SYMBOLS, UNITS, NOMENCLATURE AND FUNDAMENTAL CONSTANTS IN .
INTERNATIONAL UNION OF PURE AND APPLIED PHYSICSCommission C2 - SUNAMCOSYMBOLS, UNITS,NOMENCLATURE ANDFUNDAMENTAL CONSTANTSIN PHYSICS1987 REVISION (2010 REPRINT)Prepared byE. Richard CohenandPierre Giacomo(SUNAMCO 87-1)
PREFACE TO THE 2010 REPRINTThe 1987 revision of the SUNAMCO ‘Red Book’ has for nearly a quarter of a century providedphysicists with authoritative guidance on the use of symbols, units and nomenclature. As such, itis cited as a primary reference by the IUPAC ‘Green Book’ (Quantities, Units and Symbols inPhysical Chemistry, 3rd edition, E. R. Cohen et al., RSC Publishing, Cambridge, 2007) and theSI Brochure (The International System of Units (SI), 8th edition, BIPM, Sèvres, 2006).This electronic version has been prepared from the original TeX files and reproduces thecontent of the printed version, although there are some minor differences in formatting andlayout.In issuing this version, we recognise that there are areas of physics which have cometo prominence over the last two decades which are not covered and also that some materialhas been superseded.In particular, the values of the fundamental constants presented insection 6 have been superseded by more recent recommended values from the CODATA TaskGroup on Fundamental Constants.The currently recommended values can be obtained athttp://physics.nist.gov/constants. SUNAMCO has established a Committee for Revision of theRed Book. Suggestions for material to be included in a revised version can be directed to theSUNAMCO Secretary at stephen.lea@npl.co.uk.Copies of the 1987 printed version are available on application to the IUPAP Secretariat,c/o Insitute of Physics, 76 Portland Place, London W1B 1NT, United Kingdom, e-mail:admin.iupap@iop.org.Peter J. Mohr, ChairStephen N. Lea, SecretaryIUPAP Commission C2 - SUNAMCO
UNION INTERNATIONALE DEPHYSIQUE PURE ET APPLIQUÉEINTERNATIONAL UNION OFPURE AND APPLIED PHYSICSCommission SUNAMCOSUNAMCO CommissionSYMBOLS, UNITS,NOMENCLATURE ANDFUNDAMENTAL CONSTANTSIN PHYSICS1987 REVISIONPrepared byE. Richard CohenRockwell International Science CenterThousand Oaks, California, USAandPierre GiacomoBureau International des Poids et MesuresSèvres, FranceDocument I.U.P.A.P.-25(SUNAMCO 87-1)
UNION INTERNATIONALE DEPHYSIQUE PURE ET APPLIQUÉEINTERNATIONAL UNION OFPURE AND APPLIED PHYSICSCommission SUNAMCOSUNAMCO CommissionPRESIDENT (1984-1987)D. Allan BromleyWright Nuclear Structure Laboratory272 Whitney AvenueNew Haven, CT 06511, USAPRESIDENT (1987-1990)Larkin KerwinPhysics DepartmentUniversité LavalQuebec, PQ G1K 7P4, CANADASECRETARY-GENERALJan S. NilssonInstitute of Theoretical PhysicsChalmers Institute of TechnologyS-412 96 Göteborg, SWEDENASSOCIATE SECRETARY-GENERALJohn R. KlauderAT&T Bell Laboratories600 Mountain AvenueMurray Hill, NJ 07974, USAReprinted fromPHYSICA 146A (1987) 1-68PRINTED IN THE NETHERLANDS
INTRODUCTIONThe recommendations in this document, compiled by the Commission forSymbols, Units, Nomenclature, Atomic Masses and Fundamental Constants(SUN/AMCO Commission) of the International Union of Pure and AppliedPhysics (IUPAP), have been approved by the successive General Assemblies ofthe IUPAP held from 1948 to 1984.These recommendations are in general agreement with recommendations ofthe following international organizations:(1) International Organization for Standardization, Technical Committee ISO/TC12(2) General Conference on Weights and Measures (1948–1983)(3) International Union of Pure and Applied Chemistry (IUPAC)(4) International Electrotechnical Commission, Technical Committee IEC/TC25(5) International Commission on Illumination.This document replaces the previous recommendations of the SUNCommission published under the title Symbols, Units and Nomenclature inPhysics in 1961 (UIP-9, [SUN 61-44]), 1965 (UIP-11, [SUN 65-3]) and 1978(UIP-20, [SUN 78-5], Physica 93A (1978) 1–63).Robert C. Barber, Chairman IUPAP Commission 2International Union of Pure and Applied PhysicsCommission on Symbols, Units, Nomenclature,Atomic Masses and Fundamental ConstantsChairman, R. C. Barber (Canada); Secretary, P. Giacomo (France)Members (1981–1987): K. Birkeland (Norway), W. R. Blevin (Australia),E. R. Cohen (USA), V. I. Goldansky (USSR, Chairman, 1981–1984),E. Ingelstam (Sweden), H. H. Jensen (Denmark), M. Morimura (Japan),B. W. Petley (UK), E. Roeckl (Fed. Rep. Germany), A. Sacconi (Italy),A. H. Wapstra (The Netherlands), N. Zeldes (Israel).ii
CONTENTSPREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v1 GENERAL RECOMMENDATIONS . . . . . . . . . . . . . . . . . . . . . . 11.1 Physical quantities11.2 Units41.3 Numbers51.4 Nomenclature for intensive properties61.5 Dimensional and dimensionless ratios82 SYMBOLS FOR ELEMENTS, PARTICLES, STATES ANDTRANSITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.12.22.32.42.5Chemical elementsNuclear particles‘Fundamental’ particlesSpectroscopic notationNomenclature conventions in nuclear physics99111112153 DEFINITION OF UNITS AND SYSTEMS OF UNITS . . . . . . . . . . 183.1 Systems of units3.2 The International System of Units (SI)3.3 Non-SI units of special interest in physics1819214 RECOMMENDED SYMBOLS FOR PHYSICAL QUANTITIES . . . . . 274.1 Space and time274.2 Mechanics284.3 Statistical physics294.4 Thermodynamics304.5 Electricity and magnetism314.6 Radiation and light334.7 Acoustics344.8 Quantum mechanics344.9 Atomic and nuclear physics354.10 Molecular spectroscopy374.11 Solid state physics384.12 Chemical physics414.13 Plasma physics424.14 Dimensionless parameters44iii
iv5 RECOMMENDED MATHEMATICAL SYMBOLS . . . . . . . . . . . . 475.15.25.35.45.55.65.75.8General symbolsLetter symbolsComplex quantitiesVector calculusMatrix calculusSymbolic logicTheory of setsSymbols for special values of periodic quantities47474949505050516 RECOMMENDED VALUES OF THE FUNDAMENTALPHYSICAL CONSTANTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 52APPENDIX. NON-SI SYSTEMS OF QUANTITIES AND UNITS . . . 62A.1A.2A.3A.4A.5Systems of equations with three base quantitiesSystems of equations with four base quantitiesRelations between quantities in different systemsThe CGS system of unitsAtomic units6264646466
PREFACEThere are two broad classes of dictionaries: those that are proscriptive andattempt to establish the norms of a language and those that are descriptiveand report the language as it is used. For dictionaries of a living language,both types have their place. A manual of usage in science howevermust be primarily descriptive and should reflect the standards of practicethat are current in the field and should attempt to impose a standardonly in those cases where no accepted standards exist. This revision ofthe handbook has taken these precepts into account while expanding thediscussion of some topics and correcting typographical errors of the 1978edition. There has been some reordering of the material with the hope thatthe new arrangement will improve the logical flow, but, since physics is notone-dimensional, that goal may be unachievable.The recommended symbols in section 4, particularly those related tophysical chemistry, have been actively coordinated with the correspondingrecommendations of Commission I.1 on Symbols, Units and Terminology ofIUPAC in order to avoid any conflict between the two. The values of thephysical constants given in section 6 are drawn from the 1986 adjustmentby the CODATA Task Group on Fundamental Constants.E. Richard CohenThousand OaksPierre GiacomoSèvresJuly, 1987v
