommario/traccia e un punto di riferimento per alcuni degli argomenti svolti durante il corso, principalmente quelli che, a giudizio del sottoscritto, possono risultare pi` u ostici e quelli che sono, a giudizio del sottoscritto, meno facilmente reperibili nei testi nella forma adottata durante il corso. Un secondo scopo `e quello di fornire una referenza per i dettagli di alcuni degli argomenti svolti durante il corso, quali, ad esempio, lo svolgimento dei calcoli. Un terzo scopo specifico `e quello di fornire un punto di riferimento su tutti gli aspetti formali degli argomenti del programma, che spesso, se trattati in modo non adeguato, assorbono enormi energie allo studente, distogliendolo dalla comprensione e approfondimento degli aspetti fisici degli argomenti, che sono il vero oggetto di studio della Fisica Generale. Il fornire allo studente un punto di riferimento sintetico ma completo sul formalismo che funge da linguaggio per la Fisica Generale dovrebbe aiutare lo studente a concentrarsi sulla Fisica. Queste note sono quasi completamente prive di tutte le parti descrittive, fenomenologiche e sperimentali, per le quali si rimanda completamente ai testi consigliati. Queste note sono una versione altamente preliminare. Sono certamente presenti molti errori, sperabilmente non errori concettuali. Nel caso siano rilevati errori, o in caso di dubbi, il lettore `e invitato a segnalarlo. Il materiale esposto in queste note non `e necessariamente esposto nel modo in cui `e stato presentato a Lezione. Queste sono semplicemente un insieme di note che ho preparato per mio uso personale e che rendo disponibili agli studenti come una risorsa aggiuntiva per lo studio. Sono solo un complemento alle lezioni e allo studio dei testi di Fisica Generale. Questa versione preliminare degli appunti `e scritta in parte in italiano e in parte in inglese. Alessandro Petrolini VERSION: October 12, 2011 VERY PRELIMINARY and INCOMPLETE DRAFT RINGRAZIAMENTI Si ringraziano i molti studenti che hanno fornito numerose segnalazioni di errori da correggere e commenti vari. 2 October 12, 2011 Introduzione Consigli agli studenti e... ai docenti per risolvere un problema L'imporlanza delle ipotesi Lo studente deve essere condotto per mana dal docente, il quale deve preoccuparsi di presentare il testo del problema con la massima chiarezza, con completezza di dati e senza mai lasciare dubbi sulla natura del processo esaminato, sulle ipotesi necessarie per poterlo trattare, su che cosa si pub trascurare e che cosa invece si da per scontato. E molto importante l' attenta lettura del testa da parte della studente, che deve saper pesare attentamente qualunque sfumatura (aggettivi e avverbi compresi) . Molto spesso nel testa di un problema si parla di molle 0 di fili precisando raramente che s'intendono molle 0 fili ideali; si parla di "gas" senza precisare se reali o perfetti; si parla di pendoli senza chiarire se semplici 0 composti e neppure se stanno oscillando ad angoli piccoli 0 meno; nello studio di un mota si da troppo frequentemente per scontato che Ie costanti iniziali del mota siano nulle, corne altrettanto spesso non si ritiene necessario precisare se gli attriti sono trascurabili 0 meno, se Ie carrucole sono lisce e prive di massa, 0 se la resistenza dell' aria debba essere tenuta in considerazione; in altri casi ancora, si parla genericamente di mota senza precisare se il piano in cui avviene e orizzontale 0 verticale, oppure si pretende che 10 studente calcoli il momenta d'inerzia di un'asta senza aver precisato se e omogenea e uniforme. La soluzione letterale Lo studente tende generalmente a inserire subito nelle leggi fisiche i valori numerici dati dal testa del problema e in tal modo perde di vista il significato del risultato ottenuto: non si accorge se una soluzione perde significato all' annullarsi di un denominatore per certi valori dei parametri e neppure vede se un discriminante diventa negativo 0 nullo. L'inserimento immediato dei dati numerici impedisce di svolgere la discussione sui limiti di validita delle soluzioni trovate. 2 Introduzione E percio indispensabile che gli studenti si abituino aHo svolgimento solo letterale del problema e a sostituire i valori numerici solo nell'ultima formula ricavata; questa modo di procedere consente anche il controllo dimensionale e quindi di scoprire la presenza di eventuali errori. I dati ridondanti... Talvolta in un problema vengono forniti dati numerici del tutto inutili e 10 studente entra in crisi perche e convinto di doverli utilizzare a tutti i costi e non ci riesce. In alcuni casi si tratta di una trappola tesa dal docente per verificare illivello di sicurezza dello studente ed e una scelta che personalmente non condivido, poiche e ben raro che uno studente si trovi in una prova scritta nelle migliori condizioni per individuare trabocchetti. In altri casi, purtroppo molto frequenti, invece, l'insegnante propone il problema senza prima provare a risolverlo e nel dubbio ha pensato bene di fornire qualche dato in piu, rna anche questa non mi trova d'accordo . ...e queIii mancanti In molti casi la soluzione del problema e indipendente da certe grandezze che 10 studente ritiene invece indispensabili: e il caso della massa di due oggetti identici che entrano in collisione e la cui velocita dopo l'urto e del tutto indipendente dalla massa. Effetti dannosi della premura Un difetto comune alIa maggior parte degli studenti e di pretendere di trovare subito una formula che fornisca la grandezza incognita, senza tentare di costruire percorsi piu 0 meno elaborati che conducano gradualmente aHa soluzione. Qui e fondamentale la funzione del docente che deve dare una traccia, mediante 10 svolgimento di molti esempi, di quali sono i metodi da seguire caso per caso. II riconoscimento Un altro ostacolo aHe capacita di svolgere un problema e la generale incapacita degli studenti di riconoscere una legge fisica se appena viene presentata in modo leggermente diverso da queHo tradizionalmente esposto nei libri di testo; ho per Consigli agli studenti e... ai docenti per risolvere un problema esempio sperimentato che se si da una legge di moto del tipo v 3 =-E , chiedendo Ie costanti iniziali del mota e il tipo di moto, solo una modesta percentuale di studenti e in grado di riconoscere un mota uniformemente accelerato e di capire che tali costanti sono nulle. AHo stesso modo, se si da una relazione del tipo a + 2x = 0 (precisando il sistema di unita di misura usato) eben difficile che 10 studente si accorga che si tratta, nelIe stesse unita di misura di un mota armonico con pulsazione OJ = h. Analogie pericolose Certe tecniche di soluzione di un problema, una volta apprese in un capitolo della fisica hanno validita generale: cio accade per esempio, per il calcolo delle componenti di un vettore 0 per 10 studio della legge del moto. Spesso pero 10 studente e tentato di applicare certe tecniche anche quando non e possibile: un esempio tipico e quello del doppio piano inclinato nel quale due blocchi sono collegati da un filo ideale; dati gli angoli e i coefficienti di attrito dei piani e Ie masse dei blocchi, non si puo quasi mai stabilire a priori quale dei due blocchi trascinera l' altro e alIo studente non resta che scegliere a caso un verso di moto, scrivere Ie equazioni di movimento utilizzando il diagramma di corpo libero e calcolarsi l'accelerazione. Le cose vanno bene se l' accelerazione risulta positiva, mentre sono guai se essa risulta negativa, poiche la tentazione dello studente e in genere di concludere incautamente che non sara il blocco prescelto a trascinare l' altro, rna esattamente il contrario, limitandosi a cambiare verso al mota rna convinto che l' accelerazione calcolata sia in modulo esatta; in realta, COS! operando, 10 studente non si rende conto che e necessario riscrivere interamente Ie equazioni di moto, perche non tutti i segni cambiano invertendo la direzione di mota scelta in un primo tempo: cambieranno verso e segno la forza di attrito e l' accelerazione, rna non Ie componenti del peso lungo i piani e Ie tensioni. Ben diversa e invece la situazione nel caso dei circuiti elettrici, dove, applicando i principi di Kirchhoff e attribuendo a caso i versi delle correnti, se qualcuna di esse risulta negativa basta invertirne il verso, rna con 10 stesso valore assoluto. La concretezza del problema Per interessare 10 studente a un problema di fisica e opportuno non ricorrere troppo spesso a problemi Ie cui soluzioni non offrono alcuna possibilita di riscontro numerico con fatti osservabili nella vita quotidiana, rna rifarsi invece a problemi che possano interessare I' allievo facendogli capire come i risultati della corretta applicazione delle leggi fisiche siano in accordo con Ie nostre osservazioni reali di un fenomeno fisico. 4 Introduzione Per esempio, in generale gli studenti non hanno la minima idea dei valori di accelerazione delle auto; la maggior parte di essi econvinta che i potenti motori di una macchina di Formula 1 possano fornire accelerazioni pari a 10-20 volte g. Invece di limitarci alIa banale applicazione delle equazioni di Galileo suI mota uniformemente accelerato, perche allora non provare a far vedere agli allievi che un'auto che si porta da 0 a 100 kmIh in 10 s, nell'ipotesi di accelerazione costante, ha un'accelerazione di 2,8 rn/s2 e che la stessa auto percorre 1 Ian da fermo in 26,8 s? Allo stesso modo, oltre a far calcolare agli allievi la potenza del motore di una pompa per espellere l' acqua da una miniera, perche non provare a far loro calcolare anche la minima potenza che deve avere il motore di una fuoristrada per superare una pendenza costante con una data velocita costante? In tal modo possono rendersi conto che i risultati del calcolo teorico coincidono con quelli reali. E ancora, ~Itre a far calcolare la potenza dissipata da un circuito elettrico puramente teorico, perche non convincere gli studenti, con Ie leggi di Ohm, Kirchhoff e Joule alIa mano, che con un contatore domestico da 2,5 kW non possiamo far funzionare contemporaneamente 10 scaldabagno elettrico, il forno a microonde, la lavatrice, la lavastoviglie e il termoventilatore? Oppure potremmo facilmente dar loro una chiara idea delle dispersioni nell'isolamento termico di un boiler elettrico facendo calcolare quanta tempo in teoria e necessario per riscaldare 80 I d' acqua da 20 a 60°C con una potenza di 2 kW e facendo notare la sensibile differenza tra il tempo calcolato (6700 s) e quello reale (almeno 9000 s). Infine, un suggerimento utile per gli studenti nella soluzione degli esercizi e di introdurre incognite "ausiliarie", grandezze di cui non si conosce il valore rna che, se il procedimento seguito ecorretto, aHa fine scompaiono semplificandosi. Part Q Appendixes 735 A Mathematics 737 VECTOR IDENTITIES4 Notation: f, g, are scalars; A, B, etc., are vectors; T is a tensor; I is the unit dyad. (1) A · B × C = A × B · C = B · C × A = B × C · A = C · A × B = C × A · B (2) A × (B × C) = (C × B) × A = (A · C)B − (A · B)C (3) A × (B × C) + B × (C × A) + C × (A × B) = 0 (4) (A × B) · (C × D) = (A · C)(B · D) − (A · D)(B · C) (5) (A × B) × (C × D) = (A × B · D)C − (A × B · C)D (6) ∇(f g) = ∇(gf ) = f ∇g + g∇f (7) ∇ · (f A) = f ∇ · A + A · ∇f (8) ∇ × (f A) = f ∇ × A + ∇f × A (9) ∇ · (A × B) = B · ∇ × A − A · ∇ × B (10) ∇ × (A × B) = A(∇ · B) − B(∇ · A) + (B · ∇)A − (A · ∇)B (11) A × (∇ × B) = (∇B) · A − (A · ∇)B (12) ∇(A · B) = A × (∇ × B) + B × (∇ × A) + (A · ∇)B + (B · ∇)A (13) ∇2 f = ∇ · ∇f (14) ∇2 A = ∇(∇ · A) − ∇ × ∇ × A (15) ∇ × ∇f = 0 (16) ∇ · ∇ × A = 0 If e1 , e2 , e3 are orthonormal unit vectors, a second-order tensor T can be written in the dyadic form (17) T =
i,j Tij ei ej In cartesian coordinates the divergence of a tensor is a vector with components (18) (∇·T )i =
j (∂Tji /∂xj ) [This definition is required for consistency with Eq. (29)]. In general (19) ∇ · (AB) = (∇ · A)B + (A · ∇)B (20) ∇ · (f T ) = ∇f ·T +f ∇·T 4 B International System of Units 739 Relationships of the SI derived units with special names and symbols and the SI base units SI BASE UNITS Derived units without special names SI DERIVED UNITS WITH SPECIAL NAMES AND SYMBOLS Solid lines indicate multiplication, broken lines indicate division kilogram kg MASS newton m3 VOLUME meter m LENGTH second mole s TIME VELOCITY mol A ELECTRIC CURRENT kelvin K THERMODYNAMIC TEMPERATURE candela AREA m/s AMOUNT OF SUBSTANCE ampere m2 cd LUMINOUS INTENSITY m/s2 ACCELERATION N (kg·m/s2) FORCE Pa (N/m2) PRESSURE, STRESS (N·m) joule pascal watt (J/s) gray Gy (J/kg) ABSORBED DOSE becquerel W ENERGY, WORK, QUANTITY OF HEAT POWER, HEAT FLOW RATE (OF A RADIONUCLIDE) weber henry (mol/s) kat (V·s) MAGNETIC FLUX (A·s) coulomb T MAGNETIC FLUX DENSITY (W/A) POTENTIAL, ELECTROMOTIVE FORCE (lm/m2) lux (Wb/m2) tesla INDUCTANCE ELECTRIC CHARGE CELSIUS TEMPERATURE t/°C = T/K – 273.15 FREQUENCY (Wb/A) V (C/V) (1/s) H volt farad (J/kg) Hz C (K) degree Celsius °C hertz ACTIVITY Wb CATALYTIC ACTIVITY Bq Sv DOSE EQUIVALENT (1/s) J katal sievert (V/A) ohm (1/W) siemens F W S CAPACITANCE RESISTANCE CONDUCTANCE (cd·sr) lumen lx lm ILLUMINANCE LUMINOUS FLUX steradian 2 2 sr (m /m = 1) SOLID ANGLE radian rad (m/m = 1) PLANE ANGLE The diagram above shows graphically how the 22 SI derived units with special names and symbols are related to the seven SI base units. In the first column, the symbols of the SI base units are shown in rectangles, with the name of the unit shown toward the upper left of the rectangle and the name of the associated base quantity shown in italic type below the rectangle. In the third column the symbols of the derived units with special names are shown in solid circles, with the name of the unit shown toward the upper left of the circle, the name of the associated derived quantity shown in italic type below the circle, and an expression for the derived unit in terms of other units shown toward the upper right in parenthesis. In the second column are shown those derived units without special names [the cubic meter (m3) excepted] that are used in the derivation of the derived units with special names. In the diagram, the derivation of each derived unit is indicated by arrows that bring in units in the numerator (solid lines) and units in the denominator (broken lines), as appropriate. Two SI derived units with special names and symbols, the radian, symbol rad, and the steradian, symbol sr (bottom of the third column of the diagram), are shown without any connections to SI base units – either direct or through other SI derived units. The reason is that in the SI, the quantities plane angle and solid angle are defined in such a way that their dimension is one – they are so-called dimensionless quantities. This means that the coherent SI derived unit for each of these quantities is the number one, symbol 1. That is, because plane angle is expressed as the ratio of two lengths, and solid angle as the ratio of an area and the square of a length, the SI derived unit for plane angle is m/m = 1, and the SI derived unit for solid angle is m2/m2 = 1. To aid understanding, the special name radian with symbol rad is given to the number 1 for use in expressing values of plane angle; and the special name steradian with symbol sr is given to the number 1 for use in expressing values of solid angle. However, one has the option of using or not using these names and symbols in expressions for other SI derived units, as is convenient. The unit “degree Celsius,’’ which is equal to the unit “kelvin,” is used to express Celsius temperature t. In this case,“degree Celsius’’ is a special name used in place of “kelvin.’’ This equality is indicated in the diagram by the symbol K in parenthesis toward the upper right of the °C circle. The equation below “CELSIUS TEMPERATURE’’ relates Celsius temperature t to thermodynamic temperature T. An interval or difference of Celsius temperature can, however, be expressed in kelvins as well as in degrees Celsius. 94 2 SI units 2.1 SI base units Formal definitions of all SI base units are approved by the CGPM. The first such definition was approved in 1889 and the most recent in 1983. These definitions are modified from time to time as techniques of measurement evolve and allow more accurate realizations of the base units. 2.1.1 Definitions Current definitions of the base units, as taken from the Comptes Rendus (CR) of the corresponding CGPM, are here shown indented and in a heavy font. Related decisions which clarify these definitions but are not formally part of them, as taken from the Comptes Rendus (CR) of the corresponding CGPM or the ProcèsVerbaux (PV) of the CIPM, are also shown indented in a font of normal weight. The linking text provides historical notes and explanations but is not part of the definitions themselves. 2.1.1.1 Unit of length (metre) The 1889 definition of the metre, based upon the international prototype of platinum-iridium, was replaced by the 11th CGPM (1960) using a definition based upon a wavelength of krypton 86 radiation. This definition was adopted in order to improve the accuracy with which the metre may be realized. In turn, this was replaced in 1983 by the 17th CGPM (Resolution 1; CR, 97 and Metrologia, 1984, 20, 25): The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. Note that the effect of this definition is to fix the speed of light at exactly 299 792 458 m · s−1. The original international prototype of the metre, which was sanctioned by the 1st CGPM in 1889 (CR, 34-38), is still kept at the BIPM under conditions specified in 1889. SI Units • 95 2.1.1.2 Unit of mass (kilogram) The international prototype of the kilogram, made of platinum-iridium, is kept at the BIPM under conditions specified by the 1st CGPM in 1889 (CR, 34-38) when it sanctioned the prototype and declared: This prototype shall henceforth be considered to be the unit of mass. The 3rd CGPM (1901; CR, 70), in a declaration intended to end the ambiguity in popular usage concerning the word “weight” confirmed that: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. The complete declaration appears on page 118. 2.1.1.3 Unit of time (second) The unit of time, the second, was at one time considered to be the fraction 1/86 400 of the mean solar day. The exact definition of “mean solar day” was based on astronomical theories. However, measurement showed that irregularities in the rotation of the Earth could not be taken into account by the theory and have the effect that this definition does not allow the required accuracy to be achieved. In order to define the unit of time more precisely, the 11th CGPM (1960; CR, 86) adopted a definition given by the International Astronomical Union which was based on the tropical year. Experimental work, however, had already shown that an atomic standard of time interval, based on a transition between two energy levels of an atom or a molecule, could be realized and reproduced much more precisely. Considering that a very precise definition of the unit of time is indispensable for the International System, the 13th CGPM (1967-1968, Resolution 1; CR, 103 and Metrologia, 1968, 4, 43) replaced the definition of the second by the following: The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. At its 1997 meeting, the CIPM affirmed that: This definition refers to a caesium atom in its ground state at a temperature of 0 K. 2.1.1.4 Unit of electric current (ampere) Electric units, called “international”, for current and resistance were introduced by the International Electrical Congress held in Chicago in 1893, and definitions of the “international” ampere and the “international” ohm were confirmed by the International Conference of London in 1908. 96 • SI Units Although it was already obvious on the occasion of the 8th CGPM (1933) that there was a unanimous desire to replace those “international” units by so-called “absolute” units, the official decision to abolish them was only taken by the 9th CGPM (1948), which adopted the ampere for the unit of electric current, following a definition proposed by the CIPM (1946, Resolution 2; PV, 20, 129-137): The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10−7 newton per metre of length. The expression “MKS unit of force” which occurs in the original text of 1946 has been replaced here by “newton”, a name adopted for this unit by the 9th CGPM (1948, Resolution 7; CR, 70). Note that the effect of this definition is to fix the permeability of vacuum at exactly 4π × 10−7 H · m−1. 