Example: copper in terrestrial sources. Two isotopes are present: copper-63 (62.9) and copper-65 (64.9), in abundances 69% + 31%. The standard atomic weight (A_r°(Cu)) for copper is the average, weighted by their natural abundance, and then divided by the atomic mass constant m_u.^[1]

The standard atomic weight of a chemical element (symbol A_r°(E) for element "E") is the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope's abundance on Earth. For example, isotope ⁶³Cu (A_r = 62.929) constitutes 69% of the copper on Earth, the rest being ⁶⁵Cu (A_r = 64.927), so

${\displaystyle A_{\text{r}}{\text{°}}(_{\text{29}}{\text{Cu}})=0.69\times 62.929+0.31\times 64.927=63.55.}$

Because relative isotopic masses are dimensionless quantities, this weighted mean is also dimensionless. It can be converted into a measure of mass (with dimension M) by multiplying it with the dalton, also known as the atomic mass constant.

Among various variants of the notion of atomic weight (A_r, also known as relative atomic mass) used by scientists, the standard atomic weight (A_r°) is the most common and practical. The standard atomic weight of each chemical element is determined and published by the Commission on Isotopic Abundances and Atomic Weights (CIAAW) of the International Union of Pure and Applied Chemistry (IUPAC) based on natural, stable, terrestrial sources of the element. The definition specifies the use of samples from many representative sources from the Earth, so that the value can widely be used as "the" atomic weight for substances as they are encountered in reality—for example, in pharmaceuticals and scientific research. Non-standardized atomic weights of an element are specific to sources and samples, such as the atomic weight of carbon in a particular bone from a particular archeological site. Standard atomic weight averages such values to the range of atomic weights that a chemist might expect to derive from many random samples from Earth. This range is the rationale for the interval notation given for some standard atomic weight values.

Of the 118 known chemical elements, 80 have stable isotopes and 84 have this Earth-environment based value. Typically, such a value is, for example helium: A_r°(He) = 4.002602(2). The "(2)" indicates the uncertainty in the last digit shown, to read 4.002602±0.000002. IUPAC also publishes abridged values, rounded to five significant figures. For helium, A_{r, abridged}°(He) = 4.0026.

For fourteen elements the samples diverge on this value, because their sample sources have had a different decay history. For example, thallium (Tl) in sedimentary rocks has a different isotopic composition than in igneous rocks and volcanic gases. For these elements, the standard atomic weight is noted as an interval: A_r°(Tl) = [204.38, 204.39]. With such an interval, for less demanding situations, IUPAC also publishes a conventional value. For thallium, A_{r, conventional}°(Tl) = 204.38.

Definition

Excerpt of an IUPAC Periodic Table showing the interval notation of the standard atomic weights of boron, carbon, and nitrogen (Chemistry International, IUPAC). Example: the pie chart for boron shows it to be composed of about 20% ¹⁰B and 80% ¹¹B. This isotope mix causes the atomic weight of ordinary Earthly boron samples to be expected to fall within the interval 10.806 to 10.821. and this interval is the standard atomic weight. Boron samples from unusual sources, particularly non-terrestrial sources, might have measured atomic weights that fall outside this range. Atomic weight and relative atomic mass are synonyms.

The standard atomic weight is a special value of the relative atomic mass. It is defined as the "recommended values" of relative atomic masses of sources in the local environment of the Earth's crust and atmosphere as determined by the IUPAC Commission on Atomic Weights and Isotopic Abundances (CIAAW).^[2] In general, values from different sources are subject to natural variation due to a different radioactive history of sources. Thus, standard atomic weights are an expectation range of atomic weights from a range of samples or sources. By limiting the sources to terrestrial origin only, the CIAAW-determined values have less variance, and are a more precise value for relative atomic masses (atomic weights) actually found and used in worldly materials.

