Clarifying Atomic Weights: A 2016 Four-Figure Table of Standard

Article pubs.acs.org/jchemeduc

Clarifying Atomic Weights: A 2016 Four-Figure Table of Standard and Conventional Atomic Weights Tyler B. Coplen,*,† Fabienne Meyers,*,‡ and Norman E. Holden*,§ †

U.S. Geological Survey, Reston, Virginia 20192, United States International Union of Pure and Applied Chemistry, c/o Chemistry Department, Boston University, Boston, Massachusetts 02215, United States § National Nuclear Data Center, Brookhaven National Laboratory, Upton, New York 11973, United States ‡

S Supporting Information *

ABSTRACT: To indicate that atomic weights of many elements are not constants of nature, in 2009 and 2011 the Commission on Isotopic Abundances and Atomic Weights (CIAAW) of the International Union of Pure and Applied Chemistry (IUPAC) replaced single-value standard atomic weight values with atomic weight intervals for 12 elements (hydrogen, lithium, boron, carbon, nitrogen, oxygen, magnesium, silicon, sulfur, chlorine, bromine, and thallium); for example, the standard atomic weight of nitrogen became the interval [14.00643, 14.00728]. CIAAW recognized that some users of atomic weight data only need representative values for these 12 elements, such as for trade and commerce. For this purpose, CIAAW provided conventional atomic weight values, such as 14.007 for nitrogen, and these values can serve in education when a single representative value is needed, such as for molecular weight calculations. Because atomic weight values abridged to four figures are preferred by many educational users and are no longer provided by CIAAW as of 2015, we provide a table containing both standard atomic weight values and conventional atomic weight values abridged to four figures for the chemical elements. A retrospective review of changes in four-digit atomic weights since 1961 indicates that changes in these values are due to more accurate measurements over time or to the recognition of the impact of natural isotopic fractionation in normal terrestrial materials upon atomic weight values of many elements. Use of the unit “u” (unified atomic mass unit on the carbon mass scale) with atomic weight is incorrect because the quantity atomic weight is dimensionless, and the unit “amu” (atomic mass unit on the oxygen scale) is an obsolete term: Both should be avoided. KEYWORDS: High School/Introductory Chemistry, First-Year Undergraduate/General, Second-Year Undergraduate, Nomenclature/Units/Symbols, Isotopes, Atomic Properties/Structure, Periodicity/Periodic Table

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ATOMIC WEIGHTS UPDATE The ability to measure atomic weight (terms in bold font are defined in a glossary in Supporting Information) values is regularly improving with time. However, variations have been measured in the atomic weight values of many chemical elements found in natural sources and in reagents on laboratory shelves, and these variations can greatly exceed the accuracy in the measurement of any one sample of the element. Unless one knows the exact source of a sample, this natural variation can limit the accuracy that can be assigned to the atomic weight of an element in a sample. It is therefore the task of the IUPAC (International Union of Pure and Applied Chemistry) Commission on Isotopic Abundances and Atomic Weights (CIAAW) to regularly review atomic weight determinations and release updated standard atomic weight values based on an evaluation of peer-reviewed publications. According to the most recent (2013) review of atomic weights by CIAAW,1 even the most simplified table abridged to four significant digits (and therefore many periodic tables, which present these values) may need updates. The most recent CIAAW evaluation (2015) notes an updated standard atomic weight value for the element ytterbium (Yb).2 © XXXX American Chemical Society and Division of Chemical Education, Inc.