1 GENERAL RECOMMENDATIONS*1.1 Physical quantitiesThere are two somewhat different meanings of the term ‘physical quantity’.One refers to the abstract metrological concept (e.g., length, mass, temperature),the other to a specific example of that concept (an attribute of a specific objector system: diameter of a steel cylinder, mass of the proton, critical temperatureof water). Sometimes it is important to distinguish between the two and, ideally,it might be useful to be able to do so in all instances. However little is tobe gained by attempting to make that distinction in this report. The primaryconcern here is with symbols and terminology in general; section 6, however,gives the symbols and numerical values of specific physical constants.1.1.1 DefinitionsA physical quantity** is expressed as the product of a numerical value (i.e., apure number) and a unit:physical quantity numerical value unit.For a physical quantity symbolized by a, this relationship is represented in theforma {a} · [a],where {a} stands for the numerical value of a and [a] stands for the unit ofa. Neither the name nor the symbol for a physical quantity should imply anyparticular choice of unit.When physical quantities combine by multiplication or division the usual rulesof arithmetic apply to both the numerical values and to the units. A quantitywhich arises (or may be considered to arise) from dividing one physical quantityby another with the same dimension has a unit which may be symbolized by thenumber 1; such a unit often has no special name or symbol and the quantity isexpressed as a pure number.Examples :E 200 JF 27 N/m2n 1.55 (refractive index)8f 3 10 Hz* For further details see International Standard ISO 31/0-1981 : General PrinciplesConcerning Quantities, Units and Symbols.** French: grandeur physique; German: physikalische Grösse; Italian: grandezza fisica;Russian: fizicheskaya velichina; Spanish: magnitud fı́sica.1
21.1.2 SymbolsSymbols for physical quantities should be single letters of the Latin or Greekalphabet with or without modifying signs (subscripts, superscripts, primes,etc.). The two-letter symbols used to represent dimensionless combinations ofphysical quantities are an exception to this rule (see section 4.14 “Dimensionlessparameters”). When such a two-letter symbol appears as a factor in a productit should be separated from the other symbols by a dot, by a space, or byparentheses. It is treated as a single symbol and can be raised to a positive ornegative power without using parentheses.Abbreviations (i.e., shortened forms of names or expressions, such as p.f. forpartition function) may be used in text, but should not be used in physicalequations. Abbreviations in text should be written in ordinary roman type.Symbols for physical quantities and symbols for numerical variables shouldbe printed in italic (sloping) type, while descriptive subscripts and numericalsubscripts are to be printed in roman (upright) type.Examples :Cg(g gas)Cpgn(n normal)Σ an ψnµr(r relative)Σ br xEk(k kinetic)gi,kχe(e electric)pχnrrbutg1,2It is convenient to use symbols with distinctive typefaces in order todistinguish between the components of a vector (or a tensor) and the vector (ortensor) as an entity in itself, or to avoid the use of subscripts. The followingstandard conventions should be adhered to whenever the appropriate typefacesare available:(a) Vectors should be printed in bold italic type, e.g., a, A.(b) Tensors should be printed in slanted bold sans serif type, e.g., S, T .Remark : When such type is not available, a vector may be indicated by an arrow above the symbol: e.g., a , B . Second-rank tensors may be indicated by a double arrow or by a double-headed arrow: e.g., S , S . The extension ofthis to higher order tensors becomes awkward; in such cases the index notationshould be used uniformly for tensors and vectors:Examples :Ai ,Sij ,Rijkl ,Rijkl ,i.lR.jk.1.1.3 Simple mathematical operationsAddition and subtraction of two physical quantities are indicated by:a banda b.
