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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 (Ar°(Cu)) for copper is the average, weighted by their natural abundance, and then divided by the atomic mass constant mu.[1]

The standard atomic weight of a chemical element (symbol Ar°(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 (Ar = 62.929) constitutes 69% of the copper on Earth, the rest being 65Cu (Ar = 64.927), so

Relative isotopic mass is dimensionless, and so is the weighted average. It can be converted into a measure of mass (with dimension M) by multiplying it with the atomic mass constant dalton.

Among various variants of the notion of atomic weight (Ar, also known as relative atomic mass) used by scientists, the standard atomic weight (Ar°) 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 archaeological 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, 84 have this Earth-environment based value, all but 4 of which have stable isotopes. Typically, such a value is, for example helium: Ar°(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, Ar, 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: Ar°(Tl) = [204.38, 204.39]. With such an interval, for less demanding situations, IUPAC also publishes a conventional value. For thallium, Ar, conventional°(Tl) = 204.38.

Definition

[edit]
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.[citation needed][dubious – discuss]

Terrestrial definition

[edit]

An example of why "conventional terrestrial sources" must be specified in giving standard atomic weight values is the element argon. Between locations in the Solar System, the atomic weight of argon varies as much as 10%, due to extreme variance in isotopic composition. Where the major source of argon is the decay of 40
K in rocks, 40
Ar will be the dominant isotope. Such locations include the planets Mercury and Mars, and the moon Titan. On Earth, the ratios of the three isotopes 36Ar : 38Ar : 40Ar are approximately 5 : 1 : 1600, giving terrestrial argon a standard atomic weight of 39.948(1).

However, such is not the case in the rest of the universe. Argon produced directly, by stellar nucleosynthesis, is dominated by the alpha-process nuclide 36
Ar. Correspondingly, solar argon contains 84.6% 36
Ar (according to solar wind measurements),[4] and the ratio of the three isotopes 36Ar : 38Ar : 40Ar in the atmospheres of the outer planets is 8400 : 1600 : 1.[5] The atomic weight of argon in the Sun and most of the universe, therefore, would be only approximately 36.3.[6]

Causes of uncertainty on Earth

[edit]

Famously, the published atomic weight value comes with an uncertainty. This uncertainty (and related: precision) follows from its definition, the source being "terrestrial and stable". Systematic causes for uncertainty are:

  1. Measurement limits. As always, the physical measurement is never finite. There is always more detail to be found and read. This applies to every single, pure isotope found. For example, today the mass of the main natural fluorine isotope (fluorine-19) can be measured to the accuracy of eleven decimal places: 18.998403163(6). But a still more precise measurement system could become available, producing more decimals.
  2. Imperfect mixtures of isotopes. In the samples taken and measured the mix (relative abundance) of those isotopes may vary. For example, copper. While in general its two isotopes make out 69.15% and 30.85% each of all copper found, the natural sample being measured can have had an incomplete 'stirring' and so the percentages are different. The precision is improved by measuring more samples of course, but there remains this cause of uncertainty. (Example: lead samples vary so much, it can not be noted more precise than four figures: 207.2)
  3. Earthly sources with a different history. A source is the greater area being researched, for example 'ocean water' or 'volcanic rock' (as opposed to a 'sample': the single heap of material being investigated). It appears that some elements have a different isotopic mix per source. For example, thallium in igneous rock has more lighter isotopes, while in sedimentary rock it has more heavy isotopes. There is no Earthly mean number. These elements show the interval notation: Ar°(Tl) = [204.38, 204.39]. For practical reasons, a simplified 'conventional' number is published too (for Tl: 204.38).

These three uncertainties are accumulative. The published value is a result of all these.

Determination of relative atomic mass

[edit]
Main article: Isotope geochemistry

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.

Isotope Atomic mass[8] Abundance[9]
Standard Range
28Si 27.976 926 532 46(194) 92.2297(7)% 92.21–92.25%
29Si 28.976 494 700(22) 4.6832(5)% 4.67–4.69%
30Si 29.973 770 171(32) 3.0872(5)% 3.08–3.10%

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

Ar(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

[edit]

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.[15]

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;[16]
  • 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

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

[edit]

IUPAC publishes one formal value for each stable chemical element, called the standard atomic weight.[17][1]: Table 1  Any updates are published biannually (in uneven years). In 2015, the atomic weight of ytterbium was updated.[17] 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 Ar is a relative atomic mass, for example from a specific sample. To be specific, the standard atomic weight can be noted as Ar°(E), where (E) is the element symbol.

Abridged atomic weight

[edit]

The abridged atomic weight, also published by CIAAW, is derived from the standard atomic weight, reducing the numbers to five digits (five significant figures). The name does not say 'rounded'.