WHAT IS AN ATOMIC WEIGHT? The atomic weight of an element E, symbol Ar(E), in a given sample is the sum of the products of the relative atomic mass and the fraction of the amount of each stable isotope and each radioactive isotope (having a sufficiently long half-life and sufficiently large mole fraction that a characteristic terrestrial isotopic composition can be listed for it in IUPAC’s Table of Isotopic Compositions of the Elements3) of that element in a given sample. The fraction of the amount of a specified isotope in a sample is also called the mole fraction, the amount fraction, the atom fraction, and the isotopic abundance. Because relative atomic masses are known with high accuracy, the standard atomic weights of elements having only one stable or long-lived radioactive isotope (greater than 32,500 years, e.g., for protactinium) are also known with high accuracy. For example, gold-197 (197Au) is the only stable isotope of gold and its relative atomic mass = Ar(197Au) = 196.96657, Received: July 11, 2016 Revised: December 16, 2016

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DOI: 10.1021/acs.jchemed.6b00510 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

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Figure 1. Variation in atomic weight and mole fraction of 11B of selected boron-bearing materials. Adapted with permission from ref 5.

these four, a standard atomic weight can be determined. Note that atomic weights are dimensionless quantities because relative atomic masses are scaled (expressed relative) to 1/12 the mass of a carbon-12 atom. The unit “u” (unified atomic mass unit on the carbon mass scale) and the unit “amu” (the atomic mass unit on the oxygen mass scale) are sometimes seen in the literature as a unit for the atomic weight. Use of either of these units is incorrect because atomic weight is a dimensionless quantity. In addition, “amu” is an obsolete term because the oxygen mass scale has not been used in science in more than a half-century since IUPAC and the International Union of Pure and Applied Physics (IUPAP) agreed to use the carbon mass scale for atomic masses.4

expressed to 8 digits. Thus, gold’s standard atomic weight, Ar(Au), is equal to its relative atomic mass and is expressed relatively accurately as 196.96657, which would be rounded to 197.0 in a four-digit table. For elements with more than one stable or long-lived radioactive isotope, the accuracy of an atomic weight is substantially lower because the accuracy with which the mole fraction of each isotope in a given specimen can be determined is lower. For example, boron has two stable isotopes, 10B and 11B, having relative atomic masses, respectively, of 10.0129370 and 11.0093054, expressed to 9 digits. The best measurement of the mole fractions of 10B and 11 B in a specimen gives 0.1982 ± 0.0002 and 0.8018 ± 0.0002, respectively.3 This yields an atomic weight, Ar(B), of

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A r (B) = (10.0129370 × 0.1982 ± 0.0002)

MANY STANDARD ATOMIC WEIGHTS ARE NOT CONSTANTS OF NATURE Although many of us were taught that standard atomic weight values found on the periodic table in our chemistry classrooms are constants of nature, it has been known for more than half a century that atomic weights of many elements are not constants of nature. However, only in the past few years was the IUPAC Table of Standard Atomic Weights updated to clarify this fact by replacing single-value atomic weight values by atomic weight intervals.6−8 For example, starting in the 2009 Table, the standard atomic weight of boron was changed from 10.811 ± 0.007 to the interval standard atomic weight value [10.806, 10.821] to indicate that the atomic weight of naturally occurring boron samples, which includes normal chemical reagents, can range between 10.806 and 10.821, depending upon the

+ (11.0093054 × 0.8018 ± 0.0002) A r (B) = 10.8118 ± 0.0002

for the substance analyzed for the best measurement. Analytical uncertainty in the measurement of the amounts of the two boron isotopes in a sample limits the atomic weight of boron to an accuracy of approximately 2 parts in 108,000 parts, i.e., about 1 part in 54,000 parts. The natural variation of the fraction of the amount of 11B in a sample further limits the atomic weight, as shown in Figure 1 for selected boron-bearing materials. For elements with no stable isotopes and only radioactive isotopes, a standard atomic weight cannot be calculated, except for four elements (bismuth, thorium, protactinium, and uranium) that do have a characteristic terrestrial isotopic composition; for B



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Table 1. Four-Place Table of Standard Atomic Weight Values of Hydrogen through Uranium Compared Since 1961a Atomic Number

