Atomic mass

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In chemistry and physics, atomic mass (formerly known as atomic weight) is the mass of an atom expressed in unified atomic mass units (u). Atomic mass is numerically equal to relative atomic mass, denoted by Ar( X), where X is the isotope of which the mass is indicated. The relative atomic mass is the ratio of atomic mass to one twelfth of the mass of the nuclide 12C at rest in its nuclear and electronic ground state.

The difference between atomic mass and relative atomic mass is that the former has a dimension (u), while the latter is dimensionless.

Handling of isotopic masses

Different isotopes of an element have different numbers of neutrons and the same number (the atomic number Z) of protons. So, different isotopes of a given element have the same charge but differ in mass. For example, the element carbon (atomic number Z = 6, i.e., 6 protons) has two stable isotopes and one radioactive—but long-lived—isotope. The respective atomic masses are: 12C: 12 u (six neutrons), 13C: 13.0033548378 u (seven neutrons), and 14C: 14.003241988 u (eight neutrons). The relative atomic mass of those three isotopes are, respectively, the dimensionless numbers 12, 13.0033548378, and 14.003241988.

In practice there are two ways of dealing with the different masses of isotopes:

  1. In high resolution spectroscopy and mass spectrometry masses of isotopes are observed in the spectra. That is, one can distinguish the spectral peaks arising from the different isotopologues, (same molecule, different isotopic composition) in the sample. In these fields it is common to consider the samples as mixtures of of different isotopologues, in much the same way as when the sample consists of different compounds. Hydrogen chloride, for instance, would be seen as a mixture of the following isotopologues: H–35Cl, D–35Cl, H–37Cl, and D–37Cl.
  2. In most of practical chemistry different isotopologues—always present in "off-the-shelf" chemicals—are of no concern whatsoever. In off-the-shelf chemicals the concentrations of different isotopologues are determined by the terrestrial natural abundances of the isotopes. Take the element chlorine as an example. It has two stable isotopes:  35Cl (with a mass of 34.96885271 u) and 37Cl (with a mass of 36.96590260 u). Of all the chlorine atoms occurring on earth 75.78 % is of the lighter kind, while 24.22 % is the heavier isotope. The average mass of the Cl atom is
(34.969×75.78 + 36.966×24.22)/100 = 35.453 u.
The atomic mass averaged over isotopic abundances is called the standard atomic weight. (For historical reasons the term "weight" is still used here.) In most of practical chemistry the standard weight is used as "the" mass of an element. By using averaged masses the chemist accounts for the fact that different isotopes occur in nature. For instance, the HCl molecule has standard atomic weight 1.00794 + 35.453 = 36.461, which is the value used in almost all chemical calculations.

Note on nomenclature

The concept of "relative atomic mass" is in principle a simple one, yet there is some confusion about its definition. NIST clearly and unambiguously defines the relative mass of an isotope:

Relative Atomic Mass (of the isotope): Ar(X), where X is an isotope

This usage is followed by Mohr and Taylor,[1] who state that (the atomic mass constant mu is a twelfth of the mass of 12C):

The relative atomic mass Ar(X) of an elementary particle, atom, or more generally an entity X, is defined by Ar(X) = m(X) / mu, where m(X) is the mass of X. Thus Ar(X) is the numerical value of m(X) when m(X) is expressed in u, and evidently Ar(12C)=12.

On the other hand, the official IUPAC publication, IUPAC Goldbook, defines:

relative atomic mass (atomic weight), Ar
The ratio of the average mass of the atom to the unified atomic mass unit

Although it is not stated explicitly in the Goldbook what is meant by "average mass", it is likely and plausible that the averaging is over different isotopes weighted by terrestrial isotopic abundance. Hence, according to IUPAC's definition, the relative atomic mass is the dimensionless version of the standard atomic weight defined above.

IUPAC also defines standard atomic weight, but adds recommended to its definition, that is, IUPAC defines standard atomic weight as recommended relative atomic mass, which suggests that the recommended value may change in the future when more accurate data become available.