Interval borders are rounded downwards for the first (low most) border, and upwards for the upward (upmost) border. This way, the more precise original interval is fully covered.[1]: Table 2 

Examples:

  • Calcium: Ar°(Ca) = 40.078(4) → Ar, abridged°(Ca) = 40.078
  • Helium: Ar°(He) = 4.002602(2) → Ar, abridged°(He) = 4.0026
  • Hydrogen: Ar°(H) = [1.00784, 1.00811] → Ar, abridged°(H) = [1.0078, 1.0082]

Conventional atomic weight

[edit]

Fourteen chemical elements – hydrogen, lithium, boron, carbon, nitrogen, oxygen, magnesium, silicon, sulfur, chlorine, argon, bromine, thallium, and lead – have a standard atomic weight that is defined not as a single number, but as an interval. For example, hydrogen has Ar°(H) = [1.00 784, 1.00811]. This notation states that the various sources on Earth have substantially different isotopic constitutions, and that the uncertainties in all of them are just covered by the two numbers. For these elements, there is not an 'Earth average' constitution, and the 'right' value is not its middle (which would be 1.007975 for hydrogen, with an uncertainty of (±0.000135) that would make it just cover the interval). However, for situations where a less precise value is acceptable, for example in trade, CIAAW has published a single-number conventional atomic weight. For hydrogen, Ar, conventional°(H) = 1.008.[1]: Table 3 

A formal short atomic weight

[edit]

By using the abridged value, and the conventional value for the fourteen interval values, a short IUPAC-defined value (5 digits plus uncertainty) can be given for all stable elements. In many situations, and in periodic tables, this may be sufficiently detailed.[1]: Tables 2 and 3 

Overview: formal value types of the standard atomic weight[20]
Element (E)
​ 		Ar°(E)
 Value type
​ 		Ar°(E), abridged
or conventional 		Mass number
[most stable isotope]
hydrogen 1H [1.00784, 1.00811] interval 1.0080±0.0002
nitrogen 7N [14.00643, 14.00728] interval 14.007±0.001
fluorine 9F 18.998403162±0.000000005 number ± uncertainty 18.998±0.001
calcium 20Ca 40.078±0.004 number ± uncertainty 40.078±0.004
technetium 43Tc (none) most stable isotope [97]