Symbol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La Ce Pr Nd

Value 1961b 1.008 4.003 6.939 9.012 10.81 12.01 14.01 16.00 19.00 20.18 22.99 24.31 26.98 28.09 30.97 32.06 35.45 39.95 39.10 40.08 44.96 47.90 50.94 52.00 54.94 55.85 58.93 58.71 63.54 65.37 69.72 72.59 74.92 78.96 79.91 83.80 85.47 87.62 88.91 91.22 92.91 95.94

Value 1975c

Value 2007e

Value 2009f

Value 2011g

Value 2013h

[1.007, 1.009] 6.941k

6.941(2)

10.81k

10.81

24.31k

24.31

[6.938, 6.997] 10.81k

[10.80, [12.00, [14.00, [15.99,

10.83] 12.02] 14.01] 16.00]

[24.30, 24.31] [28.08, 28.09]

32.06k

32.07

39.95k

39.95

40.08k

40.08

40.08k

47.88(3)

47.87

58.70 63.55 65.38

32.07k

[32.05, 32.08] [35.44, 35.46]

58.69 65.39(2)

65.38(2)

72.59(3)

72.64

72.63

78.96(3)

78.97

79.90

87.62k

[79.90, 79.91]

87.62

83.80k 85.47k 87.61k

87.62k

91.22k 95.96(2)k (97)

101.1 102.9 106.4 107.9 112.4 114.8 118.7 121.8 127.6 126.9 131.3 132.9 137.3 138.9 140.1 140.9 144.2

Value 1983d

95.95k

Value 2015i

Current Valuej [1.007, 1.009] 4.003 [6.938, 6.997] 9.012 [10.80, 10.83] [12.00, 12.02] [14.00, 14.01] [15.99, 16.00] 19.00 20.18 22.99 [24.30, 24.31] 26.98 [28.08, 28.09] 30.97 [32.05, 32.08] [35.44, 35.46] 39.95 39.10 40.08k 44.96 47.87 50.94 52.00 54.94 55.85 58.93 58.69 63.55 65.38(2) 69.72 72.63 74.92 78.97 [79.90, 79.91] 83.80k 85.47k 87.62k 88.91 91.22k 92.91 95.95k

98.91 101.1k

101.1k 102.9 106.4k 107.9k 112.4k 114.8 118.7k 121.8k 127.6k 126.9 131.3k 132.9 137.3 138.9 140.1k 140.9 144.2k

106.4k 107.9k 112.4k 118.7k 121.8k 127.6k 131.3k

140.1k 144.2k C



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Table 1. continued

a

Atomic Number

Symbol

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92

Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Th Pa U

Value 1961b 150.4 152.0 157.3 158.9 162.5 164.9 167.3 168.9 173.0 175.0 178.5 180.9 183.9 186.2 190.2 192.2 195.1 197.0 200.6 204.4 207.2 209.0

Value 1975c

Value 1983d

(145)

144.9

Value 2007e

Value 2009f

Value 2013h

Value 2015i

150.4k 152.0k 157.3k 162.5k 167.3k 173.1k

173.0k

183.8 190.2k

207.2k (209) (210) (222) (223) (226) (227)

207.2

[204.3, 204.4] 207.2 209.0k

207.2k

209.0

232.0k (231) 238.0k

Current Valuej 150.4k 152.0k 157.3k 158.9 162.5k 164.9 167.3k 168.9 173.0k 175.0 178.5 180.9 183.8 186.2 190.2k 192.2 195.1 197.0 200.6 [204.3, 204.4] 207.2 209.0