2.1.1.5 Unit of thermodynamic temperature (kelvin) The definition of the unit of thermodynamic temperature was given in substance by the 10th CGPM (1954, Resolution 3; CR, 79) which selected the triple point of water as the fundamental fixed point and assigned to it the temperature 273.16 K so defining the unit. The 13th CGPM (1967-1968, Resolution 3; CR, 104 and Metrologia, 1968, 4, 43) adopted the name kelvin (symbol K) instead of “degree Kelvin” (symbol °K) and defined the unit of thermodynamic temperature as follows (Resolution 4; CR, 104 and Metrologia, 1968, 4, 43): The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. Because of the way temperature scales used to be defined, it remains common practice to express a thermodynamic temperature, symbol T, in terms of its difference from the reference temperature T0 = 273.15 K, the ice point. This temperature difference is called the Celsius temperature, symbol t, and is defined by the quantity equation t = T – T0. The unit of Celsius temperature is the degree Celsius, symbol °C, which is by definition equal in magnitude to the kelvin. A difference or interval of temperature may be expressed in kelvins or in degrees Celsius (13th CGPM, 1967-1968, Resolution 3, mentioned above). The numerical value of a Celsius temperature t expressed in degrees Celsius is given by t/°C = T/K − 273.15. The kelvin and the degree Celsius are also the units of the International Temperature Scale of 1990 (ITS-90) adopted by the CIPM in 1989 in its Recommendation 5 (CI-1989) (PV, 57, 115 and Metrologia, 1990, 27, 13). SI Units • 97 2.1.1.6 Unit of amount of substance (mole) Following the discovery of the fundamental laws of chemistry, units called, for example, “gram-atom” and “gram-molecule”, were used to specify amounts of chemical elements or compounds. These units had a direct connection with “atomic weights” and “molecular weights”, which are in fact relative masses. “Atomic weights” were originally referred to the atomic weight of oxygen, by general agreement taken as 16. But whereas physicists separated isotopes in the mass spectrometer and attributed the value 16 to one of the isotopes of oxygen, chemists attributed that same value to the (slightly variable) mixture of isotopes 16, 17 and 18, which was for them the naturally occurring element oxygen. Finally, an agreement between the International Union of Pure and Applied Physics (IUPAP) and the International Union of Pure and Applied Chemistry (IUPAC) brought this duality to an end in 1959/60. Physicists and chemists have ever since agreed to assign the value 12, exactly, to the “atomic weight”, correctly the relative atomic mass, of the isotope of carbon with mass number 12 (carbon 12, 12C). The unified scale thus obtained gives values of relative atomic mass. It remained to define the unit of amount of substance by fixing the corresponding mass of carbon 12; by international agreement this mass was fixed at 0.012 kg, and the unit of the quantity “amount of substance” was given the name mole (symbol mol). Following proposals by the IUPAP, the IUPAC and the ISO, the CIPM gave a definition of the mole in 1967 and confirmed it in 1969: this was adopted by the 14th CGPM (1971, Resolution 3; CR, 78 and Metrologia, 1972, 8, 36): 1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is “mol”. 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. In 1980 the CIPM approved the report of the CCU (1980) which specified that In this definition, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. 2.1.1.7 Unit of luminous intensity (candela) The units of luminous intensity based on flame or incandescent filament standards in use in various countries before 1948 were replaced initially by the “new candle” based on the luminance of a Planckian radiator (a black body) at the temperature of freezing platinum. This modification had been prepared by the International Commission on Illumination (CIE) and by the CIPM before 1937 and the decision was promulgated by the CIPM in 1946. It was then ratified in 1948 by the 9th CGPM which adopted a new international name for this unit, When the definition of the mole is quoted, it is conventional also to include this remark. 98 • SI Units the candela (symbol cd); in 1967 the 13th CGPM (Resolution 5; CR, 104 and Metrologia, 1968, 4, 43-44) gave an amended version of the 1946 definition. In 1979, because of the experimental difficulties in realizing a Planck radiator at high temperatures and the new possibilities offered by radiometry, i.e. the measurement of optical radiation power, the 16th CGPM (1979, Resolution 3; CR, 100 and Metrologia, 1980, 16, 56) adopted a new definition of the candela: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. 2.1.2 Symbols for base units The base units of the International System are listed in Table l which relates the base quantity to the unit name and unit symbol (10th CGPM (1954, Resolution 6; CR, 80); 11th CGPM (1960, Resolution 12; CR, 87); 13th CGPM (1967-1968, Resolution 3; CR, 104 and Metrologia, 1968, 4, 43); 14th CGPM (1971, Resolution 3; CR, 78 and Metrologia, 1972, 8, 36)). Table 1. SI base units SI base unit Base quantity Name Symbol length mass time electric current thermodynamic temperature amount of substance luminous intensity metre kilogram second ampere kelvin mole candela m kg s A K mol cd 2.2 SI derived units Derived units are units which may be expressed in terms of base units by means of the mathematical symbols of multiplication and division. Certain derived units have been given special names and symbols, and these special names and symbols may themselves be used in combination with those for base and other derived units to express the units of other quantities. 2.2.1 Units expressed in terms of base units Table 2 lists some examples of derived units expressed directly in terms of base units. The derived units are obtained by multiplication and division of base units. SI Units • 99 Table 2. Examples of SI derived units expressed in terms of base units SI derived unit Derived quantity Name Symbol area volume speed, velocity acceleration wavenumber density, mass density specific volume current density magnetic field strength concentration (of amount of substance) luminance refractive index square metre cubic metre metre per second metre per second squared reciprocal metre kilogram per cubic metre cubic metre per kilogram ampere per square metre ampere per metre mole per cubic metre candela per square metre (the number) one m2 m3 m/s m / s2 m−1 k g / m3 m 3/kg A / m2 A/m m o l / m3 cd/m 2 1(a) (a) The symbol “1” is generally omitted in combination with a numerical value. 2.2.2 Units with special names and symbols; units which incorporate units with special names and symbols For convenience, certain derived units, which are listed in Table 3, have been given special names and symbols. These names and symbols may themselves be used to express other derived units: Table 4 shows some examples. The special names and symbols are a compact form for the expression of units which are used frequently. Among these names and symbols, the last three entries in Table 3 are of particular note since they were accepted by the 15th CGPM (1975, Resolutions 8 and 9; CR, 105 and Metrologia, 1975, 11, 180) and the 16th CGPM (1979, Resolution 5; CR, 100 and Metrologia, 1980, 16, 56) specifically with a view to safeguarding human health. In Tables 3 and 4, the final column shows how the SI units concerned may be expressed in terms of SI base units. In this column, factors such as m0, kg0 ..., which are all equal to 1, are not shown explicitly. 100 • SI Units Table 3. SI derived units with special names and symbols SI derived unit Expressed in terms of other SI units Expressed in terms of SI base units Derived quantity Name Symbol plane angle solid angle frequency force pressure, stress energy, work, quantity of heat power, radiant flux electric charge, quantity of electricity electric potential difference, electromotive force capacitance electric resistance electric conductance magnetic flux magnetic flux density inductance Celsius temperature radian(a) steradian(a) hertz newton pascal joule watt coulomb rad sr (c) Hz N Pa J W C volt farad ohm siemens weber tesla henry degree Celsius(d) lumen lux becquerel V F Ω S Wb T H W/A C/V V/A A/V V·s W b / m2 Wb/A °C lm lx Bq cd · sr l m / m2 Gy J/kg m2 · s−2 Sv J/kg m2 · s−2 luminous flux illuminance activity (referred to a radionuclide) absorbed dose, specific energy (imparted), kerma gray dose equivalent, ambient dose equivalent, directional dose equivalent, personal dose equivalent, organ equivalent dose sievert m · m−1 = 1(b) m2 · m−2 = 1(b ) s−1 m · kg · s−2 m−1 · kg · s−2 m2 · kg · s−2 m2 · kg · s −3 s ·A N / m2 N·m J/s (c) m2 · kg · s−3 · A−1 m−2 · kg−1 · s4 · A2 m2 · kg · s−3 · A−2 m−2 · kg−1 · s3 · A2 m2 · kg · s−2 · A−1 kg · s −2 · A−1 m2 · kg · s −2 · A−2 K m2 · m−2 · cd = cd m2 · m−4 · cd = m−2 · cd s−1 (a) The radian and steradian may be used with advantage in expressions for derived units to distinguish between quantities of different nature but the same dimension. Some examples of their use in forming derived units are given in Table 4. (b) In practice, the symbols rad and sr are used where appropriate, but the derived unit “1” is generally omitted in combination with a numerical value. (c) In photometry, the name steradian and the symbol sr are usually retained in expressions for units. (d) This unit may be used in combination with SI prefixes, e.g. millidegree Celsius, m°C. SI Units • 101 Table 4. Examples of SI derived units whose names and symbols include SI derived units with special names and symbols SI derived unit Derived quantity Name Symbol Expressed in terms of SI base unit dynamic viscosity moment of force surface tension angular velocity angular acceleration heat flux density, irradiance heat capacity, entropy specific heat capacity, specific entropy specific energy thermal conductivity energy density electric field strength electric charge density electric flux density pascal second newton metre newton per metre radian per second radian per second squared Pa · s N·m N/m rad/s rad/s 2 m−1 · kg · s−1 m2 · kg · s−2 kg · s−2 m · m−1 · s−1 = s −1 m · m−1 · s−2 = s−2 watt per square metre joule per kelvin joule per kilogram kelvin joule per kilogram watt per metre kelvin joule per cubic metre volt per metre W / m2 J/K kg · s−3 m2 · kg · s−2 · K−1 permittivity permeability molar energy molar entropy, molar heat capacity exposure (x and γ rays) absorbed dose rate radiant intensity radiance J/(kg · K) m2 · s−2 · K−1 J/kg m2 · s−2 W/(m · K) m · kg · s−3 · K−1 J/m 3 m−1 · kg · s−2 V/m m · kg · s−3 · A−1 coulomb per cubic metre coulomb per square metre farad per metre henry per metre joule per mole C / m3 m−3 · s · A C/m 2 F/m H/m J/mol m−2 · s · A m−3 · kg−1 · s4 · A2 m · kg · s−2 ·A−2 m2 · kg · s−2 · mol−1 joule per mole kelvin J/(mol · K) m2 · kg · s−2 · K−1 · mol−1 coulomb per kilogram gray per second watt per steradian C/kg Gy/s W/sr watt per square metre steradian kg−1 · s · A m2 · s−3 m4 · m−2 · kg · s−3 = m2 · kg · s−3 2 2 W/(m · sr) m · m−2 · kg · s−3 = kg · s−3 A single SI unit may correspond to several different quantities, as noted in paragraph 1.2 (p. 92). In the above table, which is not exhaustive, there are several examples. Thus the joule per kelvin (J/K) is the SI unit for the quantity heat capacity as well as for the quantity entropy; also the ampere (A) is the SI unit for the base quantity electric current as well as for the derived quantity magnetomotive force. It is therefore important not to use the unit alone to specify the quantity. This rule applies not only to scientific and technical texts but also, for example, to measuring instruments (i.e. an instrument should indicate both the unit and the quantity measured). 102 • SI Units A derived unit can often be expressed in different ways by combining the names of base units with special names for derived units. This, however, is an algebraic freedom to be governed by common-sense physical considerations. Joule, for example, may formally be written newton metre, or even kilogram metre squared per second squared, but in a given situation some forms may be more helpful than others. In practice, with certain quantities preference is given to the use of certain special unit names, or combinations of unit names, in order to facilitate the distinction between different quantities having the same dimension. For example, the SI unit of frequency is designated the hertz, rather than the reciprocal second, and the SI unit of angular velocity is designated the radian per second rather than the reciprocal second (in this case retaining the word radian emphasizes that angular velocity is equal to 2π times the rotational frequency). Similarly the SI unit of moment of force is designated the newton metre rather than the joule. In the field of ionizing radiation, the SI unit of activity is designated the becquerel rather than the reciprocal second, and the SI units of absorbed dose and dose equivalent the gray and sievert, respectively, rather than the joule per kilogram. The special names becquerel, gray and sievert were specifically introduced because of the dangers to human health which might arise from mistakes involving the units reciprocal second and the joule per kilogram. 2.2.3 Units for dimensionless quantities, quantities of dimension one Certain quantities are defined as the ratios of two quantities of the same kind, and thus have a dimension which may be expressed by the number one. The unit of such quantities is necessarily a derived unit coherent with the other units of the SI and, since it is formed as the ratio of two identical SI units, the unit also may be expressed by the number one. Thus the SI unit of all quantities having the dimensional product one is the number one. Examples of such quantities are refractive index, relative permeability, and friction factor. Other quantities having the unit 1 include “characteristic numbers” like the Prandtl number η cp /λ and numbers which represent a count, such as a number of molecules, degeneracy (number of energy levels) and partition function in statistical thermodynamics. All of these quantities are described as being dimensionless, or of dimension one, and have the coherent SI unit 1. Their values are simply expressed as numbers and, in general, the unit 1 is not explicitly shown. In a few cases, however, a special name is given to this unit, mainly to avoid confusion between some compound derived units. This is the case for the radian, steradian and neper. The CIPM, recognizing the particular importance of the health-related units, agreed a detailed text on the sievert for the 5th edition of this brochure: see p. 127, Recommendation 1 (CI-1984) adopted by the CIPM (PV, 1984, 52, 31 and Metrologia, 1985, 21, 90). 103 3 Decimal multiples and submultiples of SI units 3.1 SI prefixes The 11th CGPM (1960, Resolution 12; CR, 87) adopted a series of prefixes and p re fix symbols to form the names and symbols of the decimal multiples and submultiples of SI units ranging from 1012 to 10−12. Prefixes for 10−15 and 10−18 were added by the 12th CGPM (1964, Resolution 8; CR, 94), for 1015 and 1018 by the 15th CGPM (1975, Resolution 10; CR, 106 and Metrologia, 1975, 11, 180-181), and for 1021, 1024, 10 −21 and 10−24 by the 19th CGPM (1991, Resolution 4; CR, 185 and Metrologia, 1992, 29, 3). Table 5 lists all approved prefixes and symbols. Table 5. SI prefixes Factor Name Symbol Factor Name Symbol 10 24 10 21 1 01 8 10 15 1 01 2 1 09 1 06 10 3 10 2 10 1 yotta zetta exa peta tera giga mega kilo hecto deca Y Z E P T G M k h da 1 0− 1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24 deci centi milli micro nano pico femto atto zepto yocto d c m µ n p f a z y 3.2 The kilogram Among the base units of the International System, the unit of mass is the only one whose name, for historical reasons, contains a prefix. Names and symbols for decimal multiples and submultiples of the unit of mass are formed by attaching prefix names to the unit name “gram” and prefix symbols to the unit symbol “g” (CIPM, 1967, Recommendation 2; PV, 35, 29 and Metrologia, 1968, 4, 45), Example: 10−6 kg = 1 mg (1 milligram) but not 1 µkg (1 microkilogram). These SI prefixes refer strictly to powers of 10. They should not be used to indicate powers of 2 (for example, one kilobit represents 1000 bits and not 1024 bits). 104 4 Units outside the SI SI units are recommended for use throughout science, technology and commerce. They are agreed internationally by the CGPM, and provide the reference in terms of which all other units are now defined. The SI base units and SI derived units, including those with special names, have the important advantage of forming a coherent set with the effect that unit conversions are not required when inserting particular values for quantities in quantity equations. Nonetheless it is recognized that some non-SI units still appear widely in the scientific, technical and commercial literature, and some will probably continue to be used for many years. Other non-SI units, such as the units of time, are so widely used in everyday life, and are so deeply embedded in the history and culture of the human race, that they will continue to be used for the foreseable future. For these reasons some of the more important non-SI units are listed in the tables below. The inclusion of tables of non-SI units in this text does not imply that the use of non-SI units is to be encouraged. With a few exceptions discussed below, SI units are always to be preferred to non-SI units. It is desirable to avoid combining non-SI units with units of the SI; in particular the combination of such units with SI units to form compound units should be restricted to special cases so as to retain the advantage of coherence conferred by the use of SI units. 4.1 Units used with the SI The CIPM (1969), recognizing that users would wish to employ the SI with units which are not part of it but are important and widely used, listed three categories of non-SI units: units to be maintained; to be tolerated temporarily; and to be avoided. In reviewing this catego ri z ation the CIPM (1996) agreed a new classification of non-SI units: units accepted for use with the SI, Table 6; units accepted for use with the SI whose values are obtained experimentally, Table 7; and other units currently accepted for use with the SI to satisfy the needs of special interests, Table 8. Table 6 lists non-SI units which are accepted for use with the SI. It includes units which are in continuous everyday use, in particular the traditional units of time and of angle, together with a few other units which have assumed increasing technical importance. Units outside the SI • 105 Table 6. Non-SI units accepted for use with the International System Name Symbol Value in SI units minute hour ( a ) day min h d 1 min = 60 s 1 h = 60 min = 3600 s 1 d = 24 h = 86 400 s degree ( b ) minute second ° ′ ″ 1° = (π/180) rad 1′ = (1/60)° = (π/10 800) rad 1″ = (1/60)′ = (π/648 000) rad litre ( c ) tonne ( d, e) l, L t 1 l = 1 dm3 = 10−3 m3 1 t = 103 kg neper ( f, h) bel ( g, h) Np B 1 Np = 1 1 B = (1/2) ln 10 (Np)( i ) (a) The symbol of this unit is included in Resolution 7 of the 9th CGPM (1948; CR, 70). (b) ISO 31 recommends that the degree be subdivided decimally rather than using the minute and second. (c) This unit and the symbol l were adopted by CIPM in 1879 (PV, 1879, 41). The alternative symbol, L, was adopted by the 16th CGPM (1979, Resolution 6; CR, 101 and Metrologia, 1980, 16, 56-57) in order to avoid the risk of confusion between the letter l and the number 1. The present definition of the litre is given in Resolution 6 of the 12th CGPM (1964; CR, 93). (d) This unit and its symbol were adopted by the CIPM in 1879 (PV, 1879, 41). (e) In some English-speaking countries this unit is called “metric ton”. (f) The neper is used to express values of such logarithmic quantities as field level, power level, sound pressure level, and logarithmic decrement. Natural logarithms are used to obtain the numerical values of quantities expressed in nepers. The neper is coherent with the SI, but not yet adopted by the CGPM as an SI unit. For further information see International Standard ISO 31. (g) The bel is used to express values of such logarithmic quantities as field level, power level, sound pressure level, and attenuation. Logarithms to base ten are used to obtain the numerical values of quantities expressed in bels. The submultiple decibel, dB, is commonly used. For further info rm ation see International Standard ISO 31. (h) In using these units it is particularly important that the quantity be specified. The unit must not be used to imply the quantity. (i) Np is enclosed in parentheses because, although the neper is coherent with the SI, it has not yet been adopted by the CGPM. Table 7 lists three non-SI units which are also accepted for use with the SI, whose values expressed in SI units must be obtained by experiment and are therefore not known exactly. Their values are given with their combined standard uncertainties (coverage factor k = 1), which apply to the last two digits, shown in parentheses. These units are in common use in certain specialized fields. 106 • Units outside the SI Table 7. Non-SI units accepted for use with the International System, whose values in SI units are obtained experimentally Name Symbol Definition Value in SI units electronvolt (a) unified atomic mass unit (a) astronomical unit eV (b) 1 eV = 1 . 6 0 2 1 7 7 3 3 (49) × 10−19 J u ua (c) 1 u = 1 . 6 6 0 5 4 0 2 (10) × 10−27 kg 1 ua = 1 . 