The CIAAW-published values are used and sometimes lawfully required in mass calculations. The values have an uncertainty (noted in brackets), or are an expectation interval (see example in illustration immediately above). This uncertainty reflects natural variability in isotopic distribution for an element, rather than uncertainty in measurement (which is much smaller with quality instruments).^[3]

Although there is an attempt to cover the range of variability on Earth with standard atomic weight figures, there are known cases of mineral samples which contain elements with atomic weights that are outliers from the standard atomic weight range.^[2]

For synthetic elements the isotope formed depends on the means of synthesis, so the concept of natural isotope abundance has no meaning. Therefore, for synthetic elements the total nucleon count of the most stable isotope (i.e., the isotope with the longest half-life) is listed in brackets, in place of the standard atomic weight.

When the term "atomic weight" is used in chemistry, usually it is the more specific standard atomic weight that is implied. It is standard atomic weights that are used in periodic tables and many standard references in ordinary terrestrial chemistry.

Lithium represents a unique case where the natural abundances of the isotopes have in some cases been found to have been perturbed by human isotopic separation activities to the point of affecting the uncertainty in its standard atomic weight, even in samples obtained from natural sources, such as rivers.

Determination of relative atomic mass

Modern relative atomic masses (a term specific to a given element sample) are calculated from measured values of atomic mass (for each nuclide) and isotopic composition of a sample. Highly accurate atomic masses are available^[7][8] for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples.^[9][10] For this reason, the relative atomic masses of the 22 mononuclidic elements (which are the same as the isotopic masses for each of the single naturally occurring nuclides of these elements) are known to especially high accuracy.

The calculation is exemplified for silicon, whose relative atomic mass 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 ±0.001% (see table). The calculation is

A_r(Si) = (27.97693 × 0.922297) + (28.97649 × 0.046832) + (29.97377 × 0.030872) = 28.0854

The estimation of the uncertainty is complicated,^[11] especially as the sample distribution is not necessarily symmetrical: the IUPAC standard relative atomic masses are quoted with estimated symmetrical uncertainties,^[12] and the value for silicon is 28.0855(3). The relative standard uncertainty in this value is 1×10^–5 or 10 ppm. To further reflect this natural variability, in 2010, IUPAC made the decision to list the relative atomic masses of 10 elements as an interval rather than a fixed number.^[13]

Naming controversy

The use of the name "atomic weight" has attracted a great deal of controversy among scientists.^[14] 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 or poundal.

In reply, supporters of the term "atomic weight" point out (among other arguments)^[14] that:

• the name has been in continuous use for the same quantity since it was first conceptualized in 1808;^[15]
• for most of that time, atomic weights really were measured by weighing (that is by gravimetric analysis) and the name of a physical quantity should not 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 does not correspond to the property of any individual atom. The same argument could be made against "relative atomic mass" used in this sense.

Published values

IUPAC publishes one formal value for each stable chemical element, called the standard atomic weight.^[16][17] Any updates are published biannually (in uneven years). In 2015, the atomic weight of ytterbium was updated.^[16] Per 2017, 14 atomic weights were changed, including argon changing from single number to interval value.^[18][19]

The value published can have an uncertainty, like for neon: 20.1797(6), or can be an interval, like for boron: [10.806, 10.821].

Next to these 84 values, IUPAC also publishes abridged values (up to five digits per number only), and for the twelve interval values, conventional values (single number values).

Symbol A_r is a relative atomic mass, for example from a specific sample. To be specific, the standard atomic weight can be noted as A_r°(E), where (E) is the element symbol.

