Atomic mass

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 A_r( X), where X is the isotope of which the mass is indicated. The difference between atomic mass and relative atomic mass is that the former has a dimension (u), while the latter is dimensionless. 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.

Handling of isotopic masses

Recall first that 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, look at the element carbon (atomic number Z = 6, i.e., 6 protons). It 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 e.g. the isotope ¹³C is the dimensionless number 13.0033548378.

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. We followed NIST, see the NIST web site, where clearly and unambiguously the relative mass is defined of an isotope. The site states:

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

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

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

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

relative atomic mass (atomic weight), A_r
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.

From reading Ref. it becomes clear that the confusion is created by too many international committees addressing the same, basically very simple, problem of definition.

Standard Atomic Weights of the Elements

The following table lists the standard atomic weights. 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 this article for a list of the full names of the elements.

Z	CS	Mass		Z	CS	Mass		Z	CS	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	[222]
13	Al	26.981538(2)		50	Sn	118.710(7)		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]
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	[261]
31	Ga	69.723(1)		68	Er	167.259(3)		105	Db	[262]
32	Ge	72.64(1)		69	Tm	168.93421(2)		106	Sg	[266]
33	As	74.92160(2)		70	Yb	173.04(3)		107	Bh	[264]
34	Se	78.96(3)		71	Lu	174.967(1)		108	Hs	[277]
35	Br	79.904(1)		72	Hf	178.49(2)		109	Mt	[268]
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	[272]