List of atomic weights

[edit]
Standard atomic weight of the elements (IUPAC 2009–2021[ref 1])
Z Symbol Name Ar, standard Abridged Year changed
1 H hydrogen [1.00784, 1.00811] 1.0080±0.0002 2009
2 He helium 4.002602±0.000002 4.0026±0.0001 1983
3 Li lithium [6.938, 6.997] 6.94±0.06 2009
4 Be beryllium 9.0121831±0.0000005 9.0122±0.0001 2013
5 B boron [10.806, 10.821] 10.81±0.02 2009
6 C carbon [12.0096, 12.0116] 12.011±0.002 2009
7 N nitrogen [14.00643, 14.00728] 14.007±0.001 2009
8 O oxygen [15.99903, 15.99977] 15.999±0.001 2009
9 F fluorine 18.998403162±0.000000005 18.998±0.001 2021
10 Ne neon 20.1797±0.0006 20.180±0.001 1985
11 Na sodium 22.98976928±0.00000002 22.990±0.001 2005
12 Mg magnesium [24.304, 24.307] 24.305±0.002 2011
13 Al aluminium 26.9815384±0.0000003 26.982±0.001 2017
14 Si silicon [28.084, 28.086] 28.085±0.001 2009
15 P phosphorus 30.973761998±0.000000005 30.974±0.001 2013
16 S sulfur [32.059, 32.076] 32.06±0.02 2009
17 Cl chlorine [35.446, 35.457] 35.45±0.01 2009
18 Ar argon [39.792, 39.963] 39.95±0.16 2017
19 K potassium 39.0983±0.0001 39.098±0.001 1979
20 Ca calcium 40.078±0.004 40.078±0.004 1983
21 Sc scandium 44.955907±0.000004 44.956±0.001 2021
22 Ti titanium 47.867±0.001 47.867±0.001 1993
23 V vanadium 50.9415±0.0001 50.942±0.001 1977
24 Cr chromium 51.9961±0.0006 51.996±0.001 1983
25 Mn manganese 54.938043±0.000002 54.938±0.001 2017
26 Fe iron 55.845±0.002 55.845±0.002 1993
27 Co cobalt 58.933194±0.000003 58.933±0.001 2017
28 Ni nickel 58.6934±0.0004 58.693±0.001 2007
29 Cu copper 63.546±0.003 63.546±0.003 1969
30 Zn zinc 65.38±0.02 65.38±0.02 2007
31 Ga gallium 69.723±0.001 69.723±0.001 1987
32 Ge germanium 72.630±0.008 72.630±0.008 2009
33 As arsenic 74.921595±0.000006 74.922±0.001 2013
34 Se selenium 78.971±0.008 78.971±0.008 2013
35 Br bromine [79.901, 79.907] 79.904±0.003 2011
36 Kr krypton 83.798±0.002 83.798±0.002 2001
37 Rb rubidium 85.4678±0.0003 85.468±0.001 1969
38 Sr strontium 87.62±0.01 87.62±0.01 1969
39 Y yttrium 88.905838±0.000002 88.906±0.001 2021
40 Zr zirconium 91.222±0.003 91.222±0.003 2024
41 Nb niobium 92.90637±0.00001 92.906±0.001 2017
42 Mo molybdenum 95.95±0.01 95.95±0.01 2013
43 Tc technetium -
44 Ru ruthenium 101.07±0.02 101.07±0.02 1983
45 Rh rhodium 102.90549±0.00002 102.91±0.01 2017
46 Pd palladium 106.42±0.01 106.42±0.01 1979
47 Ag silver 107.8682±0.0002 107.87±0.01 1985
48 Cd cadmium 112.414±0.004 112.41±0.01 2013
49 In indium 114.818±0.001 114.82±0.01 2011
50 Sn tin 118.710±0.007 118.71±0.01 1983
51 Sb antimony 121.760±0.001 121.76±0.01 1993
52 Te tellurium 127.60±0.03 127.60±0.03 1969
53 I iodine 126.90447±0.00003 126.90±0.01 1985
54 Xe xenon 131.293±0.006 131.29±0.01 1999
55 Cs caesium 132.90545196±0.00000006 132.91±0.01 2013
56 Ba barium 137.327±0.007 137.33±0.01 1985
57 La lanthanum 138.90547±0.00007 138.91±0.01 2005
58 Ce cerium 140.116±0.001 140.12±0.01 1995
59 Pr praseodymium 140.90766±0.00001 140.91±0.01 2017
60 Nd neodymium 144.242±0.003 144.24±0.01 2005
61 Pm promethium -
62 Sm samarium 150.36±0.02 150.36±0.02 2005
63 Eu europium 151.964±0.001 151.96±0.01 1995
64 Gd gadolinium 157.249±0.002 157.25±0.01 2024
65 Tb terbium 158.925354±0.000007 158.93±0.01 2021
66 Dy dysprosium 162.500±0.001 162.50±0.01 2001
67 Ho holmium 164.930329±0.000005 164.93±0.01 2021
68 Er erbium 167.259±0.003 167.26±0.01 1999
69 Tm thulium 168.934219±0.000005 168.93±0.01 2021
70 Yb ytterbium 173.045±0.010 173.05±0.02 2015
71 Lu lutetium 174.96669±0.00005 174.97±0.01 2024
72 Hf hafnium 178.486±0.006 178.49±0.01 2019
73 Ta tantalum 180.94788±0.00002 180.95±0.01 2005
74 W tungsten 183.84±0.01 183.84±0.01 1991
75 Re rhenium 186.207±0.001 186.21±0.01 1973
76 Os osmium 190.23±0.03 190.23±0.03 1991
77 Ir iridium 192.217±0.002 192.22±0.01 2017
78 Pt platinum 195.084±0.009 195.08±0.02 2005
79 Au gold 196.966570±0.000004 196.97±0.01 2017
80 Hg mercury 200.592±0.003 200.59±0.01 2011
81 Tl thallium [204.382, 204.385] 204.38±0.01 2009
82 Pb lead [206.14, 207.94] 207.2±1.1 2020
83 Bi bismuth 208.98040±0.00001 208.98±0.01 2005
84 Po polonium -
85 At astatine -
86 Rn radon -
87 Fr francium -
88 Ra radium -
89 Ac actinium -
90 Th thorium 232.0377±0.0004 232.04±0.01 2013
91 Pa protactinium 231.03588±0.00001 231.04±0.01 2017
92 U uranium 238.02891±0.00003 238.03±0.01 1999
93 Np neptunium -
94 Pu plutonium -
95 Am americium -
96 Cm curium -
97 Bk berkelium -
98 Cf californium -
99 Es einsteinium -
100 Fm fermium -
101 Md mendelevium -
102 No nobelium -
103 Lr lawrencium -
104 Rf rutherfordium -
105 Db dubnium -
106 Sg seaborgium -
107 Bh bohrium -
108 Hs hassium -
109 Mt meitnerium -
110 Ds darmstadtium -
111 Rg roentgenium -
112 Cn copernicium -
113 Nh nihonium -
114 Fl flerovium -
115 Mc moscovium -
116 Lv livermorium -
117 Ts tennessine -
118 Og oganesson -
  1. ^
      (This list:
    )
    CIAAW may publish changes to atomic weights (including its precision and derived values). Since 1947, any update this is done in odd years nominally; the actual date of publication may be some time later.
    • 2009 (introducing interval notation; Ge):
    "Atomic weights of the elements 2009 (IUPAC Technical Report)". Pure and Applied Chemistry. 83 (2): 359–396. 12 December 2010. doi:10.1351/PAC-REP-10-09-14.
    • 2011 (interval for Br, Mg):
    "Atomic weights of the elements 2011 (IUPAC Technical Report)". Pure and Applied Chemistry. 85 (5): 1047–1078. 29 April 2013. doi:10.1351/PAC-REP-13-03-02.
    • 2013 (all elements listed):
    Meija, Juris; et al. (2016). "Atomic weights of the elements 2013 (IUPAC Technical Report)". Pure and Applied Chemistry. 88 (3): 265–291. doi:10.1515/pac-2015-0305.
    • 2015 (ytterbium changed):
    "Standard Atomic Weight of Ytterbium Revised". Chemistry International. 37 (5–6): 26. October 2015. doi:10.1515/ci-2015-0512. eISSN 0193-6484. ISSN 0193-6484.
    • 2017 (14 values changed):
    "Standard atomic weights of 14 chemical elements revised". CIAAW. 2018-06-05.
    * "2020" is an inconsistent year for change publication: CIAAW maintains that only odd years, changes are publicised.
    • 2021 (all elements listed); (4 values changed; introduced new symbol; merge "conventional" into "abridged" columns; change uncertainty notation (use "±")
    Prohaska, Thomas; Irrgeher, Johanna; Benefield, Jacqueline; Böhlke, John K.; Chesson, Lesley A.; Coplen, Tyler B.; Ding, Tiping; Dunn, Philip J. H.; Gröning, Manfred; Holden, Norman E.; Meijer, Harro A. J. (2022-05-04). "Standard atomic weights of the elements 2021 (IUPAC Technical Report)". Pure and Applied Chemistry. doi:10.1515/pac-2019-0603. ISSN 1365-3075.
    Uncertainty handling