4 9 5 9 7 8 7 0 6 9 1 (30) × 10 11 m (a) (d) (a) For the electronvolt and the unified atomic mass unit, values are quoted from CODATA Bulletin, 1986, No. 63. The value given for the astronomical unit is quoted from the IERS Conventions (1996), D.D. McCarthy ed., IERS Technical Note 21, Observatoire de Paris, July 1996. (b) The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of 1 V in vacuum. (c) The unified atomic mass unit is equal to 1/12 of the mass of an unbound atom of the nuclide 12C, at rest, and in its ground state. In the field of biochemistry, the unified atomic mass unit is also called the dalton, symbol Da. (d) The astronomical unit is a unit of length approximatively equal to the mean Earth-Sun distance. Its value is such that, when used to describe the motion of bodies in the Solar System, the heliocentric gravitational constant is (0.017 202 098 95) 2 ua 3 ⋅ d −2. Table 8 lists some other non-SI units which are currently accepted for use with the SI to satisfy the needs of commercial, legal and specialized scientific interests. These units should be defined in relation to the SI in every document in which they are used. Their use is not encouraged. Table 8. Other non-SI units currently accepted for use with the International System Name nautical mile(a) knot are(b) hectare(b) bar(c) ångström barn (d) Symbol Value in SI units a ha bar Å b 1 nautical mile = 1852 m 1 nautical mile per hour = (1852/3600) m/s 1 a = 1 dam2 = 102 m2 1 ha = 1 hm2 = 104 m2 1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 105 Pa 1 Å = 0.1 nm = 10−10 m 1 b = 100 fm2 = 10−28 m 2 (a) The nautical mile is a special unit employed for marine and aerial navigation to express distance. The conventional value given above was adopted by the First International Extraordinary Hydrographic Conference, Monaco, 1929, under the name “International nautical mile”. As yet there is no internationally agreed symbol. This unit was originally chosen because one nautical mile on the surface of the Earth subtends approximately one minute of angle at the centre. (b) The units are and hectare and their symbols were adopted by the CIPM in 1879 (PV, 1879, 41) and are used to express areas of land. (c) The bar and its symbol are included in Resolution 7 of the 9th CGPM (1948; CR, 70). (d) The barn is a special unit employed in nuclear physics to express effective cross-sections. Units outside the SI • 107 4.2 Other non-SI units Certain other non-SI units are still occasionally used. Some are important for the interpretation of older scientific texts. These are listed in Tables 9 and 10, but their use is not encouraged. Table 9 deals with the relationship between CGS units and the SI, and lists those CGS units that were assigned special names. In the field of mechanics, the CGS system of units was built upon three quantities and the corresponding base units: the centimetre, the gram and the second. In the field of electricity and magnetism, units were expressed in terms of these three base units. Because this can be done in different ways, it led to the establishment of several different systems, for example the CGS Electrostatic System, the CGS Electromagnetic System and the CGS Gaussian System. In these three last-mentioned systems, the system of quantities and the corresponding system of equations differ from those used with SI units. Table 9. Derived CGS units with special names Name Symbol Value in SI units erg (a) dyne (a) poise (a) stokes gauss (b) oersted (b) maxwell (b) stilb (a) phot gal (c) erg dyn P St G Oe Mx sb ph Gal 1 erg = 10−7 J 1 dyn = 10−5 N 1 P = 1 dyn · s/cm2 = 0.1 Pa · s 1 St = 1 cm2/s = 10−4 m2/s 1 G ^ 10−4 T 1 Oe ^ (1000/4π) A/m 1 Mx ^ 10−8 Wb 1 sb = 1 cd/cm2 = 104 cd/m2 1 ph = 104 lx 1 Gal = 1 cm/s2 = 10−2 m/s2 (a) This unit and its symbol were included in Resolution 7 of the 9th CGPM (1948; CR, 70). (b) This unit is part of the so-called “electromagnetic” three-dimensional CGS system and cannot strictly be compared with the corresponding unit of the International System, which has four dimensions when only mechanical and electric quantities are considered. For this reason, this unit is linked to the SI unit using the mathematical symbol for “corresponds to” (^). (c) The gal is a special unit employed in geodesy and geophysics to express acceleration due to gravity. Table 10 lists units which are common in older texts. For current texts, it should be noted that if these units are used the advantages of the SI are lost. The relation of these units to the SI should be specified in every document in which they are used. 108 • Units outside the SI Table 10. Examples of other non-SI units Name Symbol Value in SI units curie (a) röntgen (b) rad (c,f) rem (d,f) X unit (e) gamma (f) jansky fermi (f) metric carat (g) torr standard atmosphere calorie micron (f) Ci R rad rem 1 Ci = 3.7 × 1010 Bq 1 R = 2.58 × 10 −4 C/kg 1 rad = 1 cGy = 10 −2 Gy 1 rem = 1 cSv = 10 −2 Sv 1 X unit ≈ 1.002 × 10 −4 nm 1 γ = 1 nT = 10−9 T 1 Jy = 10 −26 W ⋅ m−2 · Hz−1 1 fermi = 1 fm = 10−15 m 1 metric carat = 200 mg = 2 × 10−4 kg 1 Torr = (101 325/760) Pa 1 atm = 101 325 Pa γ Jy Torr atm (h) cal µ (j) (i) 1 µ = 1 µm = 10−6 m (a) The curie is a special unit employed in nuclear physics to express activity of radionuclides (12th CGPM, 1964, Resolution 7; CR, 94). (b) The röntgen is a special unit employed to express exposure to x or γ radiation. (c) The rad is a special unit employed to express absorbed dose of ionizing radiation. When there is risk of confusion with the symbol for radian, rd may be used as the symbol for rad. (d) The rem is a special unit used in radioprotection to express dose equivalent. (e) The X unit was employed to express the wavelengths of x rays. Its relationship with the SI unit is an approximate one. (f) Note that this non-SI unit is exactly equivalent to an SI unit with an appropriate submultiple prefix. (g) The metric carat was adopted by the 4th CGPM in 1907 (CR, 89-91) for commercial dealings in diamonds, pearls and precious stones. (h) Resolution 4 of the 10th CGPM (1954; CR, 79). The designation “standard atmosphere” for a re fe rence pressure of 101 325 Pa is still acceptable. (i) Several “calories” have been in use: • a calorie labelled “at 15 °C”: 1 cal15 = 4.1855 J (value adopted by the CIPM in l950; PV, 1950, 22, 79-80); • a calorie labelled “IT” (International Table): 1 cal IT = 4.1868 J (5th International Conference on the Properties of Steam, London, 1956); • a calorie labelled “thermochemical”: 1 calth = 4.184 J. (j) The micron and its symbol, adopted by the CIPM in 1879 (PV, 1879, 41) and repeated in Resolution 7 of the 9th CGPM (1948; CR, 70) were abolished by the 13th CGPM (1967-1968, Resolution 7; CR, 105 and Metrologia, 1968, 4, 44). B: International System of Units 756 November 1, 2010 C Physical Constants 757 (1 (1 (1 (1 (1 m−1 )c m−1 )hc/k m−1 )hc m−1 )h/c Hz)/c = = = = = 299 792 458 Hz 1.438 7752(25) × 10−2 K 1.239 841 91(11) × 10−6 eV 1.331 025 0506(89) × 10−15 u 3.335 640 951 . . . × 10−9 m−1 energy equivalent in eV Bohr radius α/4πR∞ = 4π0 h ¯ 2/me e2 Hartree energy e2/4π0 a0 = 2R∞ hc = α2 me c2 in eV electron mass in u energy equivalent in MeV electron-muon mass ratio electron-proton mass ratio electron charge to mass quotient Compton wavelength h/me c λC /2π = αa0 = α2/4πR∞ classical electron radius α2 a0 Thomson cross section (8π/3)re2 electron magnetic moment to Bohr magneton ratio to nuclear magneton ratio electron magnetic moment anomaly |µe |/µB − 1 electron g-factor −2(1 + ae ) electron-proton magnetic moment ratio muon mass in u energy equivalent in MeV muon-electron mass ratio muon magnetic moment to Bohr magneton ratio to nuclear magneton ratio muon magnetic moment anomaly |µµ |/(e¯ h/2mµ ) − 1 0 G h electric constant 1/µ0 c2 Newtonian constant of gravitation Planck constant in eV s h/2π in eV s elementary charge magnetic flux quantum h/2e Josephson constant 2e/h von Klitzing constant h/e2 = µ0 c/2α Bohr magneton e¯ h/2me in eV T−1 nuclear magneton e¯ h/2mp in eV T−1 fine-structure constant e2/4π0 h ¯c inverse fine-structure constant 2 Rydberg constant α me c/2h aµ (1 (1 (1 (1 (1 Numerical value = = = = = Unit Quantity (1 (1 (1 (1 (1 J) eV) eV)/hc eV)/h eV)/k = = = = = 6.241 509 47(53) × 1018 eV 1.602 176 53(14) × 10−19 J 8.065 544 45(69) × 105 m−1 2.417 989 40(21) × 1014 Hz 1.160 4505(20) × 104 K neutron mass in u energy equivalent in MeV neutron-proton mass ratio neutron magnetic moment to nuclear magneton ratio deuteron mass in u energy equivalent in MeV deuteron-proton mass ratio deuteron magnetic moment to nuclear magneton ratio helion (3 He nucleus) mass in u energy equivalent in MeV shielded helion magnetic moment (gas, sphere, 25 ◦ C) to Bohr magneton ratio to nuclear magneton ratio alpha particle mass in u energy equivalent in MeV Avogadro constant 1 atomic mass constant 12 m(12 C) = 1 u energy equivalent in MeV Faraday constant NA e molar gas constant Boltzmann constant R/NA in eV K−1 molar volume of ideal gas RT /p (T = 273.15 K, p = 101.325 kPa) Stefan-Boltzmann constant π2 k4/60¯ h 3 c2 first radiation constant 2πhc2 second radiation constant hc/k Wien displacement law constant b = λmax T = c2 /4.965 114 231... Cu x unit: λ(Cu Kα1 )/1 537.400 Mo x unit: λ(Mo Kα1 )/707.831 shielded proton gyromagnetic ratio 2µ0p /¯ h (H2 O, sphere, 25 ◦ C) muon g-factor −2(1 + aµ ) muon-proton magnetic moment ratio proton mass in u energy equivalent in MeV proton-electron mass ratio proton magnetic moment to nuclear magneton ratio proton magnetic shielding correction 1 − µ0p /µp (H2 O, sphere, 25 ◦ C) proton gyromagnetic ratio 2µp /¯ h Energy equivalents J T−1 u MeV C kg−1 m m m m2 J T−1 m−1 Hz eV m J eV kg u MeV m s−1 N A−2 N A−2 F m−1 m3 kg−1 s−2 Js eV s Js eV s C Wb Hz V−1 Ω J T−1 eV T−1 J T−1 eV T−1 4.799 2374(84) × 10−11 K 4.135 667 43(35) × 10−15 eV 69.503 56(12) m−1 2.083 6644(36) × 1010 Hz 8.617 343(15) × 10−5 eV 1.165 919 81(62) × 10 −3 299 792 458 (exact) 4π × 10−7 (exact) = 12.566 370 614... × 10−7 8.854 187 817... × 10−12 6.6742(10) × 10−11 6.626 0693(11) × 10−34 4.135 667 43(35) × 10−15 1.054 571 68(18) × 10−34 6.582 119 15(56) × 10−16 1.602 176 53(14) × 10−19 2.067 833 72(18) × 10−15 483 597.879(41) × 109 25 812.807 449(86) 927.400 949(80) × 10−26 5.788 381 804(39) × 10−5 5.050 783 43(43) × 10−27 3.152 451 259(21) × 10−8 7.297 352 568(24) × 10−3 137.035 999 11(46) 10 973 731.568 525(73) 3.289 841 960 360(22) × 1015 13.605 6923(12) 0.529 177 2108(18) × 10−10 4.359 744 17(75) × 10−18 27.211 3845(23) 9.109 3826(16) × 10−31 5.485 799 0945(24) × 10−4 0.510 998 918(44) 4.836 331 67(13) × 10−3 5.446 170 2173(25) × 10−4 −1.758 820 12(15) × 1011 2.426 310 238(16) × 10−12 386.159 2678(26) × 10−15 2.817 940 325(28) × 10−15 0.665 245 873(13) × 10−28 −928.476 412(80) × 10−26 −1.001 159 652 1859(38) −1838.281 971 07(85) 1.159 652 1859(38) × 10−3 −2.002 319 304 3718(75) −658.210 6862(66) 0.113 428 9264(30) 105.658 3692(94) 206.768 2838(54) −4.490 447 99(40) × 10−26 −4.841 970 45(13) × 10−3 −8.890 596 98(23) Hz)h/k Hz)h K)k/hc K)k/h K)k m e c2 me /mµ me /mp −e/me λC λC re σe µe µe /µB µe /µN ae ge µe /µp mµ m µ c2 mµ /me µµ µµ /µB µµ /µN me α α−1 R∞ R∞ c R∞ hc a0 Eh µN e Φ0 KJ RK µB h ¯ c, c0 µ0 Symbol speed of light in vacuum magnetic constant Quantity Numerical value 42.576 3875(37) 1.008 664 915 60(55) 939.565 360(81) 1.001 378 418 70(58) −0.966 236 45(24) × 10−26 −1.913 042 73(45) 2.013 553 212 70(35) 1875.612 82(16) 1.999 007 500 82(41) 0.433 073 482(38) × 10−26 0.857 438 2329(92) 3.014 932 2434(58) 2808.391 42(24) −1.074 553 024(93) × 10−26 −1.158 671 474(14) × 10−3 −2.127 497 723(25) 4.001 506 179 149(56) 3727.379 17(32) 6.022 1415(10) × 1023 1.660 538 86(28) × 10−27 931.494 043(80) 96 485.3383(83) 8.314 472(15) 1.380 6505(24) × 10−23 8.617 343(15) × 10−5 22.413 996(39) × 10−3 5.670 400(40) × 10−8 3.741 771 38(64) × 10−16 1.438 7752(25) × 10−2 γp0 /2π mn m n c2 mn /mp µn µn /µN md m d c2 md /mp µd µd /µN mh m h c2 µ0h µ0h /µB µ0h /µN mα m α c2 NA , L mu m u c2 F R k σ c1 c2 (1 (1 (1 (1 (1 eV)/c2 kg) u) u)c/h u)c2 = = = = = mK m m W m−2 K−4 W m2 mK u MeV mol−1 kg MeV C mol−1 J mol−1 K−1 J K−1 eV K−1 m3 mol−1 u MeV J T−1 J T−1 u MeV J T−1 MHz T−1 u MeV s−1 T−1 MHz T−1 s−1 T−1 J T−1 kg u MeV Unit 1.073 544 171(92) × 10−9 u 6.022 1415(10) × 1026 u 1.660 538 86(28) × 10−27 kg 7.513 006 608(50) × 1014 m−1 931.494 043(80) × 106 eV b 2.897 7685(51) × 10−3 xu(Cu Kα1 ) 1.002 077 10(29) × 10−13 xu(Mo Kα1 ) 1.002 099 66(53) × 10−13 Vm 2.675 222 05(23) × 108 42.577 4813(37) 2.675 153 33(23) × 108 −2.002 331 8396(12) −3.183 345 118(89) 1.672 621 71(29) × 10−27 1.007 276 466 88(13) 938.272 029(80) 1836.152 672 61(85) 1.410 606 71(12) × 10−26 2.792 847 351(28) 25.689(15) × 10−6 γp γp /2π γp0 m p c2 mp /me µp µp /µN σp0 gµ µµ /µp mp Symbol NIST SP 961 (Dec/2005) Values from: P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 77, 1 (2005). A more extensive listing of constants is available in the above references and on the NIST Physics Laboratory Web site physics.nist.gov/constants. The number in parenthesis is the one-standard-deviation uncertainty in the last two digits of the given value. CODATA RECOMMENDED VALUES OF THE FUNDAMENTAL PHYSICAL CONSTANTS: 2002 1. Physical constants 010001-77 1. PHYSICAL CONSTANTS Table 1.1. Reviewed 2002 by P.J. Mohr and B.N. Taylor (NIST). Based mainly on the “CODATA Recommended Values of the Fundamental Physical Constants: 1998” by P.J. Mohr and B.N. Taylor, J. Phys. Chem. Ref. Data 28, 1713 (1999) and Rev. Mod. Phys. 72, 351 (2000). The last group of constants (beginning with the Fermi coupling constant) comes from the Particle Data Group. The figures in parentheses after the values give the 1-standard-deviation uncertainties in the last digits; the corresponding fractional uncertainties in parts per 109 (ppb) are given in the last column. This set of constants (aside from the last group) is recommended for international use by CODATA (the Committee on Data for Science and Technology). The full 1998 CODATA set of constants may be found at http://physics.nist.gov/constants Quantity Symbol, equation speed of light in vacuum Planck constant Planck constant, reduced electron charge magnitude conversion constant conversion constant Value Uncertainty (ppb) 299 792 458 m s−1 6.626 068 76(52)×10−34 J s 1.054 571 596(82)×10−34 J s = 6.582 118 89(26)×10−22 MeV s 1.602 176 462(63)×10−19 C = 4.803 204 20(19)×10−10 esu 197.326 960 2(77) MeV fm 0.389 379 292(30) GeV2 mbarn c h ~ ≡ h/2π e ~c (~c)2 exact∗ 78 78 39 39, 39 39 78 deuteron mass unified atomic mass unit (u) 0.510 998 902(21) MeV/c2 = 9.109 381 88(72)×10−31 kg 938.271 998(38) MeV/c2 = 1.672 621 58(13)×10−27 kg = 1.007 276 466 88(13) u = 1836.152 667 5(39) me 1875.612 762(75) MeV/c2 md (mass 12 C atom)/12 = (1 g)/(NA mol) 931.494 013(37) MeV/c2 = 1.660 538 73(13)×10−27 kg permittivity of free space permeability of free space 0 = 1/µ0 c2 µ0 fine-structure constant classical electron radius (e− Compton wavelength)/2π Bohr radius (mnucleus = ∞) wavelength of 1 eV/c particle Rydberg energy Thomson cross section α = e2 /4π0 ~c re = e2 /4π0 me c2 − λe = ~/me c = re α−1 a∞ = 4π0 ~2 /me e2 = re α−2 hc/(1 eV) hcR∞ = me e4 /2(4π0 )2 ~2 = me c2 α2 /2 σT = 8πre2 /3 7.297 352 533(27)×10−3 = 1/137.035 999 76(50)† 2.817 940 285(31)×10−15 m 3.861 592 642(28)×10−13 m 0.529 177 208 3(19)×10−10 m 1.239 841 857(49)×10−6 m 13.605 691 72(53) eV 0.665 245 854(15) barn Bohr magneton nuclear magneton electron cyclotron freq./field proton cyclotron freq./field µB = e~/2me µN = e~/2mp e /B = e/m ωcycl e p /B = e/mp ωcycl 5.788 3.152 1.758 9.578 749(43)×10−11 MeV T−1 238(24)×10−14 MeV T−1 174(71)×1011 rad s−1 T−1 08(38)×107 rad s−1 T−1 7.3 7.6 40 40 gravitational constant‡ GN standard gravitational accel. gn 6.673(10)×10−11 m3 kg−1 s−2 = 6.707(10)×10−39 ~c (GeV/c2 )−2 9.806 65 m s−2 1.5 × 106 1.5 × 106 exact Avogadro constant Boltzmann constant NA k molar volume, ideal gas at STP Wien displacement law constant Stefan-Boltzmann constant NA k(273.15 K)/(101 325 Pa) b = λmax T σ = π 2 k 4 /60~3 c2 Fermi coupling constant∗∗ GF /(~c)3
Z ) (MS) sin2 θ(M mW mZ αs (mZ ) electron mass proton mass me mp weak-mixing angle W ± boson mass Z 0 boson mass strong coupling constant π = 3.141 592 653 589 793 238 −4 1 in ≡ 0.0254 m 1 G ≡ 10 T ˚ ≡ 0.1 nm 1A 1 dyne ≡ 10−5 N ∗ † 1 barn ≡ 10 −28 2 m 1 erg ≡ 10 −7 8.854 187 817 . . . ×10−12 F m−1 4π × 10−7 N A−2 = 12.566 370 614 . . . ×10−7 N A−2 381 451 820 834 6.022 141 99(47)×1023 mol−1 1.380 650 3(24)×10−23 J K−1 = 8.617 342(15)×10−5 eV K−1 22.413 996(39)×10−3 m3 mol−1 2.897 768 6(51)×10−3 m K 5.670 400(40)×10−8 W m−2 K−4 1.166 39(1)×10−5 GeV−2 1 eV = 1.602 176 462(63) × 10 2 1 eV/c = 1.782 661 731(70) × 10 9 J 2.997 924 58 × 10 esu = 1 C γ = 0.577 215 664 901 532 861 −19 −36 J exact exact 3.7, 3.7 11 7.3 3.7 39 39 22 79 1700 1700 1700 1700 7000 9000 0.23113(15)†† 80.423(39) GeV/c2 91.1876(21) GeV/c2 0.1172(20) e = 2.718 281 828 459 045 235 40, 79 40, 79 0.13, 2.1 40 40, 79 6.5 × 105 4.8 × 105 2.3 × 104 1.7 × 107 kT at 300 K = [38.681 686(67)]−1 eV 0 ◦ C ≡ 273.15 K kg 1 atmosphere ≡ 760 Torr ≡ 101 325 Pa The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second. At Q2 = 0. At Q2 ≈ m2W the value is ∼ 1/128. ‡ Absolute lab measurements of G have been made only on scales of about 1 cm to 1 m. N ∗∗ See the discussion in Sec. 10, “Electroweak model and constraints on new physics.” †† The corresponding sin2 θ for the effective angle is 0.23143(15). From: http://physics.nist.gov/constants Fundamental Physical Constants — Frequently used constants Quantity Symbol Value Unit Relative std. uncert. ur 299 792 458 4π × 10−7 = 12.566 370 614... × 10−7 8.854 187 817... × 10−12 m s−1 N A−2 N A−2 F m−1 G 6.6742(10) × 10−11 m3 kg−1 s−2 1.5 × 10−4 Planck constant h/2π elementary charge magnetic flux quantum h/2e conductance quantum 2e2/h h ¯h e Φ0 G0 6.626 0693(11) × 10−34 1.054 571 68(18) × 10−34 1.602 176 53(14) × 10−19 2.067 833 72(18) × 10−15 7.748 091 733(26) × 10−5 Js Js C Wb S 1.7 × 10−7 1.7 × 10−7 8.5 × 10−8 8.5 × 10−8 3.3 × 10−9 electron mass proton mass proton-electron mass ratio fine-structure constant e2/4π0 ¯hc inverse fine-structure constant me mp mp /me α α−1 9.109 3826(16) × 10−31 1.672 621 71(29) × 10−27 1836.152 672 61(85) 7.297 352 568(24) × 10−3 137.035 999 11(46) kg kg 1.7 × 10−7 1.7 × 10−7 4.6 × 10−10 3.3 × 10−9 3.3 × 10−9 Rydberg constant α2 me c/2h Avogadro constant Faraday constant NA e molar gas constant Boltzmann constant R/NA Stefan-Boltzmann constant (π2 /60)k 4/¯h3 c2 R∞ NA , L F R k 10 973 731.568 525(73) 6.022 1415(10) × 1023 96 485.3383(83) 8.314 472(15) 1.380 6505(24) × 10−23 m−1 mol−1 C mol−1 J mol−1 K−1 J K−1 6.6 × 10−12 1.7 × 10−7 8.6 × 10−8 1.7 × 10−6 1.8 × 10−6 σ 5.670 400(40) × 10−8 W m−2 K−4 7.0 × 10−6 eV 1.602 176 53(14) × 10−19 J 8.5 × 10−8 u 1.660 538 86(28) × 10−27 kg 1.7 × 10−7 speed of light in vacuum magnetic constant c, c0 µ0 electric constant 1/µ0 c2 Newtonian constant of gravitation 0 Non-SI units accepted for use with the SI electron volt: (e/C) J (unified) atomic mass unit 1 1 u = mu = 12 m(12 C) = 10−3 kg mol−1/NA Page 1 (exact) (exact) (exact) Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2002, published in Review of Modern Physics 77, 1 (2005). D Periodic table of the Elements 761 H Beryllium PERIODIC TABLE OF THE ELEMENTS Boron B 6 15 VA N 8 Nitrogen C 7 Carbon 14 IVA 17 VIIA Helium Neon 4.002602 F 10 Ne Fluorine O 9 Oxygen 16 VIA 10.811 12.0107 14.00674 15.9994 18.9984032 20.1797 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 5 13 IIIA 18 VIIIA 2 He Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium German. Arsenic Selenium Bromine Krypton Yttrium Zirconium Niobium Molybd. Technet. Ruthen. Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon Actinide series Lanthanide series 89–103 Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Pr 60 Nd 61 Pm 62 Sm 63 Mercury 232.0381 (227.027747) Np 94 Californ. Md 102 Mendelev. Fm 101 Fermium Es 100 167.26 Tm 70 Lu No 103 Lr 174.967 Lutetium Yb 71 Thulium Ytterbium 173.04 168.93421 Er 69 Bismuth Polonium Astatine Radon 208.98038 (208.982415) (209.987131) (222.017570) Erbium Ho 68 Einstein. Cf 99 162.50 Lead 207.2 Holmium 164.93032 Dy 67 Dyspros. Bk 98 Berkelium Cm 97 Curium Am 96 Americ. Pu 95 157.25 Terbium 158.92534 Tb 66 (277) Thallium 204.3833 Nobelium Lawrenc. 238.0289 (237.048166) (244.064197) (243.061372) (247.070346) (247.070298) (251.079579) (252.08297) (257.095096) (258.098427) (259.1011) (262.1098) U 93 Uranium Neptunium Plutonium Pa 92 Protactin. 231.03588 Th 91 Thorium Ac 90 (272) Gd 65 Gadolin. Eu 64 Praseodym. Neodym. Prometh. Samarium Europium 140.116 140.90765 144.24 (144.912745) 150.36 151.964 Ce 59 Cerium Actinium 89 138.9055 Gold 178.49 180.9479 183.84 186.207 190.23 192.217 195.078 196.96655 200.59 104 Rf 105 Db 106 Sg 107 Bh 108 Hs 109 Mt 110 111 112 La 58 Lanthan. 