List of atomic weights

In the periodic table

Periodic table

Group	1	2		3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
	Hydrogen & alkali metals	Alkaline earth metals												Triels	Tetrels	Pnicto­gens	Chal­co­gens	Halo­gens	Noble gases
Period 1	Hydro­gen1H​1.0080																		He­lium2He​4.0026
2	Lith­ium3Li​6.94	Beryl­lium4Be​9.0122												Boron5B​10.81	Carbon6C​12.011	Nitro­gen7N​14.007	Oxy­gen8O​15.999	Fluor­ine9F​18.998	Neon10Ne​20.180
3	So­dium11Na​22.990	Magne­sium12Mg​24.305												Alumin­ium13Al​26.982	Sili­con14Si​28.085	Phos­phorus15P​30.974	Sulfur16S​32.06	Chlor­ine17Cl​35.45	Argon18Ar​39.95
4	Potas­sium19K​39.098	Cal­cium20Ca​40.078		Scan­dium21Sc​44.956	Tita­nium22Ti​47.867	Vana­dium23V​50.942	Chrom­ium24Cr​51.996	Manga­nese25Mn​54.938	Iron26Fe​55.845	Cobalt27Co​58.933	Nickel28Ni​58.693	Copper29Cu​63.546	Zinc30Zn​65.38	Gallium31Ga​69.723	Germa­nium32Ge​72.630	Arsenic33As​74.922	Sele­nium34Se​78.971	Bromine35Br​79.904	Kryp­ton36Kr​83.798
5	Rubid­ium37Rb​85.468	Stront­ium38Sr​87.62		Yttrium39Y​88.906	Zirco­nium40Zr​91.224	Nio­bium41Nb​92.906	Molyb­denum42Mo​95.95	Tech­netium43Tc​[97]	Ruthe­nium44Ru​101.07	Rho­dium45Rh​102.91	Pallad­ium46Pd​106.42	Silver47Ag​107.87	Cad­mium48Cd​112.41	Indium49In​114.82	Tin50Sn​118.71	Anti­mony51Sb​121.76	Tellur­ium52Te​127.60	Iodine53I​126.90	Xenon54Xe​131.29
6	Cae­sium55Cs​132.91	Ba­rium56Ba​137.33		Lute­tium71Lu​174.97	Haf­nium72Hf​178.49	Tanta­lum73Ta​180.95	Tung­sten74W​183.84	Rhe­nium75Re​186.21	Os­mium76Os​190.23	Iridium77Ir​192.22	Plat­inum78Pt​195.08	Gold79Au​196.97	Mer­cury80Hg​200.59	Thallium81Tl​204.38	Lead82Pb​207.2	Bis­muth83Bi​208.98	Polo­nium84Po​[209]	Asta­tine85At​[210]	Radon86Rn​[222]
7	Fran­cium87Fr​[223]	Ra­dium88Ra​[226]		Lawren­cium103Lr​[266]	Ruther­fordium104Rf​[267]	Dub­nium105Db​[268]	Sea­borgium106Sg​[269]	Bohr­ium107Bh​[270]	Has­sium108Hs​[269]	Meit­nerium109Mt​[278]	Darm­stadtium110Ds​[281]	Roent­genium111Rg​[282]	Coper­nicium112Cn​[285]	Nihon­ium113Nh​[286]	Flerov­ium114Fl​[289]	Moscov­ium115Mc​[290]	Liver­morium116Lv​[293]	Tenness­ine117Ts​[294]	Oga­nesson118Og​[294]
				Lan­thanum57La​138.91	Cerium58Ce​140.12	Praseo­dymium59Pr​140.91	Neo­dymium60Nd​144.24	Prome­thium61Pm​[145]	Sama­rium62Sm​150.36	Europ­ium63Eu​151.96	Gadolin­ium64Gd​157.25	Ter­bium65Tb​158.93	Dyspro­sium66Dy​162.50	Hol­mium67Ho​164.93	Erbium68Er​167.26	Thulium69Tm​168.93	Ytter­bium70Yb​173.05
				Actin­ium89Ac​[227]	Thor­ium90Th​232.04	Protac­tinium91Pa​231.04	Ura­nium92U​238.03	Neptu­nium93Np​[237]	Pluto­nium94Pu​[244]	Ameri­cium95Am​[243]	Curium96Cm​[247]	Berkel­ium97Bk​[247]	Califor­nium98Cf​[251]	Einstei­nium99Es​[252]	Fer­mium100Fm​[257]	Mende­levium101Md​[258]	Nobel­ium102No​[259]

Primordial  From decay  Synthetic Border shows natural occurrence of the element

Standard atomic weight A_{r, std}(E)^[1]

• Ca: 40.078 — Abridged value (uncertainty omitted here)^[23]
• Po: [209] — mass number of the most stable isotope

s-block

f-block

d-block

p-block

See also

• International Union of Pure and Applied Chemistry (IUPAC)
• Commission on Isotopic Abundances and Atomic Weights (CIAAW)

References

External links

• IUPAC Commission on Isotopic Abundances and Atomic Weights
• Atomic Weights of the Elements 2011