    About notation and handling of the uncertainty in the values, including those in [ ] range values:

    See also: {{Isotopes table/references}}

In the periodic table

[edit]
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 1 asterisk 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] 1 asterisk Lawren­cium103Lr​[266] Ruther­fordium104Rf​[267] Dub­nium105Db​[268] Sea­borgium106Sg​[269] Bohr­ium107Bh​[270] Has­sium108Hs​[271] Meit­nerium109Mt​[278] Darm­stadtium110Ds​[281] Roent­genium111Rg​[282] Coper­nicium112Cn​[285] Nihon­ium113Nh​[286] Flerov­ium114Fl​[289] Moscov­ium115Mc​[290] Liver­morium116Lv​[293] Tenness­ine117Ts​[294] Oga­nesson118Og​[294]
1 asterisk 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  
1 asterisk 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]

See also

[edit]

References

[edit]
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Standard atomic weight

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The standard atomic weight of a is the recommended value for its atomic weight, expressed as a single number or an interval, applicable to normal terrestrial materials and based on the weighted average of the masses of its stable isotopes weighted by their natural abundances. These values are determined by the Commission on Isotopic Abundances and Atomic Weights (CIAAW) of the International Union of Pure and Applied Chemistry (IUPAC) through critical evaluation of isotopic composition data and atomic mass measurements from global samples. For elements with constant isotopic abundances, the standard atomic weight is given as a conventional value with an uncertainty reflecting measurement precision; for those exhibiting natural variations (such as due to geological processes), it is expressed as an interval to encompass the range observed in typical materials. The concept originated in the early , with the first international atomic weight table published in 1903 following discussions at the 1900 International Committee on Atomic Weights, and has been periodically revised to incorporate advances in and isotopic analysis. CIAAW updates these standards approximately every few years, with the most recent revisions in 2024 adjusting values for , , and , following the 2021 updates for elements such as , , , lead, and to reflect new data on isotopic variability, ensuring consistency in chemical calculations, , and . This standardization is crucial for fields ranging from to , as it accounts for the fact that atomic weights are not fixed constants but averages that can vary slightly in nature, promoting accuracy in and international standards.

Definition and Principles

Core Definition

The standard atomic weight of an element is defined as the recommended value of its , representing the weighted average of the atomic masses of its stable , weighted by their relative abundances in normal terrestrial materials such as the , oceans, and atmosphere. This value is expressed on a scale where the of the isotope is exactly 12. It is calculated using the formula Ar(E)=∑i(xi⋅Ar(i)),A_\mathrm{r}(E) = \sum_i \left( x_i \cdot A_\mathrm{r}(i) \right), where Ar(E)A_\mathrm{r}(E) is the standard atomic weight of element EE, xix_i is the relative abundance (fraction) of ii, and Ar(i)A_\mathrm{r}(i) is the of that ; the sum is taken over all of the element. Due to natural isotopic variations, many standard atomic weights are now reported as intervals rather than single values with uncertainties. The International Union of Pure and Applied Chemistry (IUPAC), through its Commission on Isotopic Abundances and Atomic Weights (CIAAW), has evaluated and published atomic weights since 1902, with the inclusion of uncertainties for all elements beginning in 1969 to reflect measurement precision and natural variability. The term "standard atomic weight" was formalized in subsequent reports to denote these recommended values applicable to normal materials. Updates occur periodically based on new isotopic abundance data, with the most recent revisions in 2024 for , , and . Unlike the nuclidic mass, which is the relative atomic mass of a single isotope (e.g., Ar(12C)=12A_\mathrm{r}(^{12}\mathrm{C}) = 12 exactly), the standard atomic weight accounts for the mixture of isotopes in nature. It is also distinct from the molar mass constant, which scales the to grams per mole using the (approximately 1×10−31 \times 10^{-3} kg/mol). For example, hydrogen's standard atomic weight is approximately 1.008, primarily due to the abundance of protium (1H^1\mathrm{H}, mass ≈1) with a small contribution from (2H^2\mathrm{H}, mass ≈2). These values provide a conventional basis for chemical calculations, though minor isotopic variations in specific terrestrial reservoirs can lead to deviations from the standard.