57 Radium Lanthanides Actinides Rutherford. Dubnium Seaborg. Bohrium Hassium Meitner. (223.019731) (226.025402) (261.1089) (262.1144) (263.1186) (262.1231) (265.1306) (266.1378) (269, 273) Francium 87 Barium 137.327 Fr 88 Ra Cesium 132.90545 126.90447 85.4678 87.62 88.90585 91.224 92.90638 95.94 (97.907215) 101.07 102.90550 106.42 107.8682 112.411 114.818 118.710 121.760 127.60 131.29 55 Cs 56 Ba 57–71 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn Rubidium Strontium 39.0983 40.078 44.955910 47.867 50.9415 51.9961 54.938049 55.845 58.933200 58.6934 63.546 65.39 69.723 72.61 74.92160 78.96 79.904 83.80 37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe Potassium 9 Sodium Magnesium 3 4 5 6 7 8 10 11 12 Aluminum Silicon Phosph. Sulfur Chlorine Argon VIII 22.989770 24.3050 32.066 35.4527 39.948 26.981538 28.0855 30.973761 IIIB IVB VB VIB VIIB IB IIB 19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 6.941 9.012182 11 Na 12 Mg Lithium Hydrogen 2 1.00794 IIA 3 Li 4 Be 1 1 IA Table 4.1. Revised 1997 by C.G. Wohl (LBNL). Heavy element updates in May 2000 by D.E. Groom. The atomic number (top left) is the number of protons in the nucleus. The atomic mass (bottom) is weighted by isotopic abundances in the Earth’s surface. Atomic masses are relative to the mass of the carbon-12 isotope, defined to be exactly 12 unified atomic mass units (u). Errors range from 1 to 9 in the last digit quoted. Relative isotopic abundances often vary considerably, both in natural and commercial samples. A number in parentheses is the mass of the longest-lived isotope of that element—no stable isotope exists. However, although Th, Pa, and U have no stable isotopes, they do have characteristic terrestrial compositions, and meaningful weighted masses can be given. For elements 110–112, the atomic numbers of known isotopes are given. Adapted from the Commission of Atomic Weights and Isotopic Abundances, “Atomic Weights of the Elements 1995,” Pure and Applied Chemistry 68, 2339 (1996), and G. Audi and A.H. Wapstra, “The 1993 Mass Evaluation,” Nucl. Phys. A565, 1 (1993). E Atomic and SubAtomic properties of the materials 763 From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Quantity Symbol Value Unit Relative std. uncert. ur UNIVERSAL 299 792 458 4π × 10−7 = 12.566 370 614... × 10−7 8.854 187 817... × 10−12 m s−1 N A−2 N A−2 F m−1 (exact) Z0 376.730 313 461... Ω (exact) G G/¯hc h 6.6742(10) × 10−11 6.7087(10) × 10−39 6.626 0693(11) × 10−34 4.135 667 43(35) × 10−15 1.054 571 68(18) × 10−34 6.582 119 15(56) × 10−16 197.326 968(17) m3 kg−1 s−2 (GeV/c2 )−2 Js eV s Js eV s MeV fm 1.5 × 10−4 1.5 × 10−4 1.7 × 10−7 8.5 × 10−8 1.7 × 10−7 8.5 × 10−8 8.5 × 10−8 2.176 45(16) × 10−8 1.416 79(11) × 1032 1.616 24(12) × 10−35 5.391 21(40) × 10−44 kg K m s 7.5 × 10−5 7.5 × 10−5 7.5 × 10−5 7.5 × 10−5 speed of light in vacuum magnetic constant c, c0 µ0 electric constant 1/µ0 c2 characteristicpimpedance of vacuum µ0 /0 = µ0 c 0 Newtonian constant of gravitation Planck constant in eV s h/2π in eV s hc in Mev fm ¯ ¯h Planck mass (¯ hc/G)1/2 Planck temperature (¯ hc5 /G)1/2 /k Planck length ¯h/mP c = (¯ hG/c3 )1/2 Planck time lP /c = (¯hG/c5 )1/2 mP TP lP tP ELECTROMAGNETIC (exact) (exact) elementary charge e e/h 1.602 176 53(14) × 10−19 2.417 989 40(21) × 1014 C A J−1 8.5 × 10−8 8.5 × 10−8 magnetic flux quantum h/2e conductance quantum 2e2/h inverse of conductance quantum Josephson constant1 2e/h von Klitzing constant2 h/e2 = µ0 c/2α Φ0 G0 G−1 0 KJ 2.067 833 72(18) × 10−15 7.748 091 733(26) × 10−5 12 906.403 725(43) 483 597.879(41) × 109 Wb S Ω Hz V−1 8.5 × 10−8 3.3 × 10−9 3.3 × 10−9 8.5 × 10−8 RK 25 812.807 449(86) Ω 3.3 × 10−9 Bohr magneton e¯h/2me in eV T−1 µB 927.400 949(80) × 10−26 5.788 381 804(39) × 10−5 13.996 2458(12) × 109 46.686 4507(40) 0.671 7131(12) J T−1 eV T−1 Hz T−1 m−1 T−1 K T−1 8.6 × 10−8 6.7 × 10−9 8.6 × 10−8 8.6 × 10−8 1.8 × 10−6 5.050 783 43(43) × 10−27 3.152 451 259(21) × 10−8 7.622 593 71(65) 2.542 623 58(22) × 10−2 3.658 2637(64) × 10−4 J T−1 eV T−1 MHz T−1 m−1 T−1 K T−1 8.6 × 10−8 6.7 × 10−9 8.6 × 10−8 8.6 × 10−8 1.8 × 10−6 µB /h µB /hc µB /k nuclear magneton e¯h/2mp in eV T−1 µN µN /h µN /hc µN /k ATOMIC AND NUCLEAR General Page 1 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2002, published in Review of Modern Physics 77, 1 (2005). From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Quantity Symbol Value Unit Relative std. uncert. ur fine-structure constant e2/4π0 ¯hc inverse fine-structure constant α α−1 7.297 352 568(24) × 10−3 137.035 999 11(46) Rydberg constant α2 me c/2h R∞ R∞ c R∞ hc 10 973 731.568 525(73) 3.289 841 960 360(22) × 1015 2.179 872 09(37) × 10−18 13.605 6923(12) m−1 Hz J eV 6.6 × 10−12 6.6 × 10−12 1.7 × 10−7 8.5 × 10−8 a0 0.529 177 2108(18) × 10−10 m 3.3 × 10−9 Eh 4.359 744 17(75) × 10−18 27.211 3845(23) 3.636 947 550(24) × 10−4 7.273 895 101(48) × 10−4 J eV m2 s−1 m2 s−1 1.7 × 10−7 8.5 × 10−8 6.7 × 10−9 6.7 × 10−9 GF /(¯ hc)3 1.166 39(1) × 10−5 GeV−2 8.6 × 10−6 sin2 θW 0.222 15(76) R∞ hc in eV Bohr radius α/4πR∞ = 4π0 ¯h2/me e2 Hartree energy e2/4π0 a0 = 2R∞ hc = α2 me c2 in eV quantum of circulation h/2me h/me 3.3 × 10−9 3.3 × 10−9 Electroweak Fermi coupling constant3 weak mixing angle4 θW (on-shell scheme) sin2 θW = s2W ≡ 1 − (mW /mZ )2 3.4 × 10−3 Electron, e− 9.109 3826(16) × 10−31 kg 1.7 × 10−7 me c 5.485 799 0945(24) × 10−4 8.187 1047(14) × 10−14 0.510 998 918(44) u J MeV 4.4 × 10−10 1.7 × 10−7 8.6 × 10−8 electron-muon mass ratio electron-tau mass ratio electron-proton mass ratio electron-neutron mass ratio electron-deuteron mass ratio electron to alpha particle mass ratio me /mµ me /mτ me /mp me /mn me /md me /mα 4.836 331 67(13) × 10−3 2.875 64(47) × 10−4 5.446 170 2173(25) × 10−4 5.438 673 4481(38) × 10−4 2.724 437 1095(13) × 10−4 1.370 933 555 75(61) × 10−4 electron charge to mass quotient electron molar mass NA me Compton wavelength h/me c λC /2π = αa0 = α2/4πR∞ classical electron radius α2 a0 Thomson cross section (8π/3)re2 −e/me M (e), Me λC λC re σe −1.758 820 12(15) × 1011 5.485 799 0945(24) × 10−7 2.426 310 238(16) × 10−12 386.159 2678(26) × 10−15 2.817 940 325(28) × 10−15 0.665 245 873(13) × 10−28 C kg−1 kg mol−1 m m m m2 8.6 × 10−8 4.4 × 10−10 6.7 × 10−9 6.7 × 10−9 1.0 × 10−8 2.0 × 10−8 electron magnetic moment to Bohr magneton ratio to nuclear magneton ratio electron magnetic moment anomaly |µe |/µB − 1 electron g-factor −2(1 + ae ) µe µe /µB µe /µN −928.476 412(80) × 10−26 −1.001 159 652 1859(38) −1838.281 971 07(85) J T−1 8.6 × 10−8 3.8 × 10−12 4.6 × 10−10 ae ge 1.159 652 1859(38) × 10−3 −2.002 319 304 3718(75) electron mass in u, me = Ar (e) u (electron relative atomic mass times u) energy equivalent in MeV Page 2 me 2 2.6 × 10−8 1.6 × 10−4 4.6 × 10−10 7.0 × 10−10 4.8 × 10−10 4.4 × 10−10 3.2 × 10−9 3.8 × 10−12 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2002, published in Review of Modern Physics 77, 1 (2005). From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Quantity Symbol electron-muon magnetic moment ratio electron-proton magnetic moment ratio electron to shielded proton magnetic moment ratio (H2 O, sphere, 25 ◦ C) electron-neutron magnetic moment ratio electron-deuteron magnetic moment ratio electron to shielded helion5 magnetic moment ratio (gas, sphere, 25 ◦ C) electron gyromagnetic ratio 2|µe |/¯h Value Unit Relative std. uncert. ur µe /µµ 206.766 9894(54) 2.6 × 10−8 µe /µp −658.210 6862(66) 1.0 × 10−8 µe /µ0p −658.227 5956(71) 1.1 × 10−8 µe /µn 960.920 50(23) 2.4 × 10−7 µe /µd −2143.923 493(23) 1.1 × 10−8 µe /µ0h 864.058 255(10) 1.2 × 10−8 γe γe /2π 1.760 859 74(15) × 1011 28 024.9532(24) s−1 T−1 MHz T−1 8.6 × 10−8 8.6 × 10−8 1.883 531 40(33) × 10−28 kg 1.7 × 10−7 mµ c 0.113 428 9264(30) 1.692 833 60(29) × 10−11 105.658 3692(94) u J MeV 2.6 × 10−8 1.7 × 10−7 8.9 × 10−8 muon-electron mass ratio muon-tau mass ratio muon-proton mass ratio muon-neutron mass ratio muon molar mass NA mµ mµ /me mµ /mτ mµ /mp mµ /mn M (µ), Mµ 206.768 2838(54) 5.945 92(97) × 10−2 0.112 609 5269(29) 0.112 454 5175(29) 0.113 428 9264(30) × 10−3 muon Compton wavelength h/mµ c λC,µ /2π muon magnetic moment to Bohr magneton ratio to nuclear magneton ratio λC,µ λC,µ µµ µµ /µB µµ /µN 11.734 441 05(30) × 10−15 1.867 594 298(47) × 10−15 −4.490 447 99(40) × 10−26 −4.841 970 45(13) × 10−3 −8.890 596 98(23) aµ gµ 1.165 919 81(62) × 10−3 −2.002 331 8396(12) 5.3 × 10−7 6.2 × 10−10 µµ /µp −3.183 345 118(89) 2.8 × 10−8 Muon, µ− muon mass in u, mµ = Ar (µ) u (muon relative atomic mass times u) energy equivalent in MeV muon magnetic moment anomaly |µµ |/(e¯h/2mµ ) − 1 muon g-factor −2(1 + aµ ) muon-proton magnetic moment ratio mµ 2 kg mol−1 m m J T−1 Tau, τ − tau mass6 in u, mτ = Ar (τ) u (tau relative atomic mass times u) energy equivalent Page 3 mτ 2 mτ c 2.6 × 10−8 1.6 × 10−4 2.6 × 10−8 2.6 × 10−8 2.6 × 10−8 2.5 × 10−8 2.5 × 10−8 8.9 × 10−8 2.6 × 10−8 2.6 × 10−8 3.167 77(52) × 10−27 kg 1.6 × 10−4 1.907 68(31) 2.847 05(46) × 10−10 u J 1.6 × 10−4 1.6 × 10−4 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2002, published in Review of Modern Physics 77, 1 (2005). From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Quantity Symbol Value 1776.99(29) in MeV Unit MeV Relative std. uncert. ur 1.6 × 10−4 1.6 × 10−4 1.6 × 10−4 1.6 × 10−4 1.6 × 10−4 1.6 × 10−4 tau-electron mass ratio tau-muon mass ratio tau-proton mass ratio tau-neutron mass ratio tau molar mass NA mτ mτ /me mτ /mµ mτ /mp mτ /mn M (τ), Mτ 3477.48(57) 16.8183(27) 1.893 90(31) 1.891 29(31) 1.907 68(31) × 10−3 tau Compton wavelength h/mτ c λC,τ /2π λC,τ λC,τ 0.697 72(11) × 10−15 0.111 046(18) × 10−15 m m 1.6 × 10−4 1.6 × 10−4 1.672 621 71(29) × 10−27 kg 1.7 × 10−7 u J MeV 1.3 × 10−10 1.7 × 10−7 8.6 × 10−8 kg mol−1 Proton, p proton mass in u, mp = Ar (p) u (proton relative atomic mass times u) energy equivalent in MeV mp mp c 1.007 276 466 88(13) 1.503 277 43(26) × 10−10 938.272 029(80) proton-electron mass ratio proton-muon mass ratio proton-tau mass ratio proton-neutron mass ratio proton charge to mass quotient proton molar mass NA mp mp /me mp /mµ mp /mτ mp /mn e/mp M (p), Mp 1836.152 672 61(85) 8.880 243 33(23) 0.528 012(86) 0.998 623 478 72(58) 9.578 833 76(82) × 107 1.007 276 466 88(13) × 10−3 proton Compton wavelength h/mp c λC,p /2π proton rms charge radius proton magnetic moment to Bohr magneton ratio to nuclear magneton ratio λC,p λC,p Rp µp µp /µB µp /µN 1.321 409 8555(88) × 10−15 0.210 308 9104(14) × 10−15 0.8750(68) × 10−15 1.410 606 71(12) × 10−26 1.521 032 206(15) × 10−3 2.792 847 351(28) proton g-factor 2µp /µN proton-neutron magnetic moment ratio shielded proton magnetic moment (H2 O, sphere, 25 ◦ C) to Bohr magneton ratio to nuclear magneton ratio proton magnetic shielding correction 1 − µ0p /µp (H2 O, sphere, 25 ◦ C) gp 5.585 694 701(56) µp /µn µ0p −1.459 898 05(34) 1.410 570 47(12) × 10−26 µ0p /µB µ0p /µN 1.520 993 132(16) × 10−3 2.792 775 604(30) 1.1 × 10−8 1.1 × 10−8 σp0 25.689(15) × 10−6 5.7 × 10−4 γp γp /2π 2.675 222 05(23) × 108 42.577 4813(37) s−1 T−1 MHz T−1 8.6 × 10−8 8.6 × 10−8 γp0 2.675 153 33(23) × 108 s−1 T−1 8.6 × 10−8 proton gyromagnetic ratio 2µp /¯h shielded proton gyromagnetic ratio 2µ0p /¯h (H2 O, sphere, 25 ◦ C) Page 4 2 C kg−1 kg mol−1 m m m J T−1 4.6 × 10−10 2.6 × 10−8 1.6 × 10−4 5.8 × 10−10 8.6 × 10−8 1.3 × 10−10 6.7 × 10−9 6.7 × 10−9 7.8 × 10−3 8.7 × 10−8 1.0 × 10−8 1.0 × 10−8 1.0 × 10−8 −1 JT 2.4 × 10−7 8.7 × 10−8 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2002, published in Review of Modern Physics 77, 1 (2005). From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Quantity Symbol Value γp0 /2π Unit Relative std. uncert. ur MHz T−1 8.6 × 10−8 1.674 927 28(29) × 10−27 kg 1.7 × 10−7 u J MeV 5.5 × 10−10 1.7 × 10−7 8.6 × 10−8 42.576 3875(37) Neutron, n neutron mass in u, mn = Ar (n) u (neutron relative atomic mass times u) energy equivalent in MeV mn mn c 1.008 664 915 60(55) 1.505 349 57(26) × 10−10 939.565 360(81) neutron-electron mass ratio neutron-muon mass ratio neutron-tau mass ratio neutron-proton mass ratio neutron molar mass NA mn mn /me mn /mµ mn /mτ mn /mp M (n), Mn 1838.683 6598(13) 8.892 484 02(23) 0.528 740(86) 1.001 378 418 70(58) 1.008 664 915 60(55) × 10−3 neutron Compton wavelength h/mn c λC,n /2π neutron magnetic moment to Bohr magneton ratio to nuclear magneton ratio λC,n λC,n µn µn /µB µn /µN 1.319 590 9067(88) × 10−15 0.210 019 4157(14) × 10−15 −0.966 236 45(24) × 10−26 −1.041 875 63(25) × 10−3 −1.913 042 73(45) neutron g-factor 2µn /µN neutron-electron magnetic moment ratio neutron-proton magnetic moment ratio neutron to shielded proton magnetic moment ratio (H2 O, sphere, 25 ◦ C) neutron gyromagnetic ratio 2|µn |/¯h gn −3.826 085 46(90) 2.4 × 10−7 µn /µe 1.040 668 82(25) × 10−3 2.4 × 10−7 µn /µp −0.684 979 34(16) 2.4 × 10−7 µn /µ0p −0.684 996 94(16) 2.4 × 10−7 γn γn /2π 1.832 471 83(46) × 108 29.164 6950(73) 2 kg mol−1 m m J T−1 2.5 × 10−7 2.5 × 10−7 3.343 583 35(57) × 10−27 kg 1.7 × 10−7 u J MeV 1.7 × 10−10 1.7 × 10−7 8.6 × 10−8 deuteron mass in u, md = Ar (d) u (deuteron relative atomic mass times u) energy equivalent in MeV md md c 2.013 553 212 70(35) 3.005 062 85(51) × 10−10 1875.612 82(16) deuteron-electron mass ratio deuteron-proton mass ratio deuteron molar mass NA md md /me md /mp M (d), Md 3670.482 9652(18) 1.999 007 500 82(41) 2.013 553 212 70(35) × 10−3 deuteron rms charge radius deuteron magnetic moment to Bohr magneton ratio to nuclear magneton ratio Rd µd µd /µB µd /µN 2.1394(28) × 10−15 0.433 073 482(38) × 10−26 0.466 975 4567(50) × 10−3 0.857 438 2329(92) Page 5 6.7 × 10−9 6.7 × 10−9 2.5 × 10−7 2.4 × 10−7 2.4 × 10−7 s−1 T−1 MHz T−1 Deuteron, d 2 7.0 × 10−10 2.6 × 10−8 1.6 × 10−4 5.8 × 10−10 5.5 × 10−10 kg mol−1 m J T−1 4.8 × 10−10 2.0 × 10−10 1.7 × 10−10 1.3 × 10−3 8.7 × 10−8 1.1 × 10−8 1.1 × 10−8 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2002, published in Review of Modern Physics 77, 1 (2005). From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Quantity Symbol deuteron-electron magnetic moment ratio deuteron-proton magnetic moment ratio deuteron-neutron magnetic moment ratio Value Unit µd /µe −4.664 345 548(50) × 10−4 1.1 × 10−8 µd /µp 0.307 012 2084(45) 1.5 × 10−8 µd /µn −0.448 206 52(11) 2.4 × 10−7 Helion, h 5.006 412 14(86) × 10−27 kg 1.7 × 10−7 mh c 3.014 932 2434(58) 4.499 538 84(77) × 10−10 2808.391 42(24) u J MeV 1.9 × 10−9 1.7 × 10−7 8.6 × 10−8 mh /me mh /mp M (h), Mh µ0h 5495.885 269(11) 2.993 152 6671(58) 3.014 932 2434(58) × 10−3 −1.074 553 024(93) × 10−26 µ0h /µB µ0h /µN −1.158 671 474(14) × 10−3 −2.127 497 723(25) 1.2 × 10−8 1.2 × 10−8 µ0h /µp −0.761 766 562(12) 1.5 × 10−8 µ0h /µ0p −0.761 786 1313(33) 4.3 × 10−9 γh0 2.037 894 70(18) × 108 s−1 T−1 8.7 × 10−8 γh0 /2π 32.434 1015(28) MHz T−1 8.7 × 10−8 6.644 6565(11) × 10−27 kg 1.7 × 10−7 mα c 4.001 506 179 149(56) 5.971 9194(10) × 10−10 3727.379 17(32) u J MeV 1.4 × 10−11 1.7 × 10−7 8.6 × 10−8 mα /me mα /mp M (α), Mα 7294.299 5363(32) 3.972 599 689 07(52) 4.001 506 179 149(56) × 10−3 helion mass5 in u, mh = Ar (h) u (helion relative atomic mass times u) energy equivalent in MeV mh helion-electron mass ratio helion-proton mass ratio helion molar mass NA mh shielded helion magnetic moment (gas, sphere, 25 ◦ C) to Bohr magneton ratio to nuclear magneton ratio shielded helion to proton magnetic moment ratio (gas, sphere, 25 ◦ C) shielded helion to shielded proton magnetic moment ratio (gas/H2 O, spheres, 25 ◦ C) shielded helion gyromagnetic ratio 2|µ0h |/¯h (gas, sphere, 25 ◦ C) 2 kg mol−1 J T−1 Alpha particle, α alpha particle mass in u, mα = Ar (α) u (alpha particle relative atomic mass times u) energy equivalent in MeV alpha particle to electron mass ratio alpha particle to proton mass ratio alpha particle molar mass NA mα mα 2 kg mol−1 PHYSICO-CHEMICAL Avogadro constant atomic mass constant 1 mu = 12 m(12 C) = 1 u Page 6 Relative std. uncert. ur 2.0 × 10−9 1.9 × 10−9 1.9 × 10−9 8.7 × 10−8 4.4 × 10−10 1.3 × 10−10 1.4 × 10−11 NA , L 6.022 1415(10) × 1023 mol−1 1.7 × 10−7 mu 1.660 538 86(28) × 10−27 kg 1.7 × 10−7 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2002, published in Review of Modern Physics 77, 1 (2005). From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Quantity Symbol = 10−3 kg mol−1/NA energy equivalent in MeV Faraday constant7 NA e 1.7 × 10−7 8.6 × 10−8 8.6 × 10−8 3.990 312 716(27) × 10−10 0.119 626 565 72(80) 8.314 472(15) 1.380 6505(24) × 10−23 8.617 343(15) × 10−5 2.083 6644(36) × 1010 69.503 56(12) J s mol−1 J m mol−1 J mol−1 K−1 J K−1 eV K−1 Hz K−1 m−1 K−1 6.7 × 10−9 6.7 × 10−9 1.7 × 10−6 1.8 × 10−6 1.8 × 10−6 1.7 × 10−6 1.7 × 10−6 Vm n0 Vm 22.413 996(39) × 10−3 2.686 7773(47) × 1025 22.710 981(40) × 10−3 m3 mol−1 m−3 m3 mol−1 1.7 × 10−6 1.8 × 10−6 1.7 × 10−6 S0 /R −1.151 7047(44) −1.164 8677(44) σ c1 c1L c2 5.670 400(40) × 10−8 3.741 771 38(64) × 10−16 1.191 042 82(20) × 10−16 1.438 7752(25) × 10−2 W m−2 K−4 W m2 W m2 sr−1 mK 7.0 × 10−6 1.7 × 10−7 1.7 × 10−7 1.7 × 10−6 b 2.897 7685(51) × 10−3 mK 1.7 × 10−6 NA h NA hc R k k/h k/hc molar volume of ideal gas RT /p T = 273.15 K, p = 101.325 kPa Loschmidt constant NA /Vm T = 273.15 K, p = 100 kPa Sackur-Tetrode constant (absolute entropy constant)8 5 2 3/2 kT1 /p0 ] 2 + ln[(2πmu kT1 /h ) T1 = 1 K, p0 = 100 kPa T1 = 1 K, p0 = 101.325 kPa Stefan-Boltzmann constant (π2 /60)k 4/¯h3 c2 first radiation constant 2πhc2 first radiation constant for spectral radiance 2hc2 second radiation constant hc/k Wien displacement law constant b = λmax T = c2 /4.965 114 231... 1 Relative std. uncert. ur J MeV C mol−1 F molar gas constant Boltzmann constant R/NA in eV K−1 Unit 1.492 417 90(26) × 10−10 931.494 043(80) 96 485.3383(83) mu c2 molar Planck constant Value 3.8 × 10−6 3.8 × 10−6 See the “Adopted values” table for the conventional value adopted internationally for realizing representations of the volt using the Josephson effect. 2 See the “Adopted values” table for the conventional value adopted internationally for realizing representations of the ohm using the quantum Hall effect. 3 Value recommended by the Particle Data Group (Hagiwara, et al., 2002). 4 Based on the ratio of the masses of the W and Z bosons mW /mZ recommended by the Particle Data Group (Hagiwara, et al., 2002). The value for sin2 θW they recommend, which is based on a particular variant of the modified minimal subtraction (MS) scheme, is sin2 θˆW (MZ ) = 0.231 24(24). 5 The helion, symbol h, is the nucleus of the 3 He atom. 6 This and all other values involving mτ are based on the value of mτ c2 in MeV recommended by the Particle Data Group, (Hagiwara, et al., 2002), but with a standard uncertainty of 0.29 MeV rather than the quoted uncertainty of −0.26 MeV, +0.29 MeV. 7 The numerical value of F to be used in coulometric chemical measurements is 96 485.336(16) [1.7 × 10−7 ] when the relevant current is measured in terms of representations of the volt and ohm based on the Josephson and quantum Hall effects and the internationally adopted conventional values of the Josephson and von Klitzing constants KJ−90 and RK−90 given in the “Adopted values” table. 8 The entropy of an ideal monoatomic gas of relative atomic mass Ar is given by S = S0 + 23 R ln Ar − R ln(p/p0 ) + 52 R ln(T /K). 9 The relative atomic mass Ar (X) of particle X with mass m(X) is defined by Ar (X) = m(X)/mu , where mu = m(12 C)/12 = Mu /NA = 1 u is the atomic mass constant, NA is the Avogadro constant, and u is the atomic mass unit. Thus the mass of particle X in u is m(X) = Ar (X) u and the molar mass of X is M (X) = Ar (X)Mu . Page 7 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2002, published in Review of Modern Physics 77, 1 (2005). From: http://physics.nist.gov/constants 10 This is the value adopted internationally for realizing representations of the volt using the Josephson effect. This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect. a This is the lattice parameter (unit cell edge length) of an ideal single crystal of naturally occurring Si free of impurities and imperfections, and is deduced from measurements on extremely pure and nearly perfect single crystals of Si by correcting for the effects of impurities. 11 Page 8 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2002, published in Review of Modern Physics 77, 1 (2005). 5. Electronic structure of the elements 1 5. ELECTRONIC STRUCTURE OF THE ELEMENTS Table 5.1. Reviewed 2005 by C.G. Wohl (LBNL). The electronic configurations and the ionization energies are from the NIST database, “Ground Levels and Ionization Energies for the Neutral Atoms,” W.C. Martin, A. Musgrove, S. Kotochigova, and J.E. Sansonetti (2003), http://physics.nist.gov (select “Physical Reference Data”). The electron configuration for, say, iron indicates an argon electronic core (see argon) plus six 3d electrons and two 4s electrons. The ionization energy is the least energy necessary to remove to infinity one electron from an atom of the element. Element Electron configuration (3d5 = five 3d electrons, etc.) 1 2 H He Hydrogen Helium 1s 1s2 3 4 5 6 7 8 9 10 Li Be B C N O F Ne Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon (He)2s (He)2s2 (He)2s2 (He)2s2 (He)2s2 (He)2s2 (He)2s2 (He)2s2 11 12 13 14 15 16 17 18 Na Mg Al Si P S Cl Ar Sodium Magnesium Aluminum Silicon Phosphorus Sulfur Chlorine Argon (Ne)3s (Ne)3s2 (Ne)3s2 (Ne)3s2 (Ne)3s2 (Ne)3s2 (Ne)3s2 (Ne)3s2 Ground state 2S+1 L J Ionization energy (eV) 2S 13.5984 24.5874 1S 2S 1S 0 1/2 0 2P 1/2 3P 0 4S 3/2 3P 2 2P 3/2 1S 0 2p 2p2 2p3 2p4 2p5 2p6 2S 1S 1/2 0 2P 1/2 3P 0 4S 3/2 3P 2 2P 3/2 1S 0 3p 3p2 3p3 3p4 3p5 3p6 19 K Potassium (Ar) 4s 20 Ca Calcium (Ar) 4s2 - - - - - - - - - - - - - - - - - - - - - - - - 21 Sc Scandium (Ar) 3d 4s2 22 Ti Titanium (Ar) 3d2 4s2 23 V Vanadium (Ar) 3d3 4s2 24 Cr Chromium (Ar) 3d5 4s 25 Mn Manganese (Ar) 3d5 4s2 26 Fe Iron (Ar) 3d6 4s2 27 Co Cobalt (Ar) 3d7 4s2 28 Ni Nickel (Ar) 3d8 4s2 29 Cu Copper (Ar) 3d10 4s 30 Zn Zinc (Ar) 3d10 4s2 - - - - - - - - - - - - - - - - - - - - - - - - 31 Ga Gallium (Ar) 3d10 4s2 4p 32 Ge Germanium (Ar) 3d10 4s2 4p2 33 As Arsenic (Ar) 3d10 4s2 4p3 34 Se Selenium (Ar) 3d10 4s2 4p4 35 Br Bromine (Ar) 3d10 4s2 4p5 36 Kr Krypton (Ar) 3d10 4s2 4p6 1/2 2S T r a n s i t i o n - 5.3917 9.3227 8.2980 11.2603 14.5341 13.6181 17.4228 21.5645 5.1391 7.6462 5.9858 8.1517 10.4867 10.3600 12.9676 15.7596 4.3407 6.1132 - - - - - - - - - - - - - 2D 6.5615 3/2 3F 6.8281 2 e 4F 6.7462 3/2 l 7S 6.7665 e 3 6S 7.4340 m 5/2 5D e 7.9024 4 4F n 7.8810 9/2 3F t 7.6398 4 s 2S 7.7264 1/2 1S 9.3942 0 - - - - - - - - - - - - - 2P 5.9993 1/2 3P 7.8994 0 4S 9.7886 3/2 3P 9.7524 2 2P 11.8138 3/2 1S 13.9996 0 1S 1/2 0 2S 37 Rb Rubidium (Kr) 5s 4.1771 1/2 2 1 S0 5.6949 38 Sr Strontium (Kr) 5s - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 2 D3/2 6.2173 39 Y Yttrium (Kr) 4d 5s T 3F r 6.6339 40 Zr Zirconium (Kr) 4d2 5s2 2 e 6D a 6.7589 41 Nb Niobium (Kr) 4d4 5s 1/2 l n 7S 42 Mo Molybdenum (Kr) 4d5 5s 7.0924 e 3 s 6S 7.28 43 Tc Technetium (Kr) 4d5 5s2 m 5/2 i 5F e 7.3605 44 Ru Ruthenium (Kr) 4d7 5s 5 t 4F n 7.4589 45 Rh Rhodium (Kr) 4d8 5s 9/2 i 1S t 8.3369 46 Pd Palladium (Kr) 4d10 0 o s 2S 47 Ag Silver (Kr) 4d10 5s 7.5762 n 1/2 1S 8.9938 48 Cd Cadmium (Kr) 4d10 5s2 0 2 5. Electronic structure of the elements 49 50 51 52 53 54 In Sn Sb Te I Xe Indium Tin Antimony Tellurium Iodine Xenon (Kr) 4d10 5s2 (Kr) 4d10 5s2 (Kr) 4d10 5s2 (Kr) 4d10 5s2 (Kr) 4d10 5s2 (Kr) 4d10 5s2 5p 5p2 5p3 5p4 5p5 5p6 2P 1/2 3P 0 4S 3/2 3P 2 2P 3/2 1S 0 5.7864 7.3439 8.6084 9.0096 10.4513 12.1298 2S 55 Cs Cesium (Xe) 6s 3.8939 1/2 2 1 S0 5.2117 56 Ba Barium (Xe) 6s - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 2 57 La Lanthanum (Xe) 5d 6s D3/2 5.5769 1G 5.5387 58 Ce Cerium (Xe)4f 5d 6s2 4 4I 6s2 5.473 59 Pr Praseodymium (Xe)4f 3 L 9/2 5I a 6s2 5.5250 60 Nd Neodymium (Xe)4f 4 4 6H n 6s2 5.582 61 Pm Promethium (Xe)4f 5 5/2 t 7F 62 Sm Samarium (Xe)4f 6 6s2 5.6437 0 h 8S 6s2 5.6704 63 Eu Europium (Xe)4f 7 7/2 a 9D 6.1498 64 Gd Gadolinium (Xe)4f 7 5d 6s2 2 n 6H 6s2 5.8638 65 Tb Terbium (Xe)4f 9 15/2 i 5I 6s2 5.9389 66 Dy Dysprosium (Xe)4f 10 8 d 4I 67 Ho Holmium (Xe)4f 11 6s2 6.0215 e 15/2 3H 6s2 6.1077 68 Er Erbium (Xe)4f 12 s 6 2F 6s2 6.1843 69 Tm Thulium (Xe)4f 13 7/2 1S 6s2 6.2542 70 Yb Ytterbium (Xe)4f 14 0 2D 5.4259 71 Lu Lutetium (Xe)4f 14 5d 6s2 3/2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 14 2 2 3 F2 6.8251 72 Hf Hafnium (Xe)4f 5d 6s T 4F r 7.5496 73 Ta Tantalum (Xe)4f 14 5d3 6s2 3/2 e 5D a 7.8640 74 W Tungsten (Xe)4f 14 5d4 6s2 0 l 6S n 7.8335 75 Re Rhenium (Xe)4f 14 5d5 6s2 e 5/2 s m 5D 8.4382 76 Os Osmium (Xe)4f 14 5d6 6s2 4 i 4F e 8.9670 77 Ir Iridium (Xe)4f 14 5d7 6s2 9/2 t 3D n 78 Pt Platinum (Xe)4f 14 5d9 6s 8.9588 3 i t 2S1/2 9.2255 79 Au Gold (Xe)4f 14 5d10 6s o s 1S 10.4375 80 Hg Mercury (Xe)4f 14 5d10 6s2 0 n - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2P 81 Tl Thallium (Xe)4f 14 5d10 6s2 6p 6.1082 1/2 3P 82 Pb Lead (Xe)4f 14 5d10 6s2 6p2 7.4167 0 4S 7.2855 83 Bi Bismuth (Xe)4f 14 5d10 6s2 6p3 3/2 3P 8.414 84 Po Polonium (Xe)4f 14 5d10 6s2 6p4 2 2P 85 At Astatine (Xe)4f 14 5d10 6s2 6p5 3/2 1S 86 Rn Radon (Xe)4f 14 5d10 6s2 6p6 10.7485 0 87 Fr Francium (Rn) 88 Ra Radium (Rn) - - - - - - - - - - - - - - - - - - 89 Ac Actinium (Rn) 6d 90 Th Thorium (Rn) 6d2 91 Pa Protactinium (Rn)5f 2 6d 92 U Uranium (Rn)5f 3 6d 93 Np Neptunium (Rn)5f 4 6d 94 Pu Plutonium (Rn)5f 6 95 Am Americium (Rn)5f 7 96 Cm Curium (Rn)5f 7 6d 97 Bk Berkelium (Rn)5f 9 98 Cf Californium (Rn)5f 10 99 Es Einsteinium (Rn)5f 11 100 Fm Fermium (Rn)5f 12 101 Md Mendelevium (Rn)5f 13 102 No Nobelium (Rn)5f 14 103 Lr Lawrencium (Rn)5f 14 - - - - - - - - - - - - - - - - - - 104 Rf Rutherfordium (Rn)5f 14 6d2 ∗ 2S 7s 4.0727 1/2 2 1 S0 5.2784 7s - - - - - - - - - - - - - - - - - - - - 2 2 7s D3/2 5.17 3F 7s2 6.3067 2 4K ∗ 7s2 5.89 A 11/2 5L ∗ c 7s2 6.1941 6 ∗ 6L t 7s2 6.2657 11/2 i 7F 7s2 6.0260 0 n 8S 7s2 5.9738 7/2 i 9D 7s2 5.9914 2 d 6H 7s2 6.1979 15/2 e 5I 7s2 6.2817 8 s 4I 7s2 6.42 15/2 3H 7s2 6.50 6 2F 7s2 6.58 7/2 1S 7s2 6.65 0 2P 7s2 7p? 4.9? 