Atomic mass

In chemistry and physics, the atomic mass (formerly atomic weight) is the mass of an atom expressed in unified atomic mass units (u). The atomic mass is equal in value to relative atomic mass, A_r(X), where X is an isotope. While atomic mass has the dimension u, relative atomic mass—the proportion of an atomic mass to one twelfth of the mass of ¹²C—is dimensionless.

Different isotopes of an atom have different numbers of neutrons in the atomic nucleus, while, by definition, an atomic nucleus has a fixed number of protons. Different isotopes of the same atom have different masses, due to the differing number of neutrons. For instance, carbon (six protons) has two stable isotopes and one radioactive—but long-lived—isotope. Their 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 ¹²C is by definition the integral number 12. By the same definition the atomic mass is 12 u.

In high resolution spectroscopy and mass spectrometry masses of different isotopes are observed in the spectra, and in these fields computations are usually done for molecules consisting of well defined isotopes. In most of chemistry this is different. Chemicals used in the laboratory are in general isotopic mixtures: their molecules consist of different isotopes of one and the same element. The proportion of different isotopes in the molecule is determined by the natural abundance of the isotope. Take chlorine as an example. This element 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 thus (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 used here.)

Note on nomenclature

Although "relative atomic mass" is in principle a simple concept, unfortunately there is confusion about its definition. We followed the lead of 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 also followed by Mohr and Taylor who state that (they define m_u as 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.

However, 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 explicitly stated here what the average mass is, it is plausible that the averaging is over different isotopes weighted by terrestrial isotopic abundance. Hence, acccording to IUPAC's definition, the relative atomic mass is nearly synonymous with the standard atomic weight defined above. In IUPAC's definition, a standard atomic weight is a recommended relative atomic mass, which means that IUPAC's standard atomic weight will change over time (because recommendations change regularly), but that IUPAC's relative atomic mass is invariant in time.

Ref. makes it clear that this—messy and unnecessary—confusion is created by too many international comittees addressing this, basically very simple, problem.

Standard Atomic Weights of the Elements

A table is given for the standard atomic weights. Brackets [ ] 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]		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]