3Multiplication of two physical quantities may be indicated in one of thefollowing ways:aba·ba b.Division of one quantity by another quantity may be indicated in one of thefollowing ways:aa/bab 1bor in any other way of writing the product of a and b 1 .These procedures can be extended to cases where one of the quantities orboth are themselves products, quotients, sums or differences of other quantities.If brackets are necessary, they should be used in accordance with the rulesof mathematics. When a solidus is used to separate the numerator from thedenominator, brackets should be inserted if there is any doubt where thenumerator starts or where the denominator ends.Examples :Expressions witha horizontal barabcd2sin kx9a cbab ca bc dac bdSame expressionswith a solidusa/bcd ora/(bcd)(2/9) sin kxa/b ca/(b c)(a b)/(c d)a/b c/d or(a/b) (c/d)The argument of a mathematical function is placed in parentheses, bracketsor braces, if necessary, in order to define its extent unambiguously.Examples :sin{2π(x x0 )/λ}exp[ V (r)/kT ]exp{(r r0 )/σ} (G/ρ)Parentheses may be omitted when the argument is a single quantity or asimple product: e.g., sin θ, tan kx. A horizontal overbar may be pused with thesquare root sign to define the outermost level of aggregation, e.g., G(t)/H(t) , and this may be preferable to {G(t)/H(t)}.
4Table 1. Prefixes for use with SI units.10 110 210 310 610 910 1210 1510 1810 2110 tadahkMGTPEZY1.2 Units1.2.1 Symbols for unitsThe full name of a unit is always printed in lower case roman (upright) type.If that name is derived from a proper name then its abbreviation is a one ortwo letter symbol whose first letter is capitalized. The symbol for a unit whosename is not derived from a proper name is printed in lower case roman type.Examples :metre, mampere, Awatt, Wweber, WbRemark : Although by the above rule the symbol for litre is l, in order toavoid confusion between the letter l and the number 1, the symbol may also bewritten L.Symbols for units do not contain a full stop (period) and remain unaltered inthe plural.Example :7 cm and not 7 cm.or 7 cms1.2.2 PrefixesThe prefixes that should be used to indicate decimal multiples or submultiplesof a unit are given in table 1. Compound prefixes formed by the juxtapositionof two or more prefixes should not be used.Not :Not :Not :mµs ,kMW ,µµF ,but :but :but :nsGWpF(nanosecond)(gigawatt)(picofarad)When a prefix symbol is used with a unit symbol the combination should beconsidered as a single new symbol that can be raised to a positive or negativepower without using brackets.
5Examples :cm3mA2µs 1Remark :cm3µs 1means (0.01 m)3 10 6 m3means (10 6 s) 1 106 s 1and never 0.01 m3and never 10 6 s 11.2.3 Mathematical operationsMultiplication of two units should be indicated in one of the following ways :NmN·mDivision of one unit by another unit should be indicated in one of thefollowing ways:mm/sm s 1sor by any other way of writing the product of m and s 1 . Not more than onesolidus should be used in an expression.Examples :Not :Not :cm/s/s ,J/K/mol ,but :but :cm/s2or cm s 2J/(K mol) or J K 1 mol 1Since the rules of algebra may be applied to units and to physical quantitiesas well as to pure numbers, it is possible to divide a physical quantity by itsunit. The result is the numerical value of the physical quantity in the specifiedunit system: {a} a/[a]. This number is the quantity that is listed in tables orused to mark the axes of graphs. The form “quantity/unit” should therefore beused in the headings of tables and as the labels on graphs for an unambiguousindication of the meaning of the numbers to which it pertains.Examples :Given p 0.1013 MPa,Given v 2200 m/s,Given T 295 K,thenthenthenp/MPa 0.1013v/(m/s) 2200T /K 295, 1000 K/T 3.38981.3 Numbers1.3.1 Decimal signIn most European languages (including Russian and other languages usingthe Cyrillic alphabet) the decimal sign is a comma on the line (,); this sign ispreferred by ISO (ISO 31/0-1981, p. 7) and is used in ISO publications even inEnglish. However, in both American and British English the decimal sign is adot on the line (.). The centered dot, (·), which has sometimes been used inBritish English, should never be used as a decimal sign in scientific writing.