1/2 ? - - - - - - - - - - - - - - - - - - - - 3F ? 7s2 ? 6.0? 2 The usual LS coupling scheme does not apply for these three elements. See the introductory note to the NIST table from which this table is taken. E: Atomic and SubAtomic properties of the materials 774 November 1, 2010 F Properties of Matter: data tables 775 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com CHAPTER 2 Tables These tables are from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with the publishers, Taylor and Francis. They may be used freely for educational purposes, but their source must be acknowledged. For more details see www.physicsofmatter.com Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 2.1 The properties of particles that are treated as fundamental in this book. The most important properties of the particles for understanding the properties of matter are the first two rows of the table: mass and electric charge. The internal angular momentum (spin) and magnetic moment of the particles are discussed in the text below. Property Units Electron 5.485 ´ 10 »1/1836 –1 Magnetic moment Atomic mass units u = 1.661 ´ 10–27 kg Proton charge e = 1.602 ´ 10–19 C Bohr magneton Magnetic moment µB = 9.274 ´ 10–24 J T–1 Nuclear magneton Intrinsic (spin) angular momentum µN = 5.051 ´ 10–27 J T–1 Planck constant divided by 2p h = 1.054 ´ 10–34 J s Electric dipole moment Cm Mass Electric charge Lifetime 1.001 1837.8 1 2 Neutron –4 Proton 1.0085 1.0071 0 +1 1.0419 ´ 10 –3 1.521 ´ 10 –3 1.913 2.793 1 2 1 2 0 0 0 Stable Stable within nuclei half life » 15 minutes in free space. Stable Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 2.2. The elements with atomic numbers up to 105 together with their date of discovery. The term ÔOldÕ as a date of discovery indicates that the element was known in antiquity. The names of the elements tell many fascinating stories about their discovery. Z 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Element, symbol, date of discovery Origin of name Hydrogen, H, (1766) Greek: Hydros Genes: meaning Water Forming Helium, He, (1895) Greek: Helios meaning Sun Lithium, Li, (1817) Greek: Lithos meaning Stone Beryllium, Be, (1797) Greek: Beryllos meaning Beryl Boron, B, (1808) Arabic: Buraq Carbon, C, (Old) Latin: Carbo meaning Charcoal Nitrogen, N, (1772) Greek: Nitron Genes meaning Nitre Forming Oxygen, O, (1774) Greek: Oxy Genes meaning Acid Forming Latin: Fluere meaning To Flow Fluorine, F, (1886) Neon, Ne, (1898) Greek: Neos meaning New English: Soda: The symbol Sodium, Na, (1807) comes from the Latin Natrium Magnesium, Mg, (1755) Greek: Magnesia, a district in Thessaly Latin: alumen meaning alum Aluminium, Al, (1825) Silicon, Si, , (1824) Latin: Silicis meaning Flint Phosphorus, P, (1669) Greek: Phosphorus meaning Bringer of Light Sulphur, S, (Old) Sanskrit: Sulvere meaning Sulphur Chlorine, Cl, (1774) Greek: Chloros meaning Pale Green Argon, Ar, (1894) Greek: Argos meaning Inactive Potassium, K, (1807) English: Potash: The symbol comes from the Latin Kalium Calcium, Ca, (1808) Latin: Calix meaning Lime Scandium, Sc, (1879) Latin: Scandia meaning Scandinavia Titanium, Ti, (1791) Titans, Sons of the Earth Goddess. Vanadium, V, (1801) Vanadis, Scandinavian goddess Chromium, Cr, (1780) Greek: Chroma meaning Colour Manganese, Mn, (1774) Latin: Magnes meaning Magnet Iron, Fe, (Old) Saxon: Iron: The symbol comes from the Latin Ferrum Cobalt, Co, (1735) German: kobald meaning Goblin Nickel, Ni, (1751) German: Kupfernickel meaning either Devil’s Copper or St Nicholas’ Copper Copper, Cu, (Old) Latin: Cuprum meaning Cyprus Zinc, Zn, (1400) German: Zink Gallium, Ga, (1875) Latin: Gallia meaning France Germanium, Ge, (1886) Latin: Germania meaning German Arsenic, As, (1280) Greek: Arsenikon meaning Yellow Orpiment Z 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 Element, symbol, date of discovery Origin of name Selenium, Se, (1817) Greek: Selene meaning Moon Bromine, Br, (1826) Greek: Bromos meaning Stench Krypton, Kr, (1898) Greek: Kryptos meaning Hidden Rubidium, Rb, (1861) Latin: Rubidius meaning Deepest Red Strontium, Sr, (1790) English: Strontian in Scotland Yttrium, Y, (1794) The town of Ytterby in Sweden Zirconium, Zr, (1789) Arabic: Zargun meaning Gold Colour Niobium, Nb, (1801) Greek: Niobe, a daughter of Tantalus: Also called Columbium in USA Molybdenum, Mo, (1781) Greek: Molybdos meaning Lead Technetium, Tc, (1937) Greek: Technikos meaning Artificial Ruthenium, Ru, (1808) Latin: Ruthenia meaning Russia Rhodium, Rh, (1803) Greek: Rhodon meaning Rose Palladium, Pd, (1803) The asteroid Pallas Silver, Ag, (Old) Saxon: Siolfur meaning Silver: The symbol comes from the Latin Argentum Cadmium, Cd, (1817) Latin: Cadmia meaning Calomine Indium, In, (1863) Indigo Tin, Sn, (Old) Saxon: Tin: The symbol comes from the Latin Stannum Antimony, Sb, (Old) Greek: Anti+Monos meaning not alone. The symbol is from Latin Stibium Tellurium, Te, (1783) Latin: Tellus meaning Earth Iodine, I, (1811) Greek: Iodes meaning Violet Xenon, Xe, (1898) Greek: Xenos meaning Stranger Caesium, Cs, (1860) Latin: Caesius meaning Sky Blue Barium, Ba, (1808) Greek: Barys meaning Heavy Lanthanum, La, (1839) Greek: Lanthanein meaning To Lie Hidden Cerium, Ce, (1803) Ceres, an asteroid discovered in 1801 Praseodymium, Pr, (1885) Greek: Prasios Didymos meaning Green Twin Neodymium, Nd, (1885) Greek: Neos Didymos meaning New Twin Promethium, Pm, (1945) Greek: Prometheus Samarium, Sm, (1879) The mineral Samarskite Europium, Eu, (1901) Europe Gadolinium, Gd, (1880) J. Gadolin, a Finnish chemist Terbium, Tb, (1843) The town of Ytterby in Sweden Dysprosium, Dy, (1886) Greek: Dysprositos meaning Hard To Obtain Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Z 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 Element, symbol, date of discovery Origin of name Latin: Holmia meaning StockHolmium, Ho, (1878) holm Erbium, Er, (1842) The town of Ytterby in Sweden Thule, meaning Ancient Thulium, Tm, (1879) Scandinavia: The Uttermost North Ytterbium, Yb, (1878) The town of Ytterby in Sweden Lutetium, Lu, (1907) Latin: Lutetia meaning Paris Latin: Hafnia meaning CopenHafnium, Hf, (1923) hagen Tantalum, Ta, (1802) Greek: Tantalos, the father of Niobe Tungsten, W, (1783) Swedish: Tung Sten meaning Heavy Stone: The symbol comes from the alternative name Wolfram Rhenium, Re, (1925) Latin: Rhenus meaning Rhine Osmium, Os, (1803) Greek: Osme meaning Smell Iridium, Ir, (1803) Latin: Iris meaning Rainbow Spanish: Platina meaning Platinum, Pt, (Old) Silver Saxon: Gold Gold, Au, (Old) Latin: The planet Mercury: The Mercury, Hg, (Old) symbol comes from the Latin Hydragyrum meaning Liquid Silver Thallium, Tl, (1861) Greek: Thallos meaning Green Twig Lead, Pb, (Old) Saxon: Lead: The symbol comes from the Latin Plumbum Z 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 Element, symbol, date of discovery Origin of name German: Bisemutem Bismuth, Bi, (1450) Poland Polonium, Po, (1898) Astatine, At, (1940) Greek: Astatos meaning unstable Radon, Rn, (1900) Radium France Francium, Fr, (1939) Radium, Ra, (1898) Latin: Radius meaning Ray Actinium, Ac, (1899) Greek: aktinos meaning Ray Thor The Scandinavian god of Thorium, Th, (1815) war Protractinium, Pa, (1917) Greek: Protos meaning First Uranium, U, (1789) The planet Uranus Neptunium, Np, (1940) The planet Neptune The planet Pluto Plutonium, Pu, (1940) English: America Americium, Am, (1944) Curium, Cm, (1944) Pierre and Marie Curie Berkelium, Bk, (1949) English: Berkeley Californium, Cf, (1950) English: California Albert Einstein Einsteinium, Es, (1952) Enrico Fermi Fermium, Fm, (1952) Mendelevium, Md, (1955) Dmitri Mendeleyev Alfred Nobel Nobelium, No, (1958) Ernest O. Lawrence Lawrencium, Lr, (1961) Rutherfordium, Rf, (1964) Ernest Rutherford Dubnium, Db, (1967) The town of Dubna, home to a centre for nuclear research Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 2.3 Photon energies, frequencies, and wavelengths. Frequency Wavelength (Hz) (m) Energy (eV) 106 107 108 109 4.14´10–9 Radio broadcasts 4.14´10–8 4.14´10–7 Television broadcasts 4.14´10–6 A gigahertz: microwave 3´102 3´101 3 3´10–1 1010 1011 1012 3´10–2 3´10–3 3´10–4 4.14´10–5 4.14´10–4 4.14´10–3 6.6 ´1012 4.55 ´10–4 2.5´10–2 1013 4 ´1014 3´10–5 7.5 ´10–7 4.14´10–2 1.654 1015 3 ´ 10–7 4.14 1016 1017 1018 1019 1020 3´10–8 3´10–9 3´10–10 3´10–11 3´10–12 4.14´101 4.14´102 4.14´103 4.14´104 4.14´105 1021 1022 1023 3´10–13 3´10–14 3´10–15 4.14´106 4.14´107 4.14´108 Comment ovens and mobile phones Infra-red Infra-red A terahertz: Infra-red: Typical frequency of atomic vibration Infra-red: corresponds to processes occurring at around room temperature (290K) Infra-red Red light: Corresponds to processes involving electrons in the outer (valence) shells of atoms Blue light: corresponds to processes involving electrons in the outer (valence) shells of atoms Ultra-violet light Ultra-violet light Ultra-violet light X-rays X-rays: corresponds to processes involving electrons in the inner shells of atoms X-rays X-rays Gamma rays: Corresponds to processes that occur within nuclei Extracted from Understanding the properties of matter by Michael de Podesta. For more details see www.physicsofmatter.com Table 3.1 The SI base units. Notice that, with the exception of the kilogram, the definitions are in terms of physical phenomena and not defining artefacts. Although the definitions seem obscure, the language is carefully chosen in order to make accurate realisations of the standards feasible. The copyright of this table belongs to the National Physical Laboratory. It has been reproduced with permission from with the National Physical Laboratory. It may be used freely for educational purposes, but its source (NPL) must be acknowledged. Quantity: Unit (abbreviation) Time: second (s) Definition The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium133 atom. Length: metre (m) The metre is the length of the path travelled by light in vacuum during a time interval 1/299,792,458 of a second. Note: This defines 299,792,458 ms–1 as the exact speed of light in a vacuum. Mass: kilogram (kg) Electric Current: ampere (A) The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram Thermodynamic temperature: kelvin (K) Amount of substance: mole (mol) The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of pure water. Luminous Intensity: candela (cd) The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation 540 ´ 101 2 hertz and that has a radiant intensity of 1/683 watt per steradian The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 ´ 10–7 newton, per metre of length. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. Table 3.2 SI supplementary units. The copyright of this table belongs to the National Physical Laboratory. It has been reproduced with permission from with the National Physical Laboratory. It may be used freely for educational purposes, but its source (NPL) must be acknowledged. Quantity plane angle solid angle Name radian steradian Symbol rad sr Expression in terms of SI base units m m–1 =1 m2 m–2 =1 Extracted from Understanding the properties of matter by Michael de Podesta. For more details see www.physicsofmatter.com Table 3.3 SI derived units with special names. The name of the units are all written with lower case letters (with the exception of degree Celsius), but that the symbols for the units have upper case letters: be careful to distinguish between seimens (S) and seconds (s). The symbol for the ohm, ½, is the greek letter ÔWÕ, called omega. The copyright of this table belongs to the National Physical Laboratory. It has been reproduced with permission from with the National Physical Laboratory. It may be used freely for educational purposes, but its source (NPL) must be acknowledged. Expression in terms of other units Expression in terms of SI base units Hz N Pa N m–2 s–1 m kg s–2 m–1 kg s–2 joule J Nm m2 kg s–2 watt W J s–1 m2 kg s–3 coulomb C volt V W A–1 m2 kg s–3 A–1 farad ohm siemens weber tesla henry degree celsius lumen lux F W S Wb T H °C lm lx C V–1 V A–1 A V–1 Vs Wb m–2 Wb A–1 m2 kg –1 s4 A–1 m2 kg s–3 A2 m2 kg –1 s3 A–1 m2 kg s–2 A–1 kg s–2 A–1 m2 kg s–2 A–2 K cd sr m–2 cd sr Quantity Name Symbol frequency force pressure stress energy work quantity of heat power radiant flux electric charge quantity of electricity electrical potential potential difference electromotive force capacitance electric resistance electric conductance magnetic flux magnetic flux density inductance Celsius temperature luminous flux illuminance hertz newton pascal sA lm m–2 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.1 The density of various gases at STP in units of kg mÐ3. The lines in the table separate gases of monatomic, diatomic and polyatomic molecules. A (u) Density (kg m–3) Helium, He Neon, Ne Argon, Ar Krypton, Kr Xenon, Xe Hydrogen, H2 Nitrogen, N2 Oxygen, O2 Chlorine, Cl2 4.0030 20.180 39.948 83.800 131.29 2.0160 28.014 31.998 70.906 0.1786 0.9003 1.782 3.739 5.858 0.08995 1.250 1.428 3.164 Methane, CH4 Ethane, C2H6 Propane, C3H8 16.043 30.070 44.097 0.7158 1.342 1.968 Gas Table 5.2 The major components of dry atmospheric air. Typically water vapour is also present at a level of roughly 0.5%. Gas Nitrogen, N2 Oxygen, O2 Argon, Ar Carbon dioxide, CO2 Molecular mass % by volume 28.01 32.00 39.95 44.00 78.09 20.95 0.93 0.03 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.3 The molar volume of various gases at STP in units of 10Ð3 m3. The lines in the table separate gases of monatomic, diatomic and polyatomic molecules. Molar density (m–3) Mass of 1 mol ´ 10–3 kg) (´ Molar volume ´ 10–3 m3) (´ Helium, He Neon, Ne Argon, Ar Krypton, Kr Xenon, Xe Hydrogen, H2 Nitrogen, N2 Oxygen, O2 Chlorine, Cl2 44.6158 44.6152 44.6162 44.6168 44.6174 44.6160 44.6168 44.6162 44.6172 4.0030 20.180 39.948 83.800 131.29 2.0160 28.014 31.998 70.906 22.4136 22.4139 22.4134 22.4131 22.4128 22.4135 22.4131 22.4134 22.4129 Methane, CH4 Ethane, C2H6 Propane, C3H8 44.6170 44.6178 44.6182 16.043 30.070 44.097 22.4130 22.4126 22.4124 Gas Table 5.4 Values of the expansivity coefficients b V and b P for gases whose initial pressure is 0.1333 MPa at 0Ê¡C, valid in the temperature range 0Ê¡C to 100Ê¡C. The pressure 0.1333 MPa is a little greater than normal atmospheric pressure. Gas bV (°C–1) bP (°C–1) Helium, He Hydrogen, H2 Nitrogen, N2 Air Neon, Ne 3.6580 ´ 10 3.6588 ´ 10–3 3.6735 ´ 10–3 3.6728 ´ 10–3 3.6600 ´ 10–3 –3 3.6605 ´ 10–3 3.6620 ´ 10–3 3.6744 ´ 10–3 3.6744 ´ 10–3 3.6617 ´ 10–3 Table 5.5 Comparison of experimental and theoretical expansivities of gases. See also Table 5.4. Gas bV (°C–1) Helium, He Hydrogen, H2 Nitrogen, N2 Air Neon, Ne 3.6580 ´ 10–3 3.6588 ´ 10–3 3.6735 ´ 10–3 3.6728 ´ 10–3 3.6600 ´ 10–3 % difference between theory and experiment – 0.082 – 0.060 + 0.342 + 0.323 – 0.027 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.6 The molar heat capacities at constant pressure CP(JÊKÐ1ÊmolÐ1) for the monatomic noble gases. These data are graphed in Figure 5.3. · The shaded figures correspond to data taken in the liquid or solid phase. For each gas the boiling temperature and melting temperature are separated by less than 5ÊK. · The data between the two double lines is from a separate source from the rest of the table. Notice that the extra measurement resolution still shows agreement between the heat capacities of the different gases. T(K) He Ne Ar Kr Xe 50 — — 24.8 25.1 25.1 100 — — 20.8 31.6 28.2 150 — — 20.8 20.8 33.6 200 — — 20.8 20.8 20.8 298.15 20.786 20.786 20.786 20.786 20.786 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 20.8 400 600 800 1000 1500 2000 2500 20.8 20.8 20.8 20.8 20.8 20.8 20.8 Table 5.7 The molar heat capacities at constant pressure CP(JÊKÐ1ÊmolÐ1) for some diatomic gases. These data are graphed in Figure 5.4. · The shaded figures correspond to data taken in the liquid or solid phase. T(K) 02 N2 Cl2 Br2 I2 50 — H2 46.1 41.5 — F2 29.2 33.3 35.8 100 150 200 — — — 29.1 29.1 29.1 29.1 29.1 29.1 — — — 42.3 51.0 54.2 43.6 49.2 53.8 45.6 49.6 51.5 400 29.2 30.1 29.2 33.0 35.3 36.7 80.3 600 800 1000 1500 2000 2500 29.3 29.6 30.2 32.3 34.3 36.0 32.1 33.7 34.9 36.6 37.8 38.9 30.1 31.4 32.7 34.9 36.0 36.0 35.2 36.3 37.0 37.9 38.4 38.8 36.6 37.2 37.5 38.0 38.3 38.6 37.3 37.5 37.7 38.0 38.2 38.5 37.6 37.8 37.9 38.2 38.5 38.8 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.8 The ratio of the principal heat capacities (gÊ=ÊCPÊ/CV) of some gases. The shaded results correspond to a pressure of 200 atmospheres (20 MPa). The notes below each section of the table summarise the results for that class of gases. There appears to be a trend towards a reduction in g as the temperature is increased. Where no temperature shown, the temperature of the measurement is not known but is probably either 0 ¡C or close to 20Ê¡C. T(°C) T(K) g Monatomic gases He 0.0 273.20 1.630 Ar 0.0 273.20 1.667 Ne 19.0 292.20 1.642 Kr 19.0 292.20 1.689 Xe 19.0 292.20 1.666 Hg 310.0 583.20 1.666 All the above results are close to 1.66 Diatomic gases H2 10.0 283.20 1.407 N2 20.0 293.20 1.401 O2 10.0 283.20 1.400 CO 1800.0 2073.2 1.297 NO — — 1.394 Most of the above results are close to 1.4 C: Air Air -79.3 193.90 1.405 Air 10.0 283.20 1.401 Air 500.0 773.20 1.357 Air 900.0 1173.2 1.320 Air 0.0 273.20 1.828 Air -79.3 193.90 2.333 Most of the above results are close to 1.4 except for those shaded. Gas Gas T(°C) T(K) Triatomic gases O3 — — H20 100.0 373.20 10.0 CO2 283.20 CO2 300.0 573.20 CO2 500.0 773.20 NH3 — — N20 — — H2S — — CS2 — — SO2 20.0 293.20 SO2 500.0 773.20 All the above results are close to 1.3 Polyatomic gases CH4 — — C2H6 — — C3H8 — — C2H2 — — C2H4 — — C6H6 20.0 293.20 C6H6 99.7 372.90 CHCl3 30.0 303.20 CHCl3 99.8 373.00 CCl4 — — The above results are between 1.1 and 1.4 g 1.290 1.334 1.300 1.220 1.200 1.336 1.324 1.340 1.239 1.260 1.200 1.313 1.220 1.130 1.260 1.264 1.400 1.105 1.110 1.150 1.130 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.9 The number of degrees of freedom p for the molecules of a variety of gases predicted from the measured value of g according to Equation 5.48. Values are plotted only for those gases included in Table 5.8. Gas g A: Some monatomic gases He 1.630 Ar 1.667 Ne 1.642 Kr 1.689 Xe 1.666 Hg 1.666 B: Some diatomic gases H2 1.407 N2 1.401 O2 1.400 CO 1.297 NO 1.394 C: Air Air Air Air Air Air Air 1.405 1.401 1.357 1.320 1.828 2.333 T(K) p 273.20 273.20 292.20 292.20 292.20 583.20 3.17 3.00 3.12 2.90 3.00 3.00 283.20 293.20 283.20 2073.2 — 4.91 4.99 5.00 6.73 5.08 193.90 283.20 773.20 1173.2 273.20 193.90 4.94 4.99 5.60 6.25 2.42 1.50 Gas g D: Some triatomic gases 1.290 O3 H20 1.334 CO2 1.300 1.220 CO2 CO2 1.200 NH3 1.336 N20 1.324 H2S 1.340 CS2 1.239 SO2 1.260 SO2 1.200 E: Some polyatomic gases CH4 1.313 C2H6 1.220 C3H8 1.130 C2H2 1.260 C2H4 1.264 C6H6 1.400 C6H6 1.105 CHCl3 1.110 CHCl3 1.150 CCl4 1.130 T(K) p 373.20 283.20 573.20 773.20 — — — — 293.20 773.20 6.90 5.99 6.67 9.09 10.00 5.95 6.17 5.88 8.37 7.69 10.00 — — — — — 293.20 372.90 303.20 373.00 — 6.39 9.09 15.4 7.69 7.58 5.00 19.0 18.2 13.3 15.4 — Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.11 Measured values of the thermal conductivities of some gases. The units are 10Ð2 WÊmÐ1ÊKÐ1. For example, the thermal conductivity of argon at 273.2ÊK is 1.63Ê´Ê10Ð2 WÊmÐ1ÊKÐ1. Gas Temperature (K) 