Terrestrial Basis and Variations

The standard atomic weights refer to the weighted average atomic masses of elements as found in normal terrestrial materials, defined as all naturally occurring substances on Earth excluding those with deliberate or inadvertent artificial isotopic modifications, extraterrestrial origins such as meteorites, or anomalous isotopic compositions from rare geological events like natural nuclear reactors. This terrestrial basis ensures that the values reflect the typical isotopic abundances encountered in 's crust, oceans, atmosphere, and , providing a consistent reference for chemical and physical calculations without incorporating non- samples unless explicitly noted. Uncertainties in standard atomic weights stem primarily from natural isotopic fractionation, where physical, chemical, and biological processes preferentially partition isotopes based on mass differences, leading to heterogeneous distributions across reservoirs. Examples include and in the hydrologic cycle, diffusion in minerals, and kinetic effects during biological uptake, which can alter isotopic ratios between sources like oceans (relatively uniform) and continental minerals or biological tissues (more variable). These processes operate over diverse timescales—from rapid atmospheric exchanges to long-term geological cycling—resulting in measurable deviations that exceed analytical precision for certain elements. Specific cases illustrate this heterogeneity: for , δD variations reach up to approximately 1000‰ across terrestrial samples due to fractionation in , , and organic matter synthesis, corresponding to the standard atomic weight interval [1.00784, 1.00811]. Similarly, carbon shows ¹³C/¹²C ratio differences of about 25‰ between the geosphere (inorganic carbonates near 0‰) and (organic matter depleted to -25‰ from photosynthetic ), yielding the interval [12.0096, 12.0116]. To denote these variations, the Commission on Isotopic Abundances and Atomic Weights (CIAAW) uses bracketed ranges [a, b] for elements where natural isotopic diversity exceeds , ensuring the interval encompasses 95% of analyzed normal samples with high confidence. For elements with negligible variation relative to analytical limits, a single value with ± is provided, such as 18.998403163 ± 0.000000006 for . The CIAAW criteria specify assigning a range when observed isotopic fluctuations surpass the combined uncertainties in isotopic abundance and determinations; otherwise, a conventional value with uncertainty is adopted to reflect the consensus precision.

Measurement and Determination

Methods for Relative Atomic Mass

The determination of relative atomic masses has evolved significantly since the early , initially relying on chemical methods grounded in and . Pioneering work by chemists like established relative atomic weights by comparing combining ratios in chemical reactions, often using as a reference standard set to unity. By the late 19th and early 20th centuries, gravimetric procedures became dominant, involving the precise measurement of mass ratios in compounds such as halides of the element versus silver halides, as refined by and others to achieve accuracies suitable for stoichiometric calculations. These chemical approaches, exemplified in Ostwald's contributions around 1900, emphasized empirical determination through reproducible reactions but were limited by assumptions of uniform atomic composition. The transition to physical methods began in the 1910s with the advent of , revolutionizing precision by directly resolving isotopic contributions. Francis Aston's development of the mass spectrograph in 1919 enabled the separation and measurement of ions by , allowing for the identification of isotopes and more accurate relative masses beyond average chemical values. This shift marked a departure from purely chemical toward isotopic analysis, with subsequent refinements in instrumentation enhancing resolution to distinguish mass differences as small as 1 part in thousands. Relative atomic mass, denoted Ar(\ceE)A_r(\ce{E}), is defined as the ratio of the average atomic mass of element E to one-twelfth of the mass of an atom of the isotope carbon-12 (12\ceC^{12}\ce{C}), rendering it a dimensionless quantity. This scale, adopted internationally in 1961 by the International Union of Pure and Applied Chemistry (IUPAC) and the International Union of Pure and Applied Physics (IUPAC/IUPAP), replaced the earlier oxygen-16 standard from 1959 to unify chemical and physical measurements. Key principles underpinning these determinations include the conservation of mass in chemical reactions for early methods and the isotopic composition of elements for modern ones, with the carbon-12 reference ensuring consistency across disciplines. The process for computing relative atomic mass involves several steps: first, identifying the stable isotopes of the element through spectroscopic or spectrometric means; second, measuring the relative isotopic masses against the standard; and third, determining the isotopic abundances in a representative sample, typically from terrestrial sources. These abundances are weighted by their fractional contributions to yield the average, accounting for natural variations that can influence precision but are bounded by IUPAC conventions for standard values. Mathematically, this is expressed as: Ar(\ceE)=∑i(Ri⋅mim(12\ceC)/12)A_r(\ce{E}) = \sum_i \left( R_i \cdot \frac{m_i}{m(^{12}\ce{C})/12} \right) where RiR_i is the fractional abundance of isotope ii, mim_i is its absolute mass, and the summation is over all isotopes, normalized to the carbon-12 scale. This weighted average provides the foundation for standard atomic weights, emphasizing the average mass per atom in a typical terrestrial environment.