The confusion is created by too many international committees addressing the same, basically very simple, problem of definition.[2]

Standard atomic weights of the elements

The following table[3] lists the standard atomic weights of the chemical elements (= for each element, the average atomic mass of all isotopes each weighted by their terrestrial abundance). The uncertainties in the last given decimal are in parentheses. Parenthesis around the entire number indicate the mass number of the most stable isotope. CS stands for chemical symbol. Z is the atomic number. See here for a list of the full names of the elements.


ZCS Mass ZCS Mass ZCS Mass

1 H 1.00794(7) 38 Sr 87.62(1) 75 Re 186.207(1)
2 He 4.002602(2) 39 Y 88.90585(2) 76 Os 190.23(3)
3 Li 6.941(2) 40 Zr 91.224(2) 77 Ir 192.217(3)
4 Be 9.012182(3) 41 Nb 92.90638(2) 78 Pt 195.078(2)
5 B 10.811(7) 42 Mo 95.94(2) 79 Au 196.96655(2)
6 C 12.0107(8) 43 Tc 98.9062 80 Hg 200.59(2)
7 N 14.0067(2) 44 Ru 101.07(2) 81 Tl 204.3833(2)
8 O 15.9994(3) 45 Rh 102.90550(2) 82 Pb 207.2(1)
9 F 18.9984032(5) 46 Pd 106.42(1) 83 Bi 208.98038(2)
10 Ne 20.1797(6) 47 Ag 107.8682(2) 84 Po 209
11 Na 22.989770(2) 48 Cd 112.411(8) 85 At (210)
12 Mg 24.3050(6) 49 In 114.818(3) 86 Rn 226
13 Al 26.981538(2) 50 Sn 118.710(7)g/mol 87 Fr (223)
14 Si 28.0855(3) 51 Sb 121.760(1) 88 Ra 226
15 P 30.973761(2) 52 Te 127.60(3) 89 Ac 227
16 S 32.065(5) 53 I 126.90447(3) 90 Th 232.0381(1)
17 Cl 35.453(2) 54 Xe 131.293(6) 91 Pa 231.03588(2)
18 Ar 39.948(1) 55 Cs 132.90545(2) 92 U 238.02891(3)
19 K 39.0983(1) 56 Ba 137.327(7) 93 Np 237.0462
20 Ca 40.078(4) 57 La 138.9055(2) 94 Pu 244
21 Sc 44.955910(8) 58 Ce 140.116(1) 95 Am 243
22 Ti 47.867(1) 59 Pr 140.90765(2) 96 Cm 247
23 V 50.9415(1) 60 Nd 144.24(3) 97 Bk 247
24 Cr 51.9961(6) 61 Pm (145) 98 Cf 251
25 Mn 54.938049(9) 62 Sm 150.36(3) 99 Es 252
26 Fe 55.845(2) 63 Eu 151.964(1) 100 Fm 257
27 Co 58.933200(9) 64 Gd 157.25(3) 101 Md 258
28 Ni 58.6934(2) 65 Tb 158.92534(2) 102 No 259
29 Cu 63.546(3) 66 Dy 162.500(1) 103 Lr 262
30 Zn 65.409(4) 67 Ho 164.93032(2) 104 Rf 265
31 Ga 69.723(1) 68 Er 167.259(3) 105 Db 268
32 Ge 72.64(1) 69 Tm 168.93421(2) 106 Sg 271
33 As 74.92160(2) 70 Yb 173.04(3) 107 Bh 272
34 Se 78.96(3) 71 Lu 174.967(1) 108 Hs 270
35 Br 79.904(1) 72 Hf 178.49(2) 109 Mt 276
36 Kr 83.798(2) 73 Ta 180.9479(1) 110 Ds 281
37 Rb 85.4678(3) 74 W 183.84(1) 111 Rg 280

Notes

  1. P. J. Mohr and B. N. Taylor, CODATA recommended values of the fundamental physical constants: 2002, Reviews of Modern Physics, vol. 77, p. 1 (2005)
  2. Article about Atomic Weights
  3. Physical Reference Data. The numbers in this table are taken from the web site of NIST on December 2, 2007.