73.2 173.2 273.2 373.2 1273 Monatomic gases Helium, He Neon, Ne Argon, Ar Krypton, Kr Xenon, Xe Radon, Ra 5.95 10.45 14.22 17.77 41.90 1.74 3.37 4.65 5.66 12.80 — 1.09 1.63 2.12 5.00 — 0.57 0.87 1.15 2.90 — 0.34 0.52 0.70 1.90 — — 0.33 0.45 — Diatomic gases Hydrogen, H2 5.09 11.24 16.82 21.18 Fluorine, Fl2 — 1.56 2.54 3.47 Chlorine, Cl2 — — 0.79 1.15 Bromine, Br2 — — 0.40 0.60 Nitrogen, N2 — 1.59 2.40 3.09 Oxygen, O2 — 1.59 2.45 3.23 Carbon monoxide, CO — 1.51 2.32 3.04 Air, N2/O2 — 1.58 2.41 3.17 — — — — 7.40 8.60 — 7.60 Polyatomic gases Ammonia, NH4 Carbon dioxide, CO2 Ethane, C2H6 Ethene, C2H4 Methane, CH4 Sulpur dioxide, SO2 Water/Steam, H20 — 7.90 — — — — — — — — — — — — — — 1.80 1.40 1.88 — — 2.18 1.45 — — 3.02 0.77 1.58 3.38 2.23 — — — — 2.35 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.12 Calculated and experimental values for k for argon at various temperatures. Also shown is the inferred value(a) for the molecular diameter. T (K) Data (W m–1 K–1) Prediction (W m–1 K–1) Ratio a (nm) 173.2 1.09 ´ 10–2 5.23 ´ 10–3 2.08 0.21 273.2 373.2 1.63 ´ 10 2.12 ´ 10–2 6.57 ´ 10 7.68 ´ 10–3 2.48 2.76 0.19 0.18 1273 5.00 ´ 10–2 14.19 ´ 10–3 3.52 0.16 –2 –3 Table 5.13 Results from an analysis of the thermal conductivity data assuming the data has the form k = ATÊÊx. The significance of a is discussed in the text. Gas Helium, He Neon, Ne Argon, Ar Krypton, Kr Xenon, Xe Radon, Ra A 30.91 ´ 10 – 4 9.14 ´ 10 – 4 2.34 ´ 10 – 4 0.93 ´ 10 – 4 0.42 ´ 10 – 4 0.12 ´ 10 –4 x a (nm) 0.685 0.695 0.108 0.198 0.754 0.806 0.391 0.620 0.857 0.994 0.923 1.73 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.14 The speed of sound in a selection of gases listed in order of increasing molecular mass M in atomic mass units u. The shaded entries in the table are gases that have a ÔpartnerÕ gas in the table with the same molecular mass. See the text for more details. csound Gas M T(K) (ms–1 ) Hydrogen, H2 Helium, He Deuterium, D2 Methane, CH4 Ammonia, NH3 Water (steam), H2O Water (steam), H2O Fluorine, F2 Heavy Water (steam), D2O Neon, Ne Acetylene, C2H2 Nitrogen, N2 Carbon monoxide, CO Ethylene, C2H4 2.0 4.0 4.0 16.0 18.0 18.0 18.0 19.0 20.0 20.2 26.0 28.0 28.0 28.0 273.2 273.2 273.2 273.2 273.2 373.2 407.2 373.2 373.2 273.2 273.2 273.2 273.2 273.2 1286 971.9 890 430 415 473 494 332 451 434 329 337 337 318 Ethane, C2H6 Ethane, C2H6 Nitric oxide, NO Nitric oxide, NO 30.0 30.0 30.0 30.0 283.2 304.2 283.2 289.2 308 316 324 334 32.0 32.0 33.1 36.5 40.0 44.0 44.0 44.0 46.0 64.0 70.9 76.0 78.0 79.9 80.9 83.8 84.0 127.9 131.3 146.0 153.8 263.8 303.2 370.2 273.2 273.2 273.2 298.2 273.2 273.2 326.2 273.2 293.2 273.2 273.2 331.2 273.2 273.2 303.2 273.2 273.2 284.2 370.2 453.2 332 335 310 296 307.8 268 238 259 258 211 219 192 177 149 200 213 181 157 170 133 145 138 Oxygen, O2 Methanol, CH3OH Hydrogen sulphide, H2S Hydrogen chloride, HCl Argon, Ar Nitrous oxide, N2O Propane, C3H8 Carbon dioxide, CO2 Ethanol, C2H5OH Sulphur dioxide, SO2 Chlorine, Cl2 Carbon disulphide, CS2 Benzene, C6H6 Bromine, Br 2 Hydrogen bromide, HBr Krypton, Kr Cyclohexane, C6H12 Hydrogen iodide, HI Xenon, Xe Sulphur hexafluoride, SF6 Carbon tetrachloride, CCl4 Iodine, I2 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.15 Details of gases whose molecules have relative molecular mass of 4 and 28. The table enables a detailed comparison of theoretical expectations and experimental results for the dependence of the speed of sound upon molecular complexity. Gas He D2 N2 CO CH2CH2 M Number of atoms per molecule Expected g T(K) 4.0 4.0 28 28 28 1 2 2 2 6 1.667 (p=3) 1.400 (p=5) 1.400 (p=5) 1.400 (p=5) 1.2 (p=10?) 273.2 273.2 273.2 273.2 273.2 Csound (theoretical) Ö(ggRT/M) 972.8 891.5 336.9 336.9 »312 Csound (experimental) Table 5.14 971.9 890.0 337.0 337.0 318.0 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.16 The relative dielectric permittivity e of various gases at atmospheric pressure (1.013Ê´Ê105 Pa). For pressures below atmospheric pressure e varies linearly with pressure. The relative permittivity of vacuum is exactly 1, and all the gases in the table have values of e within 1% of unity. The table shows the value of 104Ê(eÊÐÊ1), which clearly shows the variation between gases. The table also shows the relative molecular mass of the molecules of the gas. Different experimenters find different values of e and the data for 104Ê(e Ð 1) should all be treated as accurate to only about 10%. The entry for ethanol has two alternative values to indicate two particularly divergent values for 104Ê(e Ð 1). For other entries I have taken averages of tabulated results, or ignored entries in tables that were clearly in error. The data refer to values obtained with electric fields oscillating at radio frequencies, Å 106 Hz. The shaded entries in the table, i.e. helium, hydrogen, argon, oxygen, nitrogen, and air, are typical results for eÊvalid from DC up to optical frequencies Å 1015 Hz. The variation over that range is within ±2 of the least significant figure in the table. Gas Monatomic gases Helium, He Neon, Ne Argon, Ar Mercury, Hg Mercury, Hg Diatomic gases Hydrogen, H2 Hydrogen, H2 Nitrogen, N2 Oxygen, O2 Air (dry, no CO2) Carbon monoxide, CO Triatomic gases Carbon dioxide, CO2 Carbon dioxide, CO2 Carbon dioxide, CO2 Nitrous oxide, N2O Water (steam) H2O Polyatomic gases Ethane, C2H6 Benzene, C6H6 Methanol, CH3OH Ethanol, C2H5OH Ammonia, NH3 Ammonia, NH3 M T (°C ) 104(e – 1) 4.0 20.2 40.0 200.6 200.6 20 0 20 180 180 0.65 1.3 5.16 7.4 7.4 2.0 2.0 28.0 32.0 28.8 28.0 0 20 20 20 20 23 2.72 2.54 5.47 4.94 5.36 6.92 44.0 44.0 44.0 44.0 18.0 0 20 100 25 100 9.88 9.22 7.23 11 60 30.0 65.0 32.0 44.0 18.0 18.0 0 100 100 100 0 100 15 32.7 57 61 or 78 8.34 4.87 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.18 The refractive index of various gases as 106(nlightÐ1) together with the molecular weight of the molecules of the gas. The data refer to gases at STP (PÊ=Ê0.1013 MPa: TÊ=Ê0Ê¡C). The refractive index is that appropriate to the bright yellow ÔDÕ lines in the emission spectrum of sodium vapour and varies slightly with frequency. Gas Hydrogen, H2 Helium, He Methane, CH4 Water vapour, H2O Ammonia, NH4 Neon, Ne Nitrogen, N2 Carbon monoxide, CO Air Nitric oxide, NO Oxygen, O2 Methanol, CH3OH Hydrogen sulphide, H2S Hydrogen chloride, HCl Fluorine, F2 Argon, Ar Nitrous oxide, N2O Carbon dioxide, CO2 Ethanol, C2H5OH Sulphur dioxide, SO2 Chlorine, Cl2 Carbon disulphide, CS2 Benzene, C6H6 Hydrogen bromide, HBr Krypton, Kr Hydrogen iodide, HI Xenon, Xe Bromine, Br2 M 2 4 18 18 18 20 28 28 29 30 32 32 34 36 38 40 44 44 46 64 71 76 78 81 84 128 131 160 (nlight–1) ´ 106 132 36 444 254 376 67 297 338 293 297 271 586 633 447 195 281 516 451 878 686 773 481 1762 570 427 906 702 1132 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 5.19 Comparison of the experimental values of the refractive index of gases with the prediction of their refractive index based on Equation 2.17. Before comparing the data, the dielectric constant data have been corrected to STP using factors discussed in ¤5.6.2. The first three entries in the table are for non-polar gases and the last two are for polar gases. Notice the good agreement between theory and experiment for the non-polar gases, and the massive disagreement for water vapour. Gas Non-polar gases He Ne Ar Polar gases NH3 H2O 104(e – 1) Prediction Experiment (STP) 10 ( e – 1) 106(nlight – 1) T Correction factor 0.65 1.3 5.16 20 0 20 293/273 1 293/273 0.70 1.3 5.54 35 65 277 36 67 281 8.34 60 0 100 1 (293/273)2 8.34 69.1 416 3449 376 254 10 (e – 1) 4 6 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.1 The approximate values of the density of some solids. Solid Metals Aluminium/Dural Phosphor–bronze Brass Gold (22 carat) Gold (9 carat) Mild steel Stainless steel Wrought iron Invar Platinum/Iridium Wood Balsa Pine Oak Beech Teak Ebony Natural materials Amber Beeswax Granite Ice Coal Mica r(kg m–3) 2700–2800 8900 8400–8500 17500 11300 7900 7700–7800 7800 8000 21500 200 500 700 750 850 1200 1100 950 2700 920 1.4–1.6 2800 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.2 The density of the elements (kgÊmÐ3). Also shown is the atomic number Z and the atomic weight A in units of the atomic mass unit u = 1.66Ê´Ê10Ð27Êkg. For example, the density of magnesium, whose atoms each contain 12 protons, is 1.738Ê´Ê103 kgÊmÐ3. The mass of an atom of magnesium is 24.31Ê´Ê1.66Ê´Ê10Ð27Êkg. The densities of elements that are normally gaseous at room temperature are evaluated at a temperature just below their freezing point at atmospheric pressure. For helium, which does not solidify at atmospheric pressure at any temperature, the density is evaluated at 4.2ÊK and 25 atmospheres (25Ê´105ÊPa) pressure which is sufficient to cause solidification. Z 1 2 3 4 5 6 6 7 8 9 10 Element and symbol Hydrogen, H Helium, He Lithium , Li Beryllium, Be Boron, B Carbon (graphite), C Carbon (diamond), C Nitrogen, N Oxygen, O Fluorine, F Neon, Ne A 1.008 4.003 6.941 9.012 10.81 12.01 12.01 14.01 16.00 19.00 20.18 Density 89 120 533 1846 2466 2266 3513 1035 1460 1140 1442 Z Element and symbol A Density 51 52 53 54 55 56 57 58 59 60 Antimony, Sb Tellurium, Te Iodine, I Xenon, Xe Caesium, Cs Barium, Ba Lanthanum, La Cerium, Ce Praseodymium, Pr Neodymium, Ne 121.7 127.6 126.9 131.3 132.9 137.3 138.9 140.1 140.9 144.2 6692 6247 4953 3560 1900 3594 6174 6711 6779 7000 11 12 13 14 15 16 17 18 19 20 Sodium, Na Magnesium, Mg Aluminium, Al Silicon, Si Phosphorus, P Sulphur, S Chlorine, Cl Argon, Ar Potassium, K Calcium, Ca 22.99 24.31 26.98 28.09 30.97 32.06 35.45 39.95 39.10 40.08 966 1738 2698 2329 1820 2086 2030 1656 862 1530 61 62 63 64 65 66 67 68 69 70 Promethium, Pm Samarium, Sm Europium, Eu Gadolinium, Gd Terbium, Tb Dysprosium, Dy Holmium, Ho Erbium, Er Thulium, Th Ytterbium, Yb 145.0 150.4 152.0 157.2 158.9 162.5 164.9 167.3 168.9 173.0 7220 7536 5248 7870 8267 8531 8797 9044 9325 6966 21 22 23 24 25 26 27 28 29 30 Scandium, Sc Titanium, Ti Vanadium, V Chromium, Cr Manganese, Mn Iron, Fe Cobalt, Co Nickel, Ni Copper, Cu Zinc, Zn 44.96 47.90 50.94 52.00 54.94 55.85 58.93 58.70 63.55 65.38 2992 4508 6090 7194 7473 7873 8800 8907 8933 7135 71 72 73 74 75 76 77 78 79 80 Lutetium, Lu Hafnium, Hf Tantalum, Ta Tungsten, W Rhenium, Re Osmium, Os Iridium, Ir Platinum, Pt Gold, Au Mercury, Hg 175.0 178.5 180.9 183.9 186.2 190.2 192.2 195.1 197.0 200.6 9842 13276 16670 19254 21023 22580 22550 21450 19281 13546 31 32 33 34 35 36 37 38 39 40 Gallium, Ga Germanium, Ge Arsenic, As Selenium, Se Bromine, Br Krypton, Kr Rubidium, Rb Strontium, Sr Yttrium, Y Zirconium, Zr 69.72 72.59 74.92 78.96 79.90 83.80 85.47 87.62 88.91 91.22 5905 5323 5776 4808 3120 3000 1533 2583 4475 6507 81 82 83 84 85 86 87 88 89 90 Thallium, Th Lead, Pb Bismuth, Bi Polonium, Po Astatine, At Radon, Rn Francium, Fr Radium, Ra Actinium, Ac Thorium, Th 204.4 207.2 209.0 209.0 210.0 222.0 223.0 226.0 227.0 232.0 11871 11343 9803 9400 — 4400 — 5000 10060 11725 41 42 43 44 45 46 47 48 49 50 Niobium, Nb Molybdenum, Mo Technetium, Tc Ruthenium, Ru Rhodium, Rh Palladium, Pd Silver, Ag Cadmium, Cd Indium, In Tin, Sn 92.91 95.94 97.00 101.1 102.9 106.4 107.9 112.4 114.8 118.7 8578 10222 11496 12360 12420 11995 10500 8647 7290 7285 91 92 93 94 95 96 97 98 99 100 Protractinium, Pa Uranium, U Neptunium, Np Plutonium, Pu Americium, Am Curium, Cm Berkelium, Bk Californium, Cf Einsteinium, Es Fermium, Fm 231.0 238.0 237.0 244.0 243.0 247.0 247.0 251.0 254.0 257.0 15370 19050 20250 19840 13670 13300 14790 15100 — — Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.3 The atomic number Z, atomic mass AÊand the density r of the lanthanide elements extracted from Table 7.2. The row marked %A is the % density increase (compared with La) expected if the separation between atoms is unchanged and only the atomic mass changes. The row marked %r is the % density increase (compared with La) actually found. It shows that the 59% density increase is much greater than can be explained by the 26% increase in atomic mass alone. Z A La Ce Pr Nd 57 58 59 60 138.9 140.1 140.9 144.2 Pm 61 145 Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 62 63 64 65 66 67 68 69 70 71 150.4 152.0 157.3 158.9 162.5 164.9 167.3 168.9 173.0 175.0 %A 0 0.87 1.44 3.84 4.39 8.28 9.40 13.21 14.41 16.99 18.74 20.41 21.62 24.57 25.96 r r %r 6174 6711 6779 7000 7220 7536 5248 7870 8267 8531 8797 9044 9325 6966 9842 0 8.7 9.8 13.4 16.9 22.1 -15.0 27.4 33.9 38.2 42.5 46.5 51.4 12.8 59.4 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.4 The bulk modulus of the elements in their solid state. The temperature of the measurements varies considerably and there are discrepancies of the up to 50% in figures from different sources. Z 1 2 3 4 5 6 6 7 8 9 10 11 12 13 14 15 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Element Hydrogen Helium Lithium Beryllium Boron Carbon (diamond) Carbon (graphite) Nitrogen Oxygen Fluorine Neon Sodium Magnesium Aluminum Silicon Phosphorous (Red) Phosphorous(White) Sulphur Chlorine Argon Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel B (GPa) 0.2 0.1 11.1 100.3 178.0 542.0 33.0 1.2 1.1 6.4 44.7 75.5 98.8 10.9 4.9 17.8 2.7 3.1 17.2 43.5 105.1 161.9 160.1 118.0 169.8 191.4 186.0 Z 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 Element Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon Caesium Barium Lanthanum Cerium B (GPa) 137.8 72.0 56.9 7.7 22.0 8.3 1.9 3.5 1.9 1.2 36.6 83.3 170.2 231.0 297.0 320.8 270.4 182.0 100.7 41.6 41.1 58.2 42.0 23.0 7.7 3.6 1.6 10.3 24.3 23.9 Z 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 29 30 Element Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Copper Zinc B (GPa) 30.6 32.7 35.0 39.4 14.7 38.3 39.9 38.4 39.7 41.1 39.7 13.3 41.1 109.0 200.0 323.2 372.0 418.0 355.0 228.0 217.0 25.0 35.9 45.8 31.3 26.0 137.8 72.0 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.5 Values of the bulk modulus of the noble gas solids calculated according to Equation 7.6, compared with experimental data from Table 7.4. Ne 2.74 s (´ 10–10 m) 3.1 e (´ 10–3 eV) 75.13e/s3(´109 Pa) 1.81 Data 1.1 Ratio (theory/expt) 1.65 Substance Ar Kr 3.44 3.65 10.3 14.0 3.18 3.46 2.7 3.5 1.18 0.99 Xe 3.98 20.0 3.81 3.6 1.06 Table 7.6 Values of the bulk modulus of the alkali metals calculated according to Equation 7.11, compared with experimental data from Table 7.4. n (´ 1028 m–3) eF (´ eV) 2neF /3(´109 Pa) Data Ratio (theory/expt) Li 4.63 4.7 23.2 11.1 2.10 Na 2.53 3.14 8.5 6.4 1.33 Substance K Rb 1.33 1.08 2.05 1.78 2.9 2.06 3.1 1.9 0.94 1.08 Cs 0.86 1.53 1.41 1.6 0.88 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.7 The coefficient of linear expansivity a for various solids at temperatures around room temperature. (Kaye & Laby ). The volume expansivity of the elements is given by b = 3a as shown in Example 7.4. Elemental metals a (°C–1) Miscellaneous Aluminium (Al) Antimony (Sb) Bismuth (Bi) Cadmium (Cd) Chromium (Cr) Cobalt (Co) Copper (Cu) Gold (Au) Iridium (Ir) Iron (Fe) Lead (Pb) Magnesium (Mg) Nickel (Ni) Palladium (Pd) Platinum (Pt) Rhodium (Rh) Silver (Ag) Tantalum (Ta) Thallium (Tl) Tin (Sn) Titanium (Ti) Tungsten (W) Vanadium (V) Zinc (Zn) 23 » 11 » 13 » 30 »7 » 12 16.7 13 6.5 11.7 29 25 12.8 » 11 8.9 8.4 19 6.5 » 28 » 21 »9 4.5 »8 » 30 Brick Cement and concrete Marble Lead glass (46% pbo) Typical glass Porcelain Silica Typical wood (along grain) Typical wood (across grain) Plastics Epoxy resins Epoxy resins Polycarbonates Low-density polyethylene Medium-density polyethylene High density polyethylene Natural rubber Hard rubber Perspex Nylon Polystyrene Polyvinyl chloride (pvc) a (°C–1) 3–10 10–14 3–15 »8 » 8–10 2–6 0.4 3–5 35–60 45–65 45–65 66 40–150 80–220 200–360 220 60 50–90 80–280 34–210 70–80 Alloys Brass (68% Cu/32% Zn) Bronze (80% Cu/20% Sn) Constantan (60% Cu/40% Ni) Duralumin (95% Al/4% Cu) Magnalium (90% Al/10% Mg) Nickel steel(10% Ni/90%Fe) Nickel steel(36% Ni/64%Fe) Nickel steel(43% Ni/57%Fe) Nickel steel(58% Ni/42%Fe) Carbon steel Stainless steel (74%Fe/18%Cr/8%Ni) Phosphor-bronze Platinum–Iridium (90% Pt/10% Ir) Carbon Diamond Graphite (polycrystalline) a (°C–1) 18–19 17–18 15–17 23 » 23 13 0–1.5 7.9 11.4 »11 29 17 8.7 1.0 7.1 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.8 Expected and experimentally determined values the coefficient of linear expansivity thermal expansivity a for some alloys and their component metals. Alloy composition Aluminium alloys Duralumin (95% Al/4% Cu) Magnalium (90% Al/10% Mg) Aluminium Copper Magnesium Copper alloys Brass (68% Cu/32% Zn) Bronze (80% Cu/20% Sn) Constantan (60% Cu/40% Ni) Copper Zinc Tin Ni Platinum alloys Platinum-Iridium (90% Pt/10% Ir) Platinum Iridium Iron alloys Nickel steel (10% Ni/90%Fe) Nickel steel(36% Ni/64%Fe) Nickel steel(43% Ni/57%Fe) Nickel steel(58% Ni/42%Fe) Stainless steel (74%Fe/18% Cr/8%Ni) Iron Nickel Chromium Expected Experimental a ( °C–1 ) (see text) 22.5 ´ 10–6 23.2 ´ 10–6 — — — 23 ´ 10–6 » 23 ´ 10–6 23 ´ 10–6 16.7 ´ 10–6 »25 ´ 10–6 21 ´ 10–6 18-19 ´ 10–6 17.6 ´ 10–6 17-18 ´ 10–6 15.1 ´ 10–6 15-17 ´ 10–6 — 16.7 ´ 10–6 — »30 ´ 10–6 — »21 ´ 10–6 — 12.8 ´ 10–6 8.66 ´ 10–6 8.7 ´ 10–6 — — 8.9 ´ 10–6 6.5 ´ 10–6 11.8 ´ 10–6 13 ´ 10–6 –6 12.1 ´ 10 0–1.5 ´ 10–6 12.2 ´ 10–6 7.9 ´ 10–6 –6 12.3 ´ 10 11.4 ´ 10–6 10.9 ´ 10–6 29 ´ 10–6 — — — 11.7 ´ 10–6 12.8 ´ 10–6 7 ´ 10–6 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.9 The speed of sound in solids at 20 °C showing cL, the speed of longitudinal waves, and cT, the speed of transverse (shear waves). Elemental metals Aluminium, Al Beryllium, Be Cadmium, Cd Chromium, Cr Copper, Cu Gold, Au Iron, Fe Lead, Pb Magnesium, Mg Manganese, Mn Molybdenum, Mo Nickel, Ni Niobium, Nb Platinum, Pt Silver, Ag Tantalum, Ta Tin, Sn Titanium, Ti Tungsten, W Uranium, U Vanadium, V Zinc, Zn Zirconium, Zr Insulators Carbon (diamond) Glass (crown) Glass (heavy flint) Glass (pyrex) Quartz crystal X-cut Quartz fused Concrete Ice (-20°C) Speed of sound cL(ms–1) cT(ms–1) 6374 12890 2780 6608 4759 3240 5957 2160 5823 4600 6475 5700 5068 3260 3704 4159 3380 6130 5221 3370 6023 4187 4650 cL(ms–1) 18350 5660 5260 5640 5720 5970 4250–5250 »3840 Plastics cL(ms–1) Polyethylene Polystyrene PVC Rubber 2000 2350 2300 1600 3111 8880 — 4005 2325 1200 3224 700 3163 — 3505 3000 2092 1730 1698 2036 1594 3182 2887 1940 2774 2421 2250 cT(ms–1) 9200 3420 2960 3280 — 3765 — — cT(ms–1) 3111 1120 — 4005 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.10 The molar heat capacity at constant pressure CP of the elements at room temperature 25Ê¡C (298.15K). The shaded data are elements that are either liquids or gases at this temperature. 