Isotopic Analysis Techniques

Thermal ionization mass spectrometry (TIMS) serves as the primary technique for high-precision measurement of isotope ratios essential to standard atomic weight determinations, offering exceptional accuracy for elements with low ionization potentials such as strontium, neodymium, and lead. In TIMS, samples are loaded onto a heated filament, where thermal energy ionizes the atoms, and the resulting ion beam is analyzed by a magnetic sector mass spectrometer to resolve isotopic abundances with minimal fractionation. This method has been instrumental in CIAAW evaluations, providing data for recalculating atomic weights of elements like tin and molybdenum. Secondary methods complement TIMS for broader applications, including (ICP-MS), which excels in multi-element isotopic analysis due to its high sample throughput and ability to handle complex matrices without extensive preparation. Multi-collector ICP-MS (MC-ICP-MS) variants enhance precision for non-traditional stable isotopes, as demonstrated in determinations of and abundances. Additionally, secondary ion mass spectrometry (SIMS) enables in-situ analysis of isotopic compositions in geological samples, sputtering material from solid surfaces to ionize and detect isotopes directly, which is particularly useful for spatially resolved studies in rocks and minerals. Calibration of these techniques relies on international reference materials to ensure and comparability across laboratories; for instance, the Institute for Reference Materials and Measurements (IRMM, now part of the European Reference Materials) provides certified standards for heavy elements like lead and . Variations in isotopic ratios are often expressed using delta notation (δ), defined as the per mil deviation from a standard, such as the Vienna Pee Dee Belemnite (V-PDB) for carbon isotopes, facilitating the reporting of natural abundance differences. Modern TIMS and MC-ICP-MS measurements achieve relative precisions down to 10^{-6} for stable isotopes of abundant elements, enabling atomic weight uncertainties as low as 10^{-4} in many cases, though challenges persist for radioactive isotopes with short half-lives or rare nuclides due to low ion yields and interference issues. For elements like or , which lack stable isotopes, atomic weights are derived from nuclear data rather than direct isotopic analysis. Data from multiple laboratories are integrated through biennial CIAAW evaluations, where peer-reviewed measurements are critically assessed for consistency, with the 2024 revision incorporating new isotopic abundance to update standard atomic weights for elements including , , and . This process ensures that published values reflect the most reliable terrestrial averages, excluding anomalous sources like meteorites.

Standardization Conventions

Naming and Terminology Issues

The controversy surrounding the terminology for atomic weights dates back to the mid-20th century, when efforts to modernize highlighted the imprecision of "atomic weight," a term historically implying a gravitational force rather than an . In the , the IUPAC Commission on Atomic Weights proposed replacing it with "" to emphasize its dimensionless nature as a ratio to the atomic mass of , but this shift was rejected by the IUPAC Bureau in favor of retaining "atomic weight" due to its entrenched use in chemical literature and education. Despite the broader adoption of "" for general discussions, the specific tabulated values for elements in normal terrestrial materials continued to be designated as "standard atomic weights" to distinguish them from isotopic or nuclidic masses. A pivotal development occurred in 1975, when the Commission on Atomic Weights and Isotopic Abundances (CIAAW) issued a report that explicitly addressed naming inconsistencies, noting the imprecise definition of "atomic weight (relative atomic mass)" and calling for clearer distinctions in its application to natural samples versus theoretical constructs. This was followed by the 1979 IUPAC General Assembly in , which formalized "standard atomic weight" as the preferred term for the weighted average of an element from normal terrestrial sources, while acknowledging the ongoing debate through parenthetical references to "relative atomic mass." The 2009 CIAAW report further solidified "standard atomic weight" as the official designation for these recommended values, though it introduced "conventional atomic weight" in certain practical contexts—such as education and industry—for fixed, single-value approximations when intervals were otherwise appropriate. Criticisms of the persist, primarily centered on the of "weight" versus "mass," with physicists and metrologists arguing that it perpetuates outdated Newtonian concepts in a relativistic framework, potentially confusing learners about the quantity's dimensionless ratio. Proposals to adopt "standard relative atomic mass" have been repeatedly considered but , largely to preserve and avoid disrupting decades of published and standards. In 2018, the CIAAW issued a clarifying the use of "normal material" in defining standard atomic weights, aiming to resolve educational ambiguities by specifying that these values apply to typical terrestrial samples excluding anomalous isotopic compositions, thereby standardizing in contexts. As of 2025, the IUPAC Green Book (Quantities, Units and Symbols in , 4th edition abridged 2023) endorses "standard atomic weight" exclusively as the term for the Earth-based average relative atomic masses of elements, aligning with biennial CIAAW updates and reinforcing its role in precise scientific communication. This endorsement reflects a consensus that prioritizes historical continuity while addressing metrological accuracy, with "conventional atomic weight" reserved narrowly for simplified, non-interval representations in non-specialized applications.

