Atomic weight

Atomic weight (symbol: A_r) is a dimensionless physical quantity, the ratio of the average mass of atoms of an element (from a given source) to 1/12 of the mass of an atom of carbon-12. The term is usually used, without further qualification, to refer to the standard atomic weights published at regular intervals by the International Union of Pure and Applied Chemistry (IUPAC) and which are intended to be applicable to normal laboratory materials. These standard atomic weights are reprinted in a wide variety of textbooks, commercial catalogues, wallcharts etc, and in the table below. The fact "relative atomic mass" may also be used to describe this physical quantity, and indeed the continued use of the term "atomic weight" has attracted considerable controversy since at least the 1960s (see below).

Atomic weights, unlike atomic masses (the masses of individual atoms), are not physical constants and vary from sample to sample. Nevertheless, they are sufficiently constant in "normal" samples to be of fundamental importance in chemistry.

Definition

The IUPAC definition of atomic weight is:

An atomic weight (relative atomic mass) of an element from a specified source is the ratio of the average mass per atom of the element to 1/12 of the mass of an atom of ¹²C.

The definition deliberately specifies "An atomic weight…", as an element will have different atomic weights depending on the source. For example, boron from Turkey has a lower atomic weight than boron from California, because of its different isotopic composition. Nevertheless, given the cost and difficulty of isotope analysis, it is usual to use the tabulated values of standard atomic weights which are ubiquitous in chemical laboratories.

Values to four figures

Group →	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
↓ Period
1	H 1.008																	He 4.003
2	Li 6.941(2)†	Be 9.012											B 10.81#	C 12.01	N 14.01	O 16.00	F 19.00	Ne 20.18
3	Na 22.99	Mg 24.31											Al 26.98	Si 28.09	P 30.97	S 32.07#	Cl 35.45	Ar 39.95
4	K 39.10	Ca 40.08#	Sc  44.96	Ti 47.87	V 50.94	Cr 52.00	Mn 54.94	Fe 55.84	Co 58.93	Ni 58.69	Cu 63.55	Zn 65.38(2)	Ga 69.72	Ge 72.61	As 74.92	Se 78.96(3)	Br 79.90	Kr 83.80#
5	Rb 85.47#	Sr 87.62#	Y 88.91	Zr 91.22#	Nb 92.91	Mo 95.96(2)	Tc [98.91]	Ru 101.1#	Rh 102.9	Pd 106.4#	Ag 107.9#	Cd 112.4#	In 114.8	Sn 118.7#	Sb 121.8#	Te 127.6#	I 126.9	Xe 131.3#
6	Cs 132.9	Ba 137.3	*	Hf 178.5	Ta 180.9	W 183.9	Re 186.2	Os 190.2	Ir 192.2	Pt 195.1	Au 197.0	Hg 200.6	Tl 204.4	Pb 207.2#	Bi 209.0	Po [210.0]	At [210.0]	Rn [222.0]
7	Fr [223.0]	Ra [226.0]	**	Rf [263]	Db [262]	Sg [266]	Bh [264]	Hs [269]	Mt [268]	Ds [272]	Rg [272]	Cn [277]	Uut [284]	Uuq [289]	Uup [288]	Uuh [292]	Uus [294]	Uuo [293]
* Lanthanoids				La 138.9	Ce 140.1#	Pr 140.9	Nd 144.2#	Pm [146.9]	Sm 150.4#	Eu 152.0#	Gd 157.3#	Tb 158.9	Dy 162.5#	Ho 164.9	Er 167.3#	Tm 168.9	Yb 173.1#	Lu 175.0
** Actinoids				Ac [227.0]	Th 232.0	Pa 231.0	U 238.0#	Np [237.0]	Pu [239.1]	Am [241.1]	Cm [244.1]	Bk [249.1]	Cf [252.1]	Es [252]	Fm [257]	Md [258]	No [259]	Lr [262]

Notes 

Values apply to elements of natural terrestrial origin. The last significant figure of each tabulated value is considered reliable to ±1 except when a larger single digit uncertainty is inserted in parentheses following the atomic weight.
Values in square brackets are for elements with no stable isotopes and no characteristic terrestrial isotopic composition. For such elements up to and including Cf (Z = 98), a four-figure relative atomic mass is given for the most commonly encountered isotope: for elements from Es (Z = 99) onwards, the value quoted is the mass number of the isotope with the longest half life.
† Commercially available Li materials have atomic weights that range between 6.939 and 6.996; if a more accurate value is required, it must be determined for the specific material.
# Values may differ from the atomic weights of the relevant elements in some naturally occurring samples because of a variation in the relative isotopic abundance.

Naming controversy

The use of the name "atomic weight" has attracted a great deal of controversy among scientists. Objectors to the name usually prefer the term "relative atomic mass" (not to be confused with atomic mass). The basic objection is that atomic weight is not a weight, that is the force exerted on an object in a gravitational field, measured in units of force such as the newton.

In reply, supporters of the term "atomic weight" point out (among other arguments) that

• the name has been in continuous use for the same quantity since it was first conceptualized in 1808;
• for most of that time, atomic weights really were measured by weighing (that is by gravimetric analysis) and that the name of a physical quantity shouldn't change simply because the method of its determination has changed;
• the term "relative atomic mass" should be reserved for the mass of a specific nuclide (or isotope), while "atomic weight" be used for the weighted mean of the atomic masses over all the atoms in the sample;
• it is not uncommon to have misleading names of physical quantities which are retained for historical reasons, such as
  • electromotive force, which is not a force
  • resolving power, which is not a power quantity
  • molar concentration, which is not a molar quantity (a quantity expressed per unit amount of substance)

It could be added that atomic weight is often not truly "atomic" either, as it doesn't correspond to the property of any individual atom. The same argument could be made against "relative atomic mass" used in this sense.

Determination of atomic weight

Modern atomic weights are calculated from measured values of atomic mass (for each nuclide) and isotopic composition. Highly accurate atomic masses are available for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples. For this reason, the atomic weights of the twenty-two mononuclidic elements are known to especially high accuracy – an uncertainty of only one part in 38 million in the case of fluorine, a precision which is greater than the current best value for the Avogadro constant (one part in 20 million).

Isotope	Relative atomic mass	Abundance
		Standard	Range
28Si	27.976 926 532 46(194)	92.223(19)%	92.205–92.241%
29Si	28.976 494 700(22)	4.685(8)%	4.678–4.692%
30Si	29.973 770 171(32)	3.092(11)%	3.082–3.102%

The calculation is exemplified for silicon, whose atomic weight is especially important in metrology. Silicon exists in nature as a mixture of three isotopes: ²⁸Si, ²⁹Si and ³⁰Si. The atomic masses of these nuclides are known to a precision of one part in 14 billion for ²⁸Si and about one part in one billion for the others. However the range of natural abundance for the isotopes is such that the standard abundance can only be given to about ±0.01% (see table). The calculation is

A_r(Si) = (27.976 93 × 0.922 23) + (28.976 49 × 0.046 85) + (29.973 77 × 0.030 92) = 28.0854

The estimation of the uncertainty is complicated, especially as the sample distribution is not necessarily symmetrical: the IUPAC standard atomic weights are quoted with estimated symmetrical uncertainties, and the value for silicon is 28.0855(3). The relative standard uncertainty in this value is 1 × 10^–5 or 10 ppm.

See also

• List of standard atomic weights

External links

• IUPAC Commission on Isotopic Abundances and Atomic Weights
• NIST relative atomic masses of all isotopes and the standard atomic weights of the elements
• Atomic Weights and the International Committee — A Historical Review