1 2 3 4 5 6 6 7 8 9 10 Element Hydrogen, H Helium, He Lithium , Li Beryllium, Be Boron, B Carbon (graphite), C Carbon (diamond), C Nitrogen, N Oxygen, O Fluorine, F Neon, Ne A 1.008 4.003 6.941 9.012 10.81 12.01 12.01 14.01 16.00 19.00 20.18 CP r (kg m–3) (J K mol–1) 89 28.824 120 20.786 533 24.770 1846 16.44 2466 11.09 2266 8.53 3513 6.11 1035 29.125 1460 29.355 1140 31.300 1442 20.786 Z 49 50 51 52 53 54 55 56 57 58 59 Element Indium, In Tin, Sn Antimony, Sb Tellurium, Te Iodine, I Xenon, Xe Caesium, Cs Barium, Ba Lanthanum, La Cerium, Ce Praseodymium, Pr A 114.8 118.7 121.7 127.6 126.9 131.3 132.9 137.3 138.9 140.1 140.9 r (kg m–3) 7290 7285 6692 6247 4953 3560 1900 3594 6174 6711 6779 11 12 13 14 15 16 17 18 19 20 Sodium, Na Magnesium, Mg Aluminium, Al Silicon, Si Phosphorus, P Sulphur, S Chlorine, Cl Argon, Ar Potassium, K Calcium, Ca 22.99 24.31 26.98 28.09 30.97 32.06 35.45 39.95 39.10 40.08 966 1738 2698 2329 1820 2086 2030 1656 862 1530 28.24 24.89 24.35 20.0 23.84 22.64 33.907 20.786 29.58 25.31 60 61 62 63 64 65 66 67 68 69 Neodymium, Ne Promethium, Pm Samarium, Sm Europium, Eu Gadolinium, Gd Terbium, Tb Dysprosium, Dy Holmium, Ho Erbium, Er Thulium, Th 144.2 145.0 150.4 152.0 157.2 158.9 162.5 164.9 167.3 168.9 7000 7220 7536 5248 7870 8267 8531 8797 9044 9325 27.45 26.81 29.54 27.66 37.03 28.91 28.16 27.15 28.12 27.03 21 22 23 24 25 26 27 28 29 30 Scandium, Sc Titanium, Ti Vanadium, V Chromium, Cr Manganese, Mn Iron, Fe Cobalt, Co Nickel, Ni Copper, Cu Zinc, Zn 44.96 47.90 50.94 52.00 54.94 55.85 58.93 58.70 63.55 65.38 2992 4508 6090 7194 7473 7873 8800 8907 8933 7135 25.52 25.02 24.89 23.35 26.32 25.10 24.81 26.07 24.44 25.40 70 71 72 73 74 75 76 77 78 79 Ytterbium, Yb Lutetium, Lu Hafnium, Hf Tantalum, Ta Tungsten, W Rhenium, Re Osmium, Os Iridium, Ir Platinum, Pt Gold, Au 173.0 175.0 178.5 180.9 183.9 186.2 190.2 192.2 195.1 197.0 6966 9842 13276 16670 19254 21023 22580 22550 21450 19281 26.74 26.86 25.73 25.36 24.27 25.48 24.70 25.10 25.86 25.42 31 32 33 34 35 36 37 38 39 40 Gallium, Ga Germanium, Ge Arsenic, As Selenium, Se Bromine, Br Krypton, Kr Rubidium, Rb Strontium, Sr Yttrium, Y Zirconium, Zr 69.72 72.59 74.92 78.96 79.90 83.80 85.47 87.62 88.91 91.22 5905 5323 5776 4808 3120 3000 1533 2583 4475 6507 25.86 23.35 24.64 25.36 75.69 20.79 31.06 26.40 26.53 25.36 80 81 82 83 84 85 86 87 88 89 Mercury, Hg Thallium, Th Lead, Pb Bismuth, Bi Polonium, Po Astatine, At Radon, Rn Francium, Fr Radium, Ra Actinium, Ac 200.6 204.4 207.2 209.0 209 210 222 223 226 227 13546 11871 11343 9803 9400 27.98 26.32 26.44 25.52 25.75 4400 2410 5000 10060 20.786 31.70 25.76 27.20 41 42 43 44 45 46 47 48 Niobium, Nb Molybdenum, Mo Technetium, Tc Ruthenium, Ru Rhodium, Rh Palladium, Pd Silver, Ag Cadmium, Cd 92.91 95.94 97 101.1 102.9 106.4 107.9 112.4 8578 10222 11496 12360 12420 11995 10500 8647 24.60 24.06 25.88 24.06 24.98 25.98 25.35 25.98 90 91 92 93 94 95 96 Thorium, Th Protractinium, Pa Uranium, U Neptunium, Np Plutonium, Pu Americium, Am Curium, Cm 232 231 238 237 244 243 247 11725 15370 19050 20250 19840 13670 1330 27.32 27.20 27.66 29.62 32.80 25.86 27.70 Z CP (J K mol–1) 26.74 26.99 25.23 25.73 54.438 20.786 32.17 28.07 27.11 26.94 27.20 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.11 The predicted value of the heat capacity of monatomic solids according to the Debye theory. Also tabulated is the fraction of the high temperature limiting value (3R) expected at the temperature indicated. QD T/Q 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 C(T) J K–1 mol–1 0 1.944 × 10–3 1.555 × 10–2 5.248 × 10–2 0.1244 0.2430 0.4198 0.6658 0.9903 1.399 1.891 9.195 15.158 18.604 20.588 21.795 22.572 23.098 23.469 23.739 23.942 24.098 24.221 24.318 24.398 24.463 24.517 24.562 24.601 24.634 C(T) /R 0 7.7927 × 10–5 6.2342 × 10–4 2.1040 × 10–3 4.9873 × 10–3 9.7408 × 10–3 1.6829 × 10–2 2.6693 × 10–2 3.9702 × 10–2 5.6074 × 10–2 7.5821 × 10–2 0.36863 0.60770 0.74585 0.82541 0.87380 0.90495 0.92603 0.94089 0.95173 0.95987 0.96612 0.97103 0.97495 0.97813 0.98074 0.98291 0.98474 0.98629 0.98761 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.12 The Debye temperatures qD of several elements as determined by analysis of the TÊ3 behaviour of their low-temperature heat capacity (Equation 7.61 ). Element Beryllium C(Diamond) Magnesium Aluminium Titanium Vanadium Chromium Manganese Iron Nickel Copper Z 4 6 12 13 22 23 24 25 26 28 29 QD (K) Element 1440 Zirconium 2230 Molybdenum 400 Silver 428 Cadmium 420 Tin 380 Tantalum 630 Tungsten 410 Platinum 470 Gold 450 Lead 343 Uranium Z QD (K) 40 291 42 450 47 225 48 209 50 200 73 240 74 400 78 240 79 165 82 105 92 207 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.13 The electrical resistivity of the elements which are solid at around room temperature. Take care with the exponents of values in this table which vary from entry to entry and column to column by 46 orders of magnitude. Z Element r(W W m) 1 2 3 4 5 6 7 8 9 10 Hydrogen, H Helium, He Lithium , Li Beryllium, Be Boron, B Carbon (diamond), C Nitrogen, N Oxygen, O Fluorine, F Neon, Ne — — 8.55 ´ 10–8 4 ´ 10–8 18000 1011 — — — — 11 12 13 14 15 16 17 18 19 20 Sodium, Na Magnesium, Mg Aluminium, Al Silicon, Si Phosphorus, P Sulphur, S Chlorine, Cl Argon, Ar Potassium, K Calcium, Ca 21 22 23 24 25 26 27 28 29 30 s(S m–1) Z Element r(W W m) s(S m–1) — — 1.17 ´ 107 2.5 ´ 107 5.56 ´ 105 10–11 — — — — 49 50 51 52 53 54 55 56 57 58 Indium, In Tin, Sn Antimony, Sb Tellurium, Te Iodine, I Xenon, Xe Caesium, Cs Barium, Ba Lanthanum, La Cerium, Ce 8.37 ´ 10–8 1.1 ´ 10–7 3.9 ´ 10–7 0.00436 1.37 ´ 10–7 — 2 ´ 10–7 5 ´ 10–7 5.7 ´ 10–7 7.3 ´ 10–7 1.19 ´ 107 9.1 ´ 106 2.56´ 106 229 7.30 ´ 108 — 5 ´ 106 2 ´ 106 1.75 ´ 106 1.37 ´ 106 4.2 ´ 10–8 4.38 ´ 10–8 2.66 ´ 10–8 0.001 1 ´ 10–9 2 ´ 1015 — — 6.15 ´ 10–8 3.43 ´ 10–8 2.38 ´ 107 2.28 ´ 107 3.77 ´ 107 1000 1 ´ 109 5 ´ 10–16 — — 1.63 ´ 107 2.92 ´ 107 59 60 61 62 63 64 65 66 67 68 Praseodymium, Pr Neodymium, Ne Promethium, Pm Samarium, Sm Europium, Eu Gadolinium, Gd Terbium, Tb Dysprosium, Dy Holmium, Ho Erbium, Er 6.8 ´ 10–7 6.4 ´ 10–7 5 ´ 10–7 9.4 ´ 10–7 9 ´ 10–7 1.34 ´ 10–6 1.14 ´ 10–6 5.7 ´ 10–7 8.7 ´ 10–7 8.7 ´ 10–7 1.47 ´ 106 1.56 ´ 106 2 ´ 106 1.06 ´ 106 1.11 ´ 106 7.46 ´ 105 8.77 ´ 105 1.75 ´ 106 1.15 ´ 106 1.15 ´ 106 Scandium, Sc Titanium, Ti Vanadium, V Chromium, Cr Manganese, Mn Iron, Fe Cobalt, Co Nickel, Ni Copper, Cu Zinc, Zn 6.1 ´ 10–7 4.2 ´ 10–7 2.48 ´ 10–7 1.27 ´ 10–7 1.85 ´ 10–6 9.71 ´ 10–8 6.24 ´ 10–8 6.84 ´ 10–8 1.67 ´ 10–8 5.92 ´ 10–8 1.64 ´ 106 2.38 ´ 106 4.03 ´ 106 7.87 ´ 106 5.41 ´ 105 1.03 ´ 107 1.60 ´ 107 1.46 ´ 107 5.98 ´ 107 1.69 ´ 107 69 70 71 72 73 74 75 76 77 78 Thulium, Th Ytterbium, Yb Lutetium, Lu Hafnium, Hf Tantalum, Ta Tungsten, W Rhenium, Re Osmium, Os Iridium, Ir Platinum, Pt 7.9 ´ 10–7 2.9 ´ 10–7 7.9 ´ 10–7 3.51 ´ 10–7 1.25 ´ 10–7 5.65 ´ 10–8 1.93 ´ 10–7 8.12 ´ 10–8 5.3 ´ 10–8 1.06 ´ 10–7 1.27 ´ 106 3.45 ´ 106 1.27 ´ 106 2.85 ´ 106 8.03 ´ 106 1.77 ´ 107 5.18 ´ 106 1.23 ´ 107 1.89 ´ 107 9.43 ´ 106 31 32 33 34 35 36 37 38 39 40 Gallium, Ga Germanium, Ge Arsenic, As Selenium, Se Bromine, Br Krypton, Kr Rubidium, Rb Strontium, Sr Yttrium, Y Zirconium, Zr 2.7 ´ 10–7 0.46 2.6 ´ 10–7 0.01 — — 1.25 ´ 10–7 2.3 ´ 10–7 5.7 ´ 10–7 4.21 ´ 10–7 3.70 ´ 106 2.1739 3.85 ´ 106 100 — — 8 ´ 106 4.35 ´ 106 1.75 ´ 106 2.37 ´ 106 79 80 81 82 83 84 85 86 87 88 Gold, Au Mercury, Hg Thallium, Th Lead, Pb Bismuth, Bi Polonium, Po Astatine, At Radon, Rn Francium, Fr Radium, Ra 2.35 ´ 10–8 9.41 ´ 10–7 1.8 ´ 10–7 2.07 ´ 10–7 1.068 ´ 10–6 1.4 ´ 10–6 — — 4.26 ´ 107 1.06 ´ 106 5.56 ´ 106 4.84 ´ 106 9.36 ´ 105 7.14 ´ 105 — — 41 42 43 44 45 46 47 48 Niobium, Nb Molybdenum, Mo Technetium, Tc Ruthenium, Ru Rhodium, Rh Palladium, Pd Silver, Ag Cadmium, Cd 1.25 ´ 10–7 5.2 ´ 10–8 2.26 ´ 10–7 7.6 ´ 10–8 4.51 ´ 10–8 1.08 ´ 10–7 1.59 ´ 10–8 6.83 ´ 10–8 8 ´ 106 1.92 ´ 107 4.42 ´ 106 1.32´ 107 2.22 ´ 107 9.26 ´ 106 6.29 ´ 107 1.46 ´ 107 89 90 91 92 93 94 95 Actinium, Ac Thorium, Th Protractinium, Pa Uranium, U Neptunium, Np Plutonium, Pu Americium, Am — — 1 ´ 10–6 1 ´ 106 — — 1.3 ´ 10–7 1.77 ´ 10–7 3.08 ´ 10–7 1.22 ´ 10–6 1.46 ´ 10–6 6.8 ´ 10–7 7.69 ´ 106 5.65 ´ 106 3.25 ´ 106 8.20 ´ 105 6.85 ´ 105 1.4706 ´ 106 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.14 The resistivities (½Êm) of three alloys at around room temperature is shown in centre of the three tables below. On either side of the data for the alloy, are the resistivities of the component elements. Component 1 Alloy Component 2 Cu 1.55 ´ 10–8 Cu(Zn) 6.3 ´ 10–8 Zn 5.5 ´ 10–8 Pt 9.81 ´ 10–8 Pt(10% Ir) 24.8 ´ 10–8 Ir 4.7 ´ 10–8 Pt 9.81 ´ 10–8 Pt(10% Rh) 18.7 ´ 10–8 Rh 4.3 ´ 10–8 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.15 Examples of substances which display superconducting behaviour below the temperature shown. Substance Alloy Low-temperature superconductors: elements Aluminium 1.75 Lead 7.2 Niobium 9.25 Tin 3.72 Vanadium 5.4 Low-temperature superconductors: alloys 17.1 V3Si 18.3 Nb3Sn 39 MgB2 High-temperature superconductors 93 YBa2Cu3O7-d 133 Hg1Ba2Ca2Cu3O10 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.16 The relative dielectric permittivity e of various insulators (and semiconductors) The relative permittivity of vacuum is exactly 1. All measurements refer to 20¡C, but are insensitive to small changes Å ±10¡C around this temperature. Substance Elements Silicon Germanium Ceramics Alumina Strontium titanate Strontium zirconate Glass Quartz Borosilicate glass Lead glass Plastics Polyethylene Polystyrene Polytetrafluoroethylene Polyamide e Si Ge 11.9 16.0 Al2O3 SrTiO3 SrZrO3 8.5 200 38 SiO2 SiO2 with BO SiO2 with PbO 4.5 4–5 7 PTFE Nylon 2.3 2.6 2.1 3–4 Table 7.17 Typical orders of magnitude of the resistivity of some insulating substances at around room temperature. The data correspond to values of rÊdetermined one minute after the electric field is applied. Insulator r (W W m) Alumina Al2O3 109 – 1012 QuartzSiO2 »1016 Diamond C 1010 – 1011 Boron B 1010 – 1011 Iodine I2 1013 9 Glass 10 – 1012 Insulator r (W W m) Paper PTFE Polystyrene Varnish Soil Distilled water »1010 10 – 1019 1015 - 1019 107 2 10 –104 102 –105 15 Table 7.18 Typical values (and ranges of values) of the dielectric strength of some insulating substances. Insulator Alumina, Al2O3 Sapphire, Al2O3 Quartz, SiO2 Beryllia Vm–1 10 – 35 ´ 106 17 ´ 106 25 – 40 ´ 106 10 – 14 ´ 106 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.19 Thermal conductivity k of solid elements (WÊKÐ1 mÐ1) as a function of absolute temperature. The shaded entries refer to data above the melting temperature of the element. The labels M, I and SCÊstand for metal, insulator and semiconductor respectively. The two results for phosphorus at 173.2 K correspond to different crystal structures known as ÔblackÕ and ÔyellowÕ phosphorus respectively. Element Temperature (K) and type of material 73.2 K 173.2 K 273.2 K Lithium, Li M 94 86 82 Beryllium, Be M 367 218 168 Boron, B I 72 32 19 Carbon (Graphite), C I 70–220 80–230 75–195 Carbon (Diamond), C I 1700–4900 1000–2600 700–1700 Sodium, Na M 141 142 88 Magnesium, Mg M 160 157 154 Aluminium, Al M 241 236 240 Silicon, Si SC 330 168 108 Phosphorous, P I 20 13/0.25 0.18 Sulphur, S I 0.39 0.29 0.15 Potassium, K M 105 104 53 Scandium, Sc M 15 16 Titanium, Ti M 26 22 21 Vanadium, V M 32 31 31 Chromium, Cr M 120 96.5 92 Manganese, Mn M 7 8 — Iron, Fe M 99 83.5 72 Cobalt, Co M 130 105 89 Nickel, Ni M 113 94 83 Copper, Cu M 420 403 395 Zinc, Zn M 117 117 112 Gallium, Ga M 43 41 33 Germanium, Ge SC 113 67 46.5 Selenium (c-axis), Se I 6.8 4.8 4.8 Rubidium, Rb M 59 58 32 Yttrium, Y M 16.5 17 — Zirconium, Zr M 26 23 22 Niobium, Nb M 53 53 55 Molybdenum, Mo M 145 139 135 Technetium, Tc M — 51 50 Ruthenium, Ru M 123 117 115 Rhodium, Rh M 156 151 147 Palladium, Pd M 72 72 73 Silver, Ag M 432 428 422 Cadmium, Cd M 100 97 95 Indium, In M 92 84 76 Tin, Sn M 76 68 63 Antimony, Sb M 33 25.5 22 Tellurium(c-axis), Te I 5.1 3.6 2.9 373.2 K 47 129 11 50–130 — 78 150 233 65 0.16 0.17 45 1273 K 59 93 10 35–70 — 60 — 92 32 — — 32 19 33 82 — 56 69 67 381 104 45 29 — 29 — 21 58 127 50 108 137 79 407 89 42 32 19 2.4 21 38 66 — 34 53 71 354 66 — 17.5 — 22 — 23 64 113 — 98 — 93 377 445 — 40 27 6.3 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 7.20 Thermal conductivity of a variety materials (WKÐ1 mÐ1 ). The tables refer to metallic alloys, refractory materials, i.e. those suitable for use in high temperatures without degradation, and a selection of everyday materials. 173.2K Brass (Cu70%,Zn30%) Bronze (Cu90%,Sn10%) Carbon steel Silicon steel Stainless steel Alumina (Al2O3) Beryllia (BeO) Fire brick Silica (SiO2) fused quartz Zirconia (ZrO2) Substance Brick wall Plaster Timber Balsa wood Paper Cardboard k (WK–1 m–1) »1 »0.13 » 0.15 »0.06 0.06 0.21 89 — 48 — — — — — — — 273.2K 106 53 50 25 24.5 40 300 — 1.33 — Substance Porcelain Rubber Polystyrene Glass (crown) Glass (flint) Glass (pyrex) 373.2K 128 60 48.5 28.5 25 28 213 — 1.48 1.8 k (WK–1 m–1) 1.5 »0.2 »0.1 1.1 0.85 1.1 573.2K 873.2K 973.2K 146 80 54.5 31 25.5 — — — — — — — — — — 9.2 61 1.1 2.4 2.0 — — 30.5 28 24.8 — — — — — Substance Glass wool Cotton wool Sheep’s wool Nylon Epoxy resins Cellular polystyrene 1473.2K — — — — — 5.7 22 1.3 — 2.2 k (WK–1 m–1) 0.037 0.03 0.05 0.25 »0.2 »0.04 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.1 The density of some elements at their melting temperatures in the liquid state. Also given is the ratio of the liquid density to the density of the solid at 25Ê¡C (Table 7.2). The four elements which contract on melting: (silicon, gallium, germanium and bismuth) are shaded. Z 3 5 11 12 13 14 16 19 20 22 23 25 26 28 29 30 31 32 34 37 40 41 42 44 45 46 47 48 50 51 52 55 56 72 73 74 75 76 77 78 79 81 82 83 92 Element Lithium Boron Sodium Magnesium Aluminium Silicon Sulphur Potassium Calcium Titanium Vanadium Manganese Iron Nickel Copper Zinc Gallium Germanium Selenium Rubidium Zirconium Niobium Molybdenum Ruthenium Rhodium Palladium Silver Cadmium Tin Antimony Tellurium Caesium Barium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Thallium Lead Bismuth Uranium A 6.941 10.81 22.99 24.31 26.98 28.09 32.06 39.10 40.08 47.90 50.94 54.94 55.85 58.70 63.55 65.38 69.72 72.59 78.96 85.47 91.22 92.91 95.94 101.1 102.9 106.4 107.9 112.4 118.7 121.7 127.6 132.9 137.3 178.5 180.9 183.9 186.2 190.2 192.2 195.1 197.0 204.4 207.2 209.0 238.0 Liquid density (kg m–3) 516 2080 930 1580 2400 2525 1819 824 1365 4130 5550 6430 7100 7800 8000 6600 6113.6 5530 4000 1470 5800 7830 9350 10900 10850 10700 9300 8020 6980 6490 5770 1845 3323 12000 15000 17600 18800 20100 20000 19700 17320 11290 10690 10050 17907 Ratio of liquid/solid density 0.968 0.843 0.962 0.909 0.889 1.080 0.872 0.955 0.892 0.916 0.878 0.860 0.901 0.875 0.895 0.925 1.035 1.038 0.832 0.959 0.891 0.913 0.915 0.889 0.874 0.892 0.886 0.927 0.958 0.970 0.924 0.971 0.925 0.904 0.900 0.914 0.894 0.890 0.887 0.918 0.898 0.951 0.942 1.025 0.940 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.2 The density of substances that are liquids at room temperature. The table gives the name of the substance, the chemical formula for its molecules, the relative molecular mass of each molecule, the density and the temperature of the density measurement. Only the last three entries in the table are inorganic. Liquid and chemical formula Organic liquids Methanol CH3OH Ethanol C2H5OH Propan-1-ol C3H7OH Propan-2-ol C3H7OH 2 Methyl-propan-1-ol C4H9OH 2 Methyl-propan-2-ol C4H9OH Butan-1-ol C4H9OH Butan-2-ol C4H9OH 2 Methyl-butan-1-ol C5H11O H 2 Methyl-butan-2-ol C5H11O H Pentanol C5H11O H Octanol C8H17O H Aniline C6H7N Acetone C3H6O Benzene C6H6 Inorganic liquids Carbon disulphide CS2 Carbon tetrachloride CCl4 Water (see Table 9.3) H2O MW Density (kg m–3 ) 32 46 60 60 74 74 74 74 88 791 789 804 786 817 789 810 808 816 @20°C @20°C @20°C @20°C @20°C @20°C @20°C @20°C @20°C 88 809 @20°C 88 813 @20°C 130 827 @20°C 86 58 78 1026 787 879 @15°C @25°C @20°C 76 154 18 1293 1632 1000 @0 °C @0 °C @0 °C Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.3 The density of water (H2O) and heavy water (D2O) as a function of temperature at atmospheric pressure. T (°C) 0 2 4 5 6 8 10 15 20 25 30 35 H2O 999.84 999.94 999.97 — 999.94 999.85 999.70 — 998.20 — 995.65 — D2O — — — 1105.6 — — 1106.0 1105.9 1105.3 1104.4 1103.2 1101.7 T (°C) 40 45 50 55 60 65 70 75 80 85 90 95 100 H 2O 992.22 — 988.04 — 983.20 — 977.77 — 971.79 — 965.31 — 958.36 D2O 1100.0 1097.9 1095.7 1093.3 1090.6 1087.8 1084.8 1081.6 1078.2 1074.7 1071.1 1067.4 1063.5 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.4 The bulk modulus of some liquids at the pressure and temperature shown. The pressure is shown in units of atmospheres, where one atmosphere is approximately 0.1 MPa. Liquid and formula Organic liquids Methanol, CH3OH Ethanol, C2H5OH Propan-1-ol, C3H7OH Propan-2-ol, C3H7OH Butan-1-ol, C4H9OH Butan-2-ol, C4H9OH Ether Ether Benzene, C6H6 Inorganic liquids Carbon disulphide, CS2 Carbon tetrachloride, CCl4 Water, H2O Water, H2O Water, H2O P (Atm) B (GPa) T (°C) 37 1 8 8 8 8 1 1000 8 0.97 1.32 1.04 0.983 1.13 1.03 0.689 1.56 1.10 14.7 0 17.7 17.8 17.4 17.9 0 0 17.9 8 1 1 1000 2500 1.16 1.12 2.05 2.75 3.88. 15.6 20 15 15 14.2 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.5 The coefficient of volume expansivity b for various liquids at temperatures around room temperature. The shaded column shows the value of the volume expansivity of the corresponding solid substance. N/A indicates that data is not available. MW T (°C) b (°C–1) Liquid CH3COOH CH3COCH3 CH3OH C2H5OH C 6H 7N C 6H 6 C6H5CH3 60 58 46 32 86 78 92 20 20 20 20 20 20 20 107 ´ 10–5 143 ´ 10–5 119 ´ 10–5 108 ´ 10–5 85 ´ 10–5 121 ´ 10–5 107 ´ 10–5 N/A N/A N/A N/A N/A N/A N/A Inorganic liquids Carbon Disulphide Carbon Tetrachloride Water CS2 CCl4 H 2O 76 154 18 20 20 20 119 ´ 10–5 122 ´ 10–5 21 ´ 10–5 N/A N/A N/A Metals Lithium Sodium Potassium Rubidium Copper Copper Mercury Li Na K Rb Cu Cu Hg 23 39 85.5 133 63.6 63.6 200.6 400-1125 96.5 64 - 1400 39 1084 1084 0 - 100 19 ´ 10–5 25 ´ 10–5 29 ´ 10–5 30 ´ 10–5 10 ´ 10–5 10 ´ 10–5 18.1 ´ 10–5 16.8 ´ 10–5 @ 20 °C 21.2 ´ 10–5 @ 20 °C 24.9 ´ 10–5 @ 20 °C 27.0 ´ 10–5 @ 20 °C 4.95 ´ 10–5 @ 20 °C 6.09 ´ 10–5 @ 527 °C N/A Substance Organic liquids Acetic acid Acetone Methanol Ethanol Aniline Benzene Toluene b (°C–1) Solid Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.6 The speed of sound in liquids showing cL, the speed of longitudinal waves. For the elements, where possible, the data for the solid state (taken from Table 7.12) is also included, in the shaded column, for comparison. Data for ice is also included. Substance T (°C) cL (ms–1) Organic Liquids Acetic acid Acetone Methanol Ethanol Propanol Butanol iso-Pentanol Hexanol Hexanol Heptanol 20 20 20 20 20 20 20 20 20 20 1173 1190 1121 1162 1223 1258 1255 1331 1331 1343 Water Ice 0 –20 1402 3840 Substance T (°C) cL (ms–1) Elements Hydrogen, H2 Helium, He Nitrogen, N2 Oxygen, O2 Sodium, Na Potassium, K Rubidium, Rb Caesium, Cs –258 –269 –189 –186 110 80 50 40 1242 211 745 950 2520 1869 1427 980 Substance T (°C) cL (ms–1) cL (ms–1) Elements Cadmium, Cd Copper,Cu Gallium, Ga Mercury,Hg Silver, Ag Tin, Sn Zinc, Zn 360 1350 50 20 1150 240 450 2150 3350 2740 1454 2630 2470 2700 2780 4759 3704 3380 4187 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.7 The viscosity h of various substance in their liquid state in units of mPa s as a function of the temperature in ¡C. To obtain the viscosity in units of Pa s, multiply the entries in this table by 10Ð3. For example, the viscosity of mercury at 25 ¡C is 1.528Ê´Ê10Ð3ÊPaÊs. Substance Acetic acid Acetone Benzene Carbon disulphide Methanol Ethanol Sodium Potassium Mercury Tin –100 — — — 2.132 — 98.96 — — — — –50 — — — 0.796 2.258 8.318 — — — — 0 — 0.402 — 0.445 0.797 1.873 — — 1.616 — 25 1.116 0.310 0.603 0.357 0.543 1.084 — — 1.528 — 30 1.037 0.295 0.562 0.343 0.507 0.983 — — 1.497 — Temperature (°C) 50 75 100 0.792 0.591 0.457 0.247 0.200 0.165 0.436 0.332 0.263 — — — 0.392 0.294 0.227 0.684 0.459 0.323 0.680 — — 0.458 — — 1.401 1.322 1.255 — — — 400 — — — — — — 0.286 0.224 — 1.33 600 — — — — — — 0.215 0.172 — 1.04 700 — — — — — — 0.192 0.155 — 0.950 800 — — — — — — 0.174 0.141 — 0.890 1100 — — — — — — — — — 0.780 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.9 The surface energy or surface tension of various substances in their liquid state (10Ð3 NÊmÐ1) at a given temperature in ¡C. For example, the surface tension of benzene is 28.88Ê´Ê10Ð3 NÊmÐ1. Substance Acetic acid Acetone Benzene Carbon disulphide Methanol Ethanol Water Sodium Potassium Mercury Lead Aluminium Gold Temperature (°C) g (mN m–1) 20 27.59 20 23.46 20 28.88 20 32.32 20 22.50 20 22.39 20 72.75 100 209.9 65 110.9 25 485.5 350 444.5 700 900 1100 1120 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.13 The heat capacities at constant pressure C P for a selection of substances that are liquids at around room temperature. The table records the substance name and chemical formula, the relative molecular mass of its constituent molecules, the number of atoms per molecule, and the temperature at which the measurement is made. The molar heat capacity is then recorded as in JÊKÐ1 and as a multiple of the gas constant R. Substance MW N T (°C) CP (J K–1 mol–1 ) (R ) Organic liquids Methanol Ethanol Ethanol Ethanol Propanol Acetic acid Acetone Aniline Benzene Benzene Bromoethane Chloroform Cyclohexane 1,2 Dichloroethane Dichloromethane Ethanadiol Ethyl acetate Ethyl nitrate Formamide Formic acid Nitromethane Nitroethane Toluene CH3OH C2H5OH C2H5OH C2H5OH C3H7OH C2H4O2 C3H6O C6H7N C6H6 C6H6 C2H5Br CHCl3 C6H10 C2H4Cl2 C2H2Cl2 C2H6O2 C4H8O2 C2H5O3N CH3ON CH2O2 CH3O2N C2H5O2N C7H8 32 46 46 46 60 60 58 93 78 78 109 120 82 98 96 62 82 91 45 46 61 75 92 6 9 9 9 12 8 10 14 12 12 8 5 16 8 6 10 8 11 6 5 7 10 15 12 0 20 40 18 20 20 15 10 40 20 20 20 20 20 20 20 20 20 20 20 20 18 80.64 105.3 113.4 124.7 138.0 124.3 124.7 199.9 110.8 138.1 100.8 113.8 156.5 129.3 100.0 149.8 170.1 170.3 107.6 99.0 106.0 134.2 153.6 9.7 12.7 13.6 15.0 16.6 15.0 15.0 24.0 13.3 16.6 12.1 13.7 18.8 15.6 12.0 18.0 20.5 20.5 12.9 11.9 12.7 16.1 18.5 Inorganic liquids Arsenic trifluoride Boron trichloride Bromine Carbon disulphide Hydrogen cyanide Water Heavy water Mercury Hydrazine Silicon tetrachloride Tin tetrachloride Titanium tetrachloride AsF3 BCl3 Br2 CS2 HCN H2O D2O Hg N2H4 SiCl4 SnCl4 TiCl4 132 118 160 76 27 18 20 201 32 170 261 190 4 4 2 3 3 3 3 1 6 5 5 5 20 20 20 20 20 0 0 20 20 20 20 20 126.6 106.7 75.7 75.7 70.6 75.9 84.3 28.0 98.9 145.3 165.3 145.2 15.2 12.8 9.11 9.11 8.49 9.13 10.1 3.37 11.9 17.5 19.9 17.5 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.14 Thermal conductivity of miscellaneous non-metallic liquids in units of WKÐ1 mÐ1. The data is given at two temperatures T1 and T 2, and varies roughly linearly between these two temperatures. (Figure 9.32 (a)). Liquid Acetone Aniline Benzene Methanol Ethanol N-butanol N-propanol Toluene Carbon tetrachloride Water Xenon T1 193 293 293 233 233 213 233 193 253 273 173 T2 333 323 333 353 353 353 353 333 353 223 K1 0.198 0.172 0.147 0.223 0.189 0.167 0.168 0.159 0.115 0.561 0.07 K2 0.146 0.137 0.186 0.150 0.106 0.148 0.119 0.102 0.673 0.05 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.15 Thermal conductivity (WÊKÐ1Êm Ð1) of elemental metals in their liquid state. Shaded entries refer to the solid state. The data are graphed in Figure 9.33. Liquid Lithium Sodium Potassium Rubidium Caesium Mercury Aluminium Bismuth Gallium Tin Li Na K Rb Cs Hg Al Bi Ga Sn 173 K 98 141 105 59 37 29.5 241 11 43 76 273 K 86 142 104 58 36 7.8 236 8.2 41 68 373 K 82 88 53 32 20 9.4 240 7.2 33 63 573 K 47 78 45 29 20.6 11.7 233 13 45 32 973 K 59 60 32 22 17.7 — 92 17 — 40 KL/KS(%) 57 62 51 55 56 26 39 181 80 51 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.16 Thermal conductivity (WKÐ1 mÐ1) and electrical resistivity (½Êm) of elemental metals in their liquid state. Also evaluated is the quantity rk/T known as the Lorentz number and has theoretical value of 2.45Ê´Ê10Ð8 (Wʽ KÐ2 ). Liquid 373 K k r –8 9.7 ´ 10 88 Potassium 17.5 ´ 10–8 Sodium rk /T 573 K k r 2.3 ´ 10 –8 16.8 ´ 10 78 28.2 ´ 10–8 –8 rk /T 973 K k r 2.3 ´ 10 39.2 ´ 10 60 2.4 ´ 10–8 45 2.2 ´ 10–8 66.4 ´ 10–8 32 2.2 ´ 10–8 29 2.4 ´ 10 99 ´ 10 22 2.2 ´ 10–8 2.4 ´ 10–8 53 2.5 ´ 10–8 Rubidium –8 27.5 ´ 10 32 2.4 ´ 10 48 ´ 10 Caesium 43.5 ´ 10–8 20 2.3 ´ 10–8 67 ´ 10–8 20.6 2.4 ´ 10–8 134 ´ 10–8 17.7 Mercury 103.5 ´ 10–8 2.6 ´ 10–8 128 ´ 10–8 11.7 2.6 ´ 10–8 214 ´ 10–8 — 9.4 –8 –8 rk /T –8 –8 –8 –8 — Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.17 The resistivity (´Ê10Ð8ʽÊm) of elemental metals with low melting points. The shaded data above the line in the table refers to the metals in the solid state and data