61.3.2 Writing numbersNumbers should normally be printed in roman (upright) type. There shouldalways be at least one numerical digit both before and after the decimal sign.An integer should never be terminated by a decimal sign, and if the magnitudeof the number is less than unity the decimal sign should be preceded by a zero.Examples :35 or 35.0 but not 35.0.0035 but not .0035To facilitate the reading of long numbers (greater than four digits either tothe right or to the left of the decimal sign) the digits may be grouped in groupsof three separated by a thin space, but no comma or point should be used exceptfor the decimal sign. Instead of a single final digit, the last four digits may begrouped.Examples :1987299 792 4581.234 567 8or 1.234 56781.3.3 Arithmetical operationsThe sign for multiplication of numbers is a cross ( ) or a centered dot ( · );however, when a dot is used as a decimal sign the centered dot should not beused as the multiplication sign.Examples :2.3 3.4 or 2, 3 3, 4but not 2.3 · 3.4or2, 3 · 3, 4 or (137.036)(273.16)Division of one number by another number may be indicated either by ahorizontal bar or by a solidus (/), or by writing it as the product of numeratorand the inverse first power of the denominator. In such cases the number underthe inverse power should always be placed in brackets, parentheses or other signof aggregation.Examples :136273.16136/273.16136 (273.16) 1As in the case of quantities (see section 1.1.3), when the solidus is used andthere is any doubt where the numerator starts or where the denominator ends,brackets or parentheses should be used.1.4 Nomenclature for intensive properties1.4.1 The adjective ‘specific’ in the English name for an intensive physicalquantity should be avoided if possible and should in all cases be restricted tothe meaning ‘divided by mass’ (mass of the system, if this consists of more thanone component or more than one phase). In French, the adjective ‘massique’ isused with the sense of ‘divided by mass’ to express this concept.
7Examples :specific volume,specific energy,specific heat capacity,volume massique,énergie massique,capacité thermique massique,volume/massenergy/massheat capacity/mass1.4.2 The adjective ‘molar’ in the English name for an intensive physicalquantity should be restricted to the meaning ‘divided by amount of substance’(the amount of substance of the system if it consists of more than one componentor more than one phase).Examples :molar mass,molar volume,molar energy,molar heat capacity,mass/amount of substancevolume/amount of substanceenergy/amount of substanceheat capacity/amount of substanceAn intensive molar quantity is usually denoted by attaching the subscriptm to the symbol for the corresponding extensive quantity, (e.g., volume, V ;molar volume, Vm V /n). In a mixture the symbol XB , where X denotes anextensive quantity and B is the chemical symbol for a substance, denotes thepartial molar quantity of the substance B defined by the relation:XB ( X/ nB )T,p,nC ,. .For a pure substance B the partial molar quantity XB and the molar quantityXm are identical. The molar quantity Xm (B) of pure substance B may bedenoted by XB , where the superscript denotes ‘pure’, so as to distinguish itfrom the partial molar quantity XB of substance B in a mixture, which mayalternatively be designated XB′ .1.4.3 The noun ‘density’ in the English name for an intensive physical quantity(when it is not modified by the adjectives ‘linear’ or ‘surface’) usually implies‘divided by volume’ for scalar quantities but ‘divided by area’ for vectorquantities denoting flow or flux. In French, the adjectives volumique, surfacique,or linéique as appropriate are used with the name of a scalar quantity to expressdivision by volume, area or length, respectively.Examples :mass density,energy density,masse
4.3 Statistical physics 29 4.4 Thermodynamics 30 4.5 Electricity and magnetism 31 4.6 Radiation and light 33 4.7 Acoustics 34 4.8 Quantum mechanics 34 4.9 Atomic and nuclear physics 35 4.10 Molecular spectroscopy 37 4.11 Solid state physics 38 4.12 Chemical physics 41 4.13 Plasma physics 42 4.14 Dimensionless parameters 44 iii
4.3 More complex nomenclature systems, 49 4.4 Coordination nomenclature, an additive nomenclature, 51 4.5 Substitutive nomenclature, 70 4.6 Functional class nomenclature, 96 5 ASPECTS OF THE NOMENCLATURE OF ORGANOMETALLIC COMPOUNDS, 98 5.1 General, 98 5.2 Derivatives of Main Group elements, 98 5.3 Organometallic derivatives of transition .
Nomenclature and the Nomenclature Committee of IUBMB. He was involved with the work of these two bodies from their inception and made many valued contributions to biochemical nomenclature. Nomenclature, just like chemistry, is a subject that develops continually. New classes of compound require new adaptations of nomenclature and
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1 Unit 6 Covalent Naming Nomenclature Chemical nomenclature is a set of rules to generate systematic names for chemical compounds.The nomenclature used most frequently worldwid