Types of Atomic Weight Values

Standard atomic weights are presented in various formats to suit different applications, ranging from general educational and commercial uses to precise scientific calculations. These notations reflect the natural isotopic variability of elements and are recommended by the Commission on Isotopic Abundances and Atomic Weights (CIAAW) under the International Union of Pure and Applied Chemistry (IUPAC). Abridged atomic weights provide rounded values suitable for general purposes, such as in textbooks, periodic tables, or , where high precision is not required. These are typically limited to four or five , simplifying the data while capturing essential information; for example, carbon is given as 12.01 rather than the more detailed [12.0096, 12.0116]. This format avoids overwhelming users with uncertainties or intervals for elements that exhibit natural variation. Conventional atomic weights offer a fixed single value for elements where isotopic composition shows limited variation in normal terrestrial materials, ignoring minor ranges to provide a practical representative figure. For instance, , a mononuclidic element with essentially one stable , is assigned 18.998403163 without an interval, as its value derives directly from the measured of ^{19}F. For elements with slight variability, this notation uses a central value with minimal uncertainty, facilitating calculations in chemistry and . The formal short atomic weight presents a precise value accompanied by an uncertainty, ideal for teaching, stoichiometric computations, and scenarios requiring quantified precision. Aluminum, for example, is expressed as 26.9815385 ± 0.0000007, where the accounts for precision and negligible isotopic effects. This format is particularly useful for mononuclidic elements or those with negligible variation, where the value is an exact integer adjusted by experimental , differing from the broader intervals for polyisotopic elements. For elements with significant natural isotopic variation due to geological, biological, or other processes, interval notation denotes the range of possible atomic weights as [low, high]. Lead illustrates this with [206.14, 207.94], reflecting differences in isotopic abundances across terrestrial samples. Elements like , which do not occur naturally in significant quantities and lack a defined terrestrial isotopic composition, are marked with the no-value symbol —, indicating no standard atomic weight can be assigned. IUPAC guidelines, with the most recent revisions in the 2024 updates to the Table of Standard Atomic Weights, specify the appropriate notation based on isotopic variability: intervals for 14 elements prone to large fluctuations, conventional or formal short values for stable ones, and abridged forms for broad accessibility. In 2024, the CIAAW revised standard atomic weights for (to 157.249 ± 0.002), (to 174.96669 ± 0.00005), and (to 91.222 ± 0.001), demonstrating continued refinement for elements with low variability. These conventions ensure consistency in publications while accommodating the dynamic nature of atomic weight data, with mononuclidic elements receiving exact integer-based values without ranges.