below line refer to data in the liquid state. The last row of the table shows the ratio of the resistivities in the solid and liquid states. The figure is derived from the ratio of the last datum in the solid region to the first datum in the liquid region. T(K) 0 78.2 273.2 373.2 573.2 973.2 1473.2 rS/rL (%) Na 0 0.76 4.33 9.51 17.4 38.9 88 46 Rb Cs K 0 0 0 1.30 2.59 4.1 6.49 11.5 18.8 15.8 27.3 44.5 27.7 45.1 67.3 64.7 93 128 165 250 338 41 42 42 Hg 0 5.8 94.1 103.5 128 214 630 6 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.19 The results of calculations of the molecular polarisability of non-polar molecules based on dielectric constant data for both liquid and gaseous states. The value of on Equation 9.51 a/eoÊ=(e Ð 1)/n with n estimated by either Equation 9.49 or 9.50 as appropriate. The data for the densities of liquid hydrogen, nitrogen and oxygen are estimates based on a 10% decrease of the density of the solid. See Table 5.16 for gas data and Table 9.18 for liquid data. The gas data refer to atmospheric pressure (1.013Ê´Ê105 Pa). Notice that the inferred value of a is quite similar in liquid and gaseous states. Liquid Substance Argon Helium Hydrogen Nitrogen Oxygen 40 4 2 28 32 r (kg m–3) 1410 120 »80 »930 »1300 e–1 0.53 0.048 0.228 0.45 0.507 n a/eo ´1028 m3) (´ ´10–30) (´ 2.12 25 1.81 2.65 2.41 9.5 2.00 22.5 2.45 20.5 Gas r (kg m–3) 293 293 293 293 293 e–1 5.16 0.65 2.54 5.47 4.94 n ´1028 m3) (´ 2.50 2.50 2.50 2.50 2.50 a/eo ´10–30) (´ 21 2.6 10.2 21.9 19.8 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.20 The results of the calculations of the permanent molecular dipole moment (in CÊm) of polar molecules according to Equation 9.53. The gas data refer to atmospheric pressure (1.013Ê´Ê105 Pa). Liquid Substance Methanol Ethanol Water M 32 46 18 T (K) 298 298 293 r (kg m–3) 791 789 1000 e–1 31.6 23.3 79.4 Gas n p ´1028 m3) (´ ´10–30) (´ 1.49 15.2 1.03 15.7 3.35 16.0 T (K) 373 373 373 e–1 57 61 or 78 60 n p ´1028 m3) (´ ´10–30) (´ 1.97 6.29 1.97 6.5 or 7.4 1.97 6.45 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.18 The relative dielectric permittivity e of various insulating liquids. The relative permittivity of vacuum is exactly 1. Substance Argon, Ar Helium, He Hydrogen, H2 Nitrogen, N2 Oxygen, O2 Methanol, CH3OH Ethanol, C2H5OH Propanol, C3H7OH Butanol, C4H9OH Pentanol, C5H11OH Hexanol, C6H13OH Aniline, C6H7N Acetone, C3H6O Carbon disulphide, CS2 Water, H2O MW 40 4 2 28 32 32 46 60 74 88 102 86 58 76 18 T 82 K 4.19 K 20.4 K 70 K 80 K 25 °C 25 °C 25 °C 20 °C 25 °C 25 °C 20 °C 25 °C 20 °C 20 °C e–1 0.53 0.048 0.228 0.45 0.507 31.6 23.3 19.1 16.8 12.9 12.3 5.90 19.7 1.64 79.4 e 1.53 1.048 1.228 1.45 1.507 32.6 24.3 20.1 17.8 13.9 13.3 6.90 20.7 2.64 80.4 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.19 The results of calculations of the molecular polarisability of non-polar molecules based on dielectric constant data for both liquid and gaseous states. The value of on Equation 9.51 a/eoÊ=(e Ð 1)/n with n estimated by either Equation 9.49 or 9.50 as appropriate. The data for the densities of liquid hydrogen, nitrogen and oxygen are estimates based on a 10% decrease of the density of the solid. See Table 5.16 for gas data and Table 9.18 for liquid data. The gas data refer to atmospheric pressure (1.013Ê´Ê105 Pa). Notice that the inferred value of a is quite similar in liquid and gaseous states. Liquid Substance Argon Helium Hydrogen Nitrogen Oxygen 40 4 2 28 32 r (kg m–3) 1410 120 »80 »930 »1300 e–1 0.53 0.048 0.228 0.45 0.507 n a/eo ´1028 m3) (´ ´10–30) (´ 2.12 25 1.81 2.65 2.41 9.5 2.00 22.5 2.45 20.5 Gas r (kg m–3) 293 293 293 293 293 e–1 5.16 0.65 2.54 5.47 4.94 n ´1028 m3) (´ 2.50 2.50 2.50 2.50 2.50 a/eo ´10–30) (´ 21 2.6 10.2 21.9 19.8 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.20 The results of the calculations of the permanent molecular dipole moment (in CÊm) of polar molecules according to Equation 9.53. The gas data refer to atmospheric pressure (1.013Ê´Ê105 Pa). Liquid Substance Methanol Ethanol Water M 32 46 18 T (K) 298 298 293 r (kg m–3) 791 789 1000 e–1 31.6 23.3 79.4 Gas n p ´1028 m3) (´ ´10–30) (´ 1.49 15.2 1.03 15.7 3.35 16.0 T (K) 373 373 373 e–1 57 61 or 78 60 n p ´1028 m3) (´ ´10–30) (´ 1.97 6.29 1.97 6.5 or 7.4 1.97 6.45 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.21 The refractive index of various liquids for yellow light. Substance and chemical formula MW Water, H2O 18 Carbon tetrachloride, CCl4 152 92 Toluene, C7H8 32 Methanol, CH3OH 44 Ethanol, C2H5OH Propan-1-ol, C3H7OH 56 Propan-2-ol, C2H5OHCH2 56 Acetic acid, CH3COOH Benzene, C6H6 78 86 Aniline, C6H7N 65 Hydrogen disulphide, HS2 nlight 1.33 1.405 1.497 1.329 1.3614 1.3852 1.3742 1.3716 1.501 1.586 1.885 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 9.22 Calculation of the refractive indices of liquid water, methanol and benzene from the data on the refractive index of their vapours (Table 5.18). The predictions for n lightÐ1 are 20 to 25% below the experimental values. The method of calculation is described in Equations 9.55 to 9.61. Gas Number MW density (m–3) Substance Water Methanol Benzene H 2O CH3OH C 6H 6 18 32 78 nlight 2.689 ´ 10 1.000254 2.689 ´ 1025 1.000586 2.689 ´ 1025 1.001762 25 Molecular polarisability a (F–1m4) 1.647 ´10 3.860 ´10–40 11.61 ´ 10–40 –40 Density (kg m–3) 1000 791 879 Liquid Number Prediction density (m–3) 3.346 ´ 10 1.489 ´ 1028 6.786 ´ 1027 28 Actual nlight–1 nlight–1 0.27 0.284 0.375 0.33 0.329 0.501 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 11.1 Thermal data for the elements: the melting and boiling temperatures in kelvin, and the enthalpies of fusion (melting) and vaporisation. The data refer to standard atmospheric pressure unless otherwise stated. Two elements Ð arsenic and carbon Ð which sublime when heated at atmospheric pressure. These are discussed in ¤11.7 on the solidÊÞÊgas transition, and their the enthalpies of fusion and vaporisation are estimated from studies at high pressure. Z 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 Name Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon Sodium Magnesium Aluminium Silicon Phosphorous Sulphur Chlorine Argon Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Atomic weight 1.008 4.003 6.941 9.012 10.81 12.01 14.01 16 19 20.18 22.99 24.31 26.98 28.09 30.97 32.06 35.45 39.95 39.1 40.08 44.96 47.9 50.94 52 54.94 55.85 58.93 58.7 63.55 65.38 69.72 72.59 74.92 78.96 79.9 83.8 85.47 87.62 88.91 91.22 92.91 95.94 Density (kg m–3) 89 120 533 1846 2466 2266 1035 1460 1140 1442 966 1738 2698 2329 1820 2086 2030 1656 862 1530 2992 4508 6090 7194 7473 7873 8800 8907 8933 7135 5905 5323 5776 4808 3120 3000 1533 2583 4475 6507 8578 10222 Melting Boiling point point (K) (K) 14.01 20.28 0.95 4.216 453.7 1620 1551 3243 2365 3931 Sublimes at » 3700 63.15 77.4 54.36 90.188 53.48 85.01 24.56 27.1 371 1156.1 922 1363 933.5 2740 1683 2628 317.3 553 386 717.82 172 239.18 83.8 87.29 336.8 1047 1112 1757 1814 3104 1933 3560 2160 3650 2130 2945 1517 2235 1808 3023 1768 3143 1726 3005 1356.6 2840 692.73 1180 302.93 3676 1210.6 3103 Sublimes at 886 490 958.1 265.9 331.93 116.6 120.85 312.2 961 1042 1657 1795 3611 2125 4650 2741 5015 2890 4885 Enthalpy of fusion (kJ mol –1) 0.12 0.021 4.6 9.8 22.2 105 0.72 0.444 5.1 0.324 2.64 9.04 10.67 39.6 2.51 1.23 6.41 1.21 2.4 9.33 15.9 20.9 17.6 15.3 14.4 14.9 15.2 17.6 13 6.67 5.59 34.7 27.7 5.1 10.8 1.64 2.2 6.16 17.2 23 27.2 27.6 Enthalpy of vaporisation (kJ mol –1) 0.46 0.082 134.7 308.8 538.9 710.9 5.577 6.82 6.548 1.1736 89.04 128.7 293.72 383.3 51.9 9.62 20.403 6.53 77.53 149.95 304.8 428.9 458.6 348.78 219.7 351 382.4 371.8 304.6 115.3 256.1 334.3 31.9 26.32 30 9.05 69.2 138.91 393.3 581.6 696.6 594.1 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Z 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 Name Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon Caesium Barium Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Astatine Radon Francium Radium Actinium Atomic weight 97 101.1 102.9 106.4 107.9 112.4 114.8 118.7 121.7 127.6 126.9 131.3 132.9 137.3 138.9 140.1 140.9 144.2 145 150.4 152 157.2 158.9 162.5 164.9 167.3 168.9 173 175 178.5 180.9 183.9 186.2 190.2 192.2 195.1 197 200.6 204.4 207.2 209 209 210 222 223 226 227 Density (kg m–3) 11496 12360 12420 11995 10500 8647 7290 7285 6692 6247 4953 3560 1900 3594 6174 6711 6779 7000 7220 7536 5248 7870 8267 8531 8797 9044 9325 6966 9842 13276 16670 19254 21023 22580 22550 21450 19281 13546 11871 11343 9803 9400 — 4400 — 5000 10060 Melting point (K) 2445 2583 2239 1825 1235.1 594.1 429.32 505.12 903.9 722.7 386.7 161.3 301.6 1002 1194 1072 1204 1294 1441 1350 1095 1586 1629 1685 1747 1802 1818 1097 1936 2503 3269 3680 3453 3327 2683 2045 1337.6 234.28 576.6 600.65 544.5 527 575 202 300 973 1320 Boiling point (K) 5150 4173 4000 3413 2485 1038 2353 2543 1908 1263 457.5 166.1 951.6 1910 3730 3699 3785 3341 3000 2064 1870 3539 3396 2835 2968 3136 2220 1466 3668 5470 5698 5930 5900 5300 4403 4100 3080 629.73 1730 2013 1833 1235 610 211.4 950 1413 3470 Enthalpy of fusion (kJ mol –1) 23.81 23.7 21.55 17.2 11.3 6.11 3.27 7.2 20.9 13.5 15.27 3.1 2.09 7.66 10.04 8.87 11.3 7.113 12.6 10.9 10.5 15.5 16.3 17.2 17.2 17.2 18.4 9.2 19.2 25.5 31.4 35.2 33.1 29.3 26.4 19.7 12.7 2.331 4.31 5.121 10.48 10 23.8 2.7 — 7.15 14.2 Enthalpy of vaporisation (kJ mol –1) 585.22 567.8 495.4 393.3 255.1 99.87 226.4 290.4 67.91 50.63 41.67 12.65 65.9 150.9 399.6 313.8 332.6 283.7 — 191.6 175.7 311.7 391 293 251 292.9 247 159 428 661.1 753.1 799.1 707.1 627.6 563.6 510.5 324.4 59.15 162.1 179.4 179.1 100.8 — 19.1 — 136.8 293 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Z 90 91 92 93 94 95 Name Thorium Protactinium Uranium Neptunium Plutonium Americium Atomic weight 232 231 238 237 244 243 Density (kg m–3) 11725 15370 19050 20250 19840 13670 Melting point (K) 2023 2113 1405 913 914 1267 Boiling point (K) 5060 4300 4018 4175 3505 2880 Enthalpy of fusion (kJ mol –1) 19.2 16.7 15.5 9.46 2.8 14.4 Enthalpy of vaporisation (kJ mol –1) 543.9 481 422.6 336.6 343.5 238.5 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 11.2 Thermal data for the various substances: the melting and boiling temperatures in kelvin, and the enthalpies of fusion (melting) and vaporisation. The data refer to standard atmospheric pressure unless otherwise stated and (s) indicates that the substance sublimes rather than boils and the melting temperature is obtained under pressure. (*) indicates a large discrepancy of ± 20ÊK amongst data from different sources. Substance Acetic acid Acetone Aniline Benzene Chloroform Cyclohexane Ethyl acetate Methanol Ethanol Propan-1-ol Propan-2-ol Butan-1-ol Butan-2-ol Toluene Lithium fluoride Lithium chloride Lithium bromide Sodium chloride Sodium fluoride Sodium bromide Potassium fluoride Potassium chloride Potassium bromide Carbon dioxide Carbontetrachloride Carbon disulphide Carbon monoxide Water CH3COOH CH3COCH3 C 6H 7N C 6H 6 CHCl3 C6H10 C 4H 8O 2 CH3OH C2H5OH C3H7OH C3H7OH C4H9OH C4H9OH C 7H 8 LiF LiCl LiBr NaF NaCl NaBr KF KCl KBr CO2 CCl4 CS2 CO H 2O MW 60 58 93 78 119 82 88 32 46 60 60 74 74 92 25.9 42.39 86.9 42.0 58.4 102.9 58.1 74.6 119.0 44 154 76 28 18 Density (kg m–3) 1049 787 1026 877 — 779 — 791 789 804 786 810 808 867 2635 2068 3464 2558 2165 3203 2480 1984 2750 — 1632 1293 — 998 Melting point (K) 289.75 177.8 266.85 278.65 209.55 279.65 189.55 179.25 155.85 146.65 — 183.65 298.55 178.15 1118 878 823 1266 1074 1020 1131 1043 1007 216.55 — 162.35 74.15 273.15 Boiling point (K) 391.1 329.3 457.6 353.2 334.4 353.8 350.2 337.7 351.5 370.3 — 390.35 372.65 383.8 1949 1620(*) 1538 1968 1686 1663 1778 1273(s) 1708 194.7 — 319.6 81.7 373.15 Enthalpy of fusion (kJ mol –1) 11.535 5.691 10.555 9.951 8.800 2.630 10.481 3.177 5.021 5.195 — 9.282 6.786 6.851 — — — — — — — — — — — 4.395 — 5.994 Enthalpy of vaporisation (kJ mol –1) — — — — — — — — — — — — — — — — — — — — — — — — — — — 40.608 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these figures resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 11.3 Comparison of NAÆEe with the experimental value of the latent heat of vaporisation L. The final column shows the ratio of these two quantities NAÆEe/L. The values of ÆE e are drawn from Table 9.12. Substance Copper Silver Gold Aluminium Tin Helium Neon Argon Krypton Xenon DEe(J) NADEe L ´ 10-21 (kJ mol–1) (kJ mol–1) NADEe/L 486 292.7 300.5 0.97 403 242.7 255.06 0.95 516 310.7 324.43 0.96 447 269.2 290.8 0.92 436 262.6 290.37 0.90 0.13 0.078 0.08 0.98 3.23 1.95 1.77 1.10 10.8 6.50 6.52 0.99 17.2 10.36 9.03 1.15 24.4 14.69 12.64 1.16 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 11.4 The critical parameters of various substances discussed in Chapter 6 and Chapter 8. PC,VC and TC are the critical pressure, molar volume and temperature. ZC is the compression factor which is discussed in ¤11.5.3. The next column gives the density at the critical point, calculated from the molecular mass and V C . This may be compared with the density of the substance in the liquid state well away from TC . For the inorganic substances where the liquid density data is not available, the solid density has been used instead The final column gives the ratio of the density at the critical point to that at a temperature well below the critical point. PC Substance (MPa) Methanol, CH3OH 8.09 Ethanol, C2H5OH 6.14 Propan-1-ol , C3H7OH 5.17 5.79 Acetic acid, C2H4O2 Acetone, C3H6O 4.7 Aniline, C6H7N 5.3 Benzene, C6H6 4.9 Bromoethane, C2H5Br 6.23 Chloroform, CHCl3 5.5 Cyclohexane, C6H10 4.02 Ethyl acetate, C4H8O2 3.83 Toluene, C7H8 4.11 Carbon monoxide, CO 3.50 Carbon dioxide, CO2 7.38 Carbon disulphide, CS2 7.9 Carbon tetrachloride, 4.56 CCl4 Hydrogen, H2 1.294 Nitrogen, N2 3.39 Oxygen, O2 5.08 7.71 Chlorine, Cl2 Bromine, Br2 10.3 Helium, He 0.229 Neon, Ne 2.73 Argon, Ar 4.86 Krypton, Kr 5.50 Xenon, Xe 5.88 Radon, Rn 6.3 Water, H2O 22.12 Heavy water, D2O 21.88 VC ´10Ð6Ð1m3 (´ mol ) 118 167 219 171 213 274 254 215 240 308 286 320 93.1 94.0 173 276 TC (K) 512.6 513.9 536.8 594.5 508.1 698.9 562.2 503.8 536.4 553.4 523.2 591.8 133 304.2 552 556.4 65.5 90.1 78 124 135 58 41.7 75.2 92.3 119 Ñ 59.1 54.9 32.99 126.2 154.8 417 584 5.2 44.4 150.7 209.4 289.7 377 647.3 644.2 ZC= PCVC/R TC 0.224 0.240 0.254 0.200 0.237 0.250 0.266 0.320 0.296 0.269 0.252 0.267 0.295 0.274 0.298 0.272 Critical Density (kgÊmÐ3) 271 275 274 351 272 339 307 507 500 266 287 288 300.75 468.09 439.31 550.72 Liquid Density (kgmÐ3) 791 789 804 1049 787 1026 879 1456 1498 941.6 900.6 868.8 Ñ Ñ 1263 1604 Density Ratio 0.343 0.349 0.340 0.334 0.346 0.330 0.349 0.348 0.333 0.282 0.319 0.331 Ñ Ñ 0.348 0.343 0.309 0.291 0.308 0.276 0.287 0.307 0.309 0.292 0.292 0.291 30.534 310.77 410.26 572.58 1185.2 68.966 479.62 531.91 910.08 1100.8 Ñ 304.57 364.30 89 1035 1460 2030 3120 120 1442 1656 3000 3560 4400 1000 1100 0.343 0.300 0.281 0.282 0.380 0.575 0.333 0.321 0.303 0.309 0.243 0.224 0.305 0.331 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these figures resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 11.5 The cohesive energies Uo of the elements in units of kJ molÐ1. Uo is the energy required to separate the atoms of a solid at T = 0 K into isolated neutral atoms. Z 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Element Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon Sodium Magnesium Aluminium Silicon Phosphorous Sulphur Chlorine Argon Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Uo (kJ mol–1 ) — — 158 320 561 711 474 251 81 1.92 107 145 327 446 331 275 135 7.74 90.1 178 376 468 512 395 282 413 424 428 336 130 271 Z 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 Element Germanium Arsenic Selenium Bromine Krypton Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon Caesium Barium Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Uo (kJ mol–1 ) 372 285.3 237 118 11.2 82.2 166 422 603 730 658 661 650 554 376 284 112 243 303 265 211 107 15.9 77.6 183 431 417 357 328 — 206 Z 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 Element Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Astatine Radon Francium Radium Actinium Thorium Protactinium Uranium Uo (kJ mol–1 ) 179 400 391 294 302 317 233 154 428 621 782 859 775 788 670 564 368 65 182 196 210 144 — 18.5 — 160 410 598 — 536 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these tables resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 11.6 The equilibrium vapour pressure (Pa) of water substance above the solid or liquid surface as a function of temperature. The shaded data on the liquid corresponds to data taken on supercooled water. T (°C) –90 –80 –70 –60 –50 –40 –30 –29 –28 –27 –26 –25 –24 –23 –22 –21 –20 –19 –18 –17 –16 Solid 0.009 0.053 0.258 1.077 3.940 12.88 38.12 42.27 46.80 51.87 57.34 63.47 70.14 77.34 85.34 94.01 103.4 113.8 125.2 137.5 151.0 Liquid — — — — — — — — — — — — — — — — — — — — — T (°C) –15 –14 –13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Solid 165.5 181.5 198.7 217.6 238.0 260.0 284.2 310.2 338.3 368.7 401.8 437.4 475.8 517.4 562.4 610.6 — — — — — — — — — — — — — — — Liquid 191.50 208.03 225.50 244.57 264.98 286.58 310.18 335.26 362.06 390.86 421.80 454.74 489.81 527.55 567.83 610.6 656.9 706.0 758.1 813.6 872.5 935.2 1002 1073 1148 1228.1 1312.7 1402.6 1497.7 1598.5 1705.3 Extracted from Understanding the properties of matter by Michael de Podesta. The copyright of these figures resides with Taylor and Francis. They may be used freely for educational purposes but their source must be acknowledged. For more details see www.physicsofmatter.com Table 11.7 The melting, boiling and triple-point temperatures of various substances. The Ttr values are often known extremely accurately. The TM and TB values are typically known to within Å 10ÊmK. Substance Oxygen Nitrogen Argon Water T M (K) 54.35 63.15 83.75 273.15 T Tr (K) 54.3584 63.150 83.8058 273.16 T B (K) 90.188 77.352 87.29 373.15 UNDERSTANDING THE PROPERTIES OF MATTER: WEB CHAPTER 2 Table W2.1 Molar magnetic susceptibility of the elements at around room temperature. The data are summarised in Figure W2.3. The shading in the table corresponds to the shading in Figure and highlights elements with a large susceptibilities. Element, atomic mass (u) and denZ sity (kg m–3) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Hydrogen, H Helium, He Lithium, Li Beryllium, Be Boron, B Carbon, C Nitrogen, N Oxygen, O Fluorine, F Neon, Ne Sodium, Na Magnesium, Mg Aluminium, Al Silicon, Si Phosphorus, P Sulphur, S Chlorine, Cl Argon, A Potassium, K Calcium, Ca Scandium, Sc Titanium, Ti Vanadium, V Chromium, Cr Manganese, Mn Iron, Fe Cobalt, Co Nickel, Ni Copper, Cu Zinc, Zn Gallium, Ga Germanium, Ge Arsenic, As Selenium, Se Bromine, Br Krypton, Kr Rubidium, Rb Strontium, Sr Yttrium, Y Zirconium, Zr Niobium, Nb Molybdenum, Mo Technetium, Tc Ruthenium, Ru Rhodium, Rh Palladium, Pd Silver, Ag Cadmium, Cd Indium, In Tin, Sn W2.6 1.008 4.003 6.941 9.012 10.81 12.01 14.01 16 19 20.18 22.99 24.31 26.98 28.09 30.97 32.06 35.45 39.95 39.1 40.08 44.96 47.9 50.94 52 54.94 55.85 58.93 58.7 63.55 65.38 69.72 72.59 74.92 78.96 79.9 83.8 85.47 87.62 88.91 91.22 92.91 95.94 97 101.1 102.9 106.4 107.9 112.4 114.8 118.7 89 120 533 1846 2466 2266 1035 1460 1140 1442 966 1738 2698 2329 1820 2086 2030 1656 862 1530 2992 4508 6090 7194 7473 7873 8800 8907 8933 7135 5905 5323 5776 4808 3120 3000 1533 2583 4475 6507 8578 10222 11496 12360 12420 11995 10500 8647 7290 7285 cM (m3 mol–1) Z Element, atomic mass (u) and density (kg m–3) — — 1.78 ´ 10–10 –1.17 ´ 10–10 –8.43 ´ 10–11 –7.57 ´ 10–11 — — — –8.48 ´ 10–11 2.02 ´ 10–10 1.65 ´ 10–10 2.08 ´ 10–10 –5.06 ´ 10–11 –3.41 ´ 10–10 –1.95 ´ 10–10 — — 2.62 ´ 10–10 5.61 ´ 10–10 3.96 ´ 10–9 1.92 ´ 10–9 3.20 ´ 10–9 2.31 ´ 10–9 6.59 ´ 10–9 Ferro Ferro Ferro –6.87 ´ 10–11 –1.44 ´ 10–10 –2.72 ´ 10–10 –9.64 ´ 10–11 –6.87 ´ 10–11 –3.16 ´ 10–10 — — 2.13 ´ 10–10 1.16 ´ 10–9 2.40 ´ 10–9 1.53 ´ 10–9 2.56 ´ 10–9 1.15 ´ 10–9 3.01 ´ 10–9 5.43 ´ 10–10 1.40 ´ 10–9 7.13 ´ 10–9 –2.45 ´ 10–10 –2.48 ´ 10–10 –8.04 ´ 10–10 –4.75 ´ 10–10 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 Antimony, Sb Tellurium, Te Iodine, I Xenon, Xe Caesium, Cs Barium, Ba Lanthanum, La Cerium, Ce Praseodymium, Pr Neodymium, Nd Promethium, Pm Samarium, Sm Europium, Eu Gadolinium, Gd Terbium, Tb Dysprosium, Dy Holmium, Ho Erbium, Er Thulium, Tm Ytterbium, Yb Lutetium, Lu Hafnium, Hf Tantalum, Ta Tungsten, W Rhenium, Re Osmium, Os Iridium, Ir Platinum, Pt Gold, Au Mercury, Hg Thallium, Tl Lead, Pb Bismuth, Bi Polonium, Po Astatine, At Radon, Rn Francium, Fr Radium, Ra Actinium, Ac Thorium, Th Protactinium, Pa Uranium, U Neptunium, Np Plutonium, Pu Americium, Am © Michael de Podesta 2002 121.7 127.6 126.9 131.3 132.9 137.3 138.9 140.1 140.9 144.2 145 150.4 152 157.2 158.9 162.5 164.9 167.3 168.9 173 175 178.5 180.9 183.9 186.2 190.2 192.2 195.1 197 200.6 204.4 207.2 209 209 210 222 223 226 227 232 231 238 237 244 243 6692 6247 4953 3560 1900 3594 6174 6711 6779 7000 7220 7536 5248 7870 8267 8531 8797 9044 9325 6966 9842 13276 16670 19254 21023 22580 22550 21450 19281 13546 11871 11343 9803 9400 — 4400 — 5000 10060 11725 15370 19050 20250 19840 13670 cM (m3 mol–1) –1.22 ´ 10–9 –4.98 ´ 10–10 –5.58 ´ 10–10 –5.51 ´ 10–10 3.72 ´ 10–10 2.61 ´ 10–10 1.53 ´ 10–9 3.04 ´ 10–8 6.30 ´ 10–8 7.07 ´ 10–8 — 2.29 ´ 10–8 4.27 ´ 10–7 Ferro 1.83 ´ 10–6 1.30 ´ 10–6 9.05 ´ 10–7 5.57 ´ 10–7 3.21 ´ 10–7 3.13 ´ 10–9 2.28 ´ 10–10 9.46 ´ 10–10 1.94 ´ 10–9 7.36 ´ 10–10 8.49 ´ 10–10 1.24 ´ 10–10 3.21 ´ 10–10 2.54 ´ 10–9 –3.51 ´ 10–10 — –6.40 ´ 10-10 –2.88 ´ 10-10 –3.52 ´ 10-9 — — — — — — 1.67 ´ 10-9 — 5.14 ´ 10-9 — 7.73 ´ 10-9 1.22 ´ 10-8 F: Properties of Matter: data tables 842 November 1, 2010