Published Data and Applications

Standard Atomic Weights Table

The standard atomic weights (A_r) for the chemical elements, applicable to normal terrestrial materials, are determined and periodically revised by the IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW). These values reflect the weighted average of isotopic abundances, with uncertainties indicating measurement precision and ranges denoting natural variability due to isotopic in geological or biological processes. The triennial report provided comprehensive updates for several elements, including (Tl) with a new range of [204.382, 204.385], while the 2024 revisions adjusted values for (Gd: 157.249(3)), (Lu: 174.96669(2)), and (Zr: 91.222(3)) based on refined isotopic analyses via multi-collector ICPMS, impacting applications in rare-earth technologies and nuclear materials. For synthetic or highly unstable elements beyond (Z > 83), provisional values or mass numbers of the most stable isotopes are used, such as (U: 238.02891(3)) for radioactive cases and (He: 4.002602(2)) for monoisotopic elements with zero-valence stability. The following table presents the standard atomic weights for all elements (Z=1 to 118), sourced directly from the CIAAW database as of 2024. Values are expressed as A_r(0) on the 2005-2006 carbon scale, where (n) denotes in the nth decimal place (e.g., 12.011(1) for carbon), [a, b] indicates a range for variable elements, and footnotes denote special conditions like modified commercial compositions (m), geological variations (g), or radioactive status (r). Most elements (approximately 96) have uncertainties below 0.1%, while 22 exhibit ranges due to natural fractionation processes. Superheavy elements (Z=113 to 118) lack standard weights and are marked with em dashes, pending further evaluation.
Atomic Number (Z)SymbolNameStandard Atomic Weight A_r°Footnotes
1Hhydrogen[1.00784, 1.00811]g, m
2Hehelium4.002602(2)g, r
3Lilithium[6.938, 6.997]g, m
4Beberyllium9.0121831(5)
5Bboron[10.806, 10.821]g
6Ccarbon12.011(1)m
7Nnitrogen[14.00607, 14.00728]g
8Ooxygen15.999
9Ffluorine18.998403163(6)
10Neneon20.1797(6)g
11Nasodium22.98976928(2)
12Mgmagnesium24.3050(6)m
13Alaluminium26.9815385(7)
14Sisilicon[28.084, 28.086]m
15Pphosphorus30.973761998(5)
16Ssulfur[32.059, 32.076]g
17Clchlorine[35.446, 35.457]g
18Arargon[39.792, 39.963]g
19Kpotassium39.0983(1)m
20Cacalcium40.078(4)g
21Scscandium44.955907(5)
22Tititanium47.867(1)m
23Vvanadium50.9415(1)
24Crchromium51.9961(6)
25Mnmanganese54.938043(2)
26Feiron55.845(2)m
27Cocobalt58.933193(5)
28Ninickel58.6934(4)
29Cucopper63.546(3)
30Znzinc65.38(2)g
31Gagallium69.723(1)
32Gegermanium72.6306(8)
33Asarsenic74.921595(6)
34Seselenium78.971(8)g
35Brbromine[79.901, 79.907]g
36Krkrypton83.798(2)g
37Rbrubidium85.4678(3)g
38Srstrontium[87.59, 87.64]g
39Yyttrium88.90584(2)
40Zrzirconium91.222(3)m
41Nbniobium92.90637(2)
42Momolybdenum95.95(1)g
43Tctechnetium—r
44Ruruthenium101.07(2)g
45Rhrhodium102.90550(2)
46Pdpalladium106.42(1)g
47Agsilver107.8682(2)g
48Cdcadmium[111.91, 112.02]g
49Inindium114.818(3)
50Sntin[118.69, 118.72]g
51Sbantimony121.760(1)
52Tetellurium[127.50, 127.61]g
53Iiodine126.90447(3)
54Xexenon131.293(6)g
55Cscaesium132.90545196(6)
56Babarium[137.286, 137.344]g
57Lalanthanum138.90547(7)g
58Cecerium[140.11, 140.12]g
59Prpraseodymium140.90766(2)
60Ndneodymium[143.79, 143.83]g
61Pmpromethium—r
62Smsamarium150.36(2)g
63Eueuropium151.964(1)g
64Gdgadolinium157.249(3)
65Tbterbium158.92535(2)
66Dydysprosium162.500(1)g
67Hoholmium164.93033(2)
68Ererbium167.259(3)g
69Tmthulium168.93422(2)
70Ybytterbium173.045(10)g
71Lulutetium174.96669(2)
72Hfhafnium178.486(6)g
73Tatantalum180.94788(2)
74Wtungsten183.84(1)g
75Rerhenium186.207(1)g
76Ososmium190.23(3)g
77Iriridium192.217(2)
78Ptplatinum195.084(9)g
79Augold196.966569(4)
80Hgmercury[200.51, 200.59]g
81Tlthallium[204.382, 204.385]g
82Pblead[206.14, 207.94]g
83Bibismuth208.98040(1)
84Popolonium[208.982, 209.982]r
85Atastatine[209.987, 210.987]r
86Rnradonr
87Frfranciumr
88Raradiumr
89Acactiniumr
90Ththorium232.0377(4)g
91Paprotactinium231.03588(2)
92Uuranium238.02891(3)g
93Npneptuniumr
94Puplutoniumr
95Amamericiumr
96Cmcuriumr
97Bkberkeliumr
98Cfcaliforniumr
99Eseinsteiniumr
100Fmfermiumr
101Mdmendeleviumr
102Nonobeliumr
103Lrlawrenciumr
104Rfrutherfordium—
105Dbdubnium—
106Sgseaborgium—
107Bhbohrium—
108Hshassium—
109Mtmeitnerium—
110Dsdarmstadtium—
111Rgroentgenium—
112Cncopernicium—
113Nhnihonium—
114Flflerovium—
115Mcmoscovium—
116Lvlivermorium—
117Tstennessine—
118Ogoganesson—
Footnotes: g = geological materials may have variable isotopic composition; m = modified isotopic compositions in commercial materials; r = radioactive element with no isotopes. Non-terrestrial materials (e.g., lunar samples) may deviate from these values. The conventional form uses abridged values for practical applications, such as carbon at 12.01.

Integration in Periodic Table

In the IUPAC Periodic Table of the Elements, standard atomic weights are positioned directly below the for each element, following the and element name in a standardized layout that facilitates quick . For elements with fixed values, these are presented as single numbers with uncertainties in parentheses, such as at 6.94 ± 0.06, while variable isotopic compositions are denoted using interval notation in square brackets, for example, as [1.00784, 1.00811]. This notation, introduced by the Commission on Isotopic Abundances and Atomic Weights (CIAAW) since 2009, replaced earlier fixed values to better reflect natural terrestrial variability, differing from pre-2000s tables that used precise single figures without ranges, such as at 35.453. elements beyond , such as those with atomic numbers 113–118, lack assigned standard atomic weights due to their unstable isotopes and absence of characteristic terrestrial compositions, often marked with provisional notations or omitted in the weights column. Educational periodic tables adapt standard atomic weights for accessibility, employing abridged values rounded to fewer significant figures—typically four or five—to simplify learning without overwhelming students with full uncertainties or intervals. For instance, introductory materials might list carbon as 12.01 instead of the full [12.0096, 12.0116], prioritizing conceptual understanding in basic chemistry curricula, while advanced versions retain the IUPAC-recommended intervals and uncertainties for precise applications. The 2024 revisions to atomic weights, as incorporated in the latest IUPAC table (updated through 2024), serve as the authoritative source, ensuring consistency across global educational resources. These integrated weights form the foundation for calculations in chemical education and practice, enabling accurate determinations for reactions and compound synthesis. In reference materials, they underpin databases like the NIST Atomic Weights database, which compiles values for elements 1–118, and propagate updates to platforms such as , where revised weights—such as those for , , and in 2024—are automatically incorporated to maintain in tools.

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