210.0 210.0 222.0 223.0 226.0 227.0

232.0 238.0

Value 2011g

231.0 238.0

238.0k

232.0k 231.0 238.0k

b

See ref 15. Four-digit values based on those published in the Comptes Rendus of the 21st Conference of IUPAC, Montreal, 2−5 August 1961, and reproduced in J. Am. Chem. Soc. in 1962.4 This report constituted the most significant standard atomic weights table of the middle 20th century and was authored by A. E. Cameron and E. Wichers.4 This report corresponded with the change in the atomic mass standard from oxygen-16 to carbon12 and provided the first of a number of element-by-element reviews of all of the standard atomic weight values by the International Commission on Atomic Weights (now CIAAW). cThe first Table of Atomic Weights to Four Significant Figures was published in 1975 and developed under guidance of the Commission on Atomic Weights by the IUPAC Committee on Teaching of Chemistry,16 and it was based on the 1975 values published by the Commission on Atomic Weights.16 dFour-digit values based on the 1983 values published by the Commission on Atomic Weights and Isotopic Abundances.17 eFour-digit values as published in 2009.18 In this report, CIAAW actually evaluated and published standard atomic weight tables abridged to four and five significant figures, a practice that was repeated in the subsequent two reports. fFour-digit values as published in 2011.6 In addition, to include abridged values, this report coincides with the first publication of standard atomic weight values expressed as intervals for selected elements. Specifically, the standard atomic weights of 10 elements having two or more stable isotopes were changed to reflect the variability of atomic weight values in natural terrestrial materials. gFour-digit values as published in 2013.19 In this report, two more elements were reported in terms of intervals to reflect the common occurrence of variations in the atomic weights of those elements in normal terrestrial materials. hFour-digit values based on the latest values published in 2016 by CIAAW.1 In this report, CIAAW discontinued the publication of standard atomic weight tables abridged to four significant figures; instead, it released an unabridged table and a table abridged to five significant figures. iFour-digit value based on the IUPAC press release of 24 Aug 2015.2 jCumulative values as deduced from all previous reports. The full text of the PAC references cited above is directly accessible from Pure and Applied Chemistry.20 kValue may differ from the atomic weights of the relevant elements in some normal materials because of a variation in the mole fractions of the element’s stable isotopes; uncertainty in standard atomic weight larger than ±1 appears in parentheses, following the last significant digit to which it is attributed.

samples, which were more precise, and they chose those literature values over the IUPAC recommendations thinking that they had the best value for their sample. The interval notation was introduced to inform users about the basic problem of natural variations of amounts of isotopes of elements and why the choice of a more precise literature value is incorrect unless that value corresponds to the same source of the element as their own sample. Today, the standard atomic weight values of 12 elements are best reported as intervals; these are hydrogen, lithium, boron,

source of the material (Figure 1). Obviously, if one knows the source of boron in a sample, one may have a more accurate value for the atomic weight. However, if the source is unknown, the value of the atomic weight could be at one extreme or the other shown in Figure 1. These extremes are the end-points of the standard atomic weight interval quoted in Table 1. In the past, the standard atomic weight was quoted as a midpoint and the range as the standard atomic weight uncertainty. However, many users were aware of published atomic weight values for D



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Table 2. Standard and Conventional Atomic Weights 2016 Abridged to Four Significant Digitsa,b Atomic Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

Element Name hydrogen helium lithium beryllium boron carbon nitrogen oxygen fluorine neon sodium magnesium aluminium (aluminum) silicon phosphorus sulfur chlorine argon potassium calcium scandium titanium vanadium chromium manganese iron cobalt nickel copper zinc gallium germanium arsenic selenium bromine krypton rubidium strontium yttrium zirconium niobium molybdenum technetiumc ruthenium rhodium palladium silver cadmium indium tin antimony tellurium iodine xenon caesium (cesium)

Standard Atomic Symbol Weight

Atomic Number

Conventional Atomic Weight

H He Li Be B C N O F Ne Na Mg Al

[1.007, 4.003 [6.938, 9.012 [10.80, [12.00, [14.00, [15.99, 19.00 20.18 22.99 [24.30, 26.98

1.009]

1.008

6.997]

6.94

10.83] 12.02] 14.01] 16.00]

10.81 12.01 14.01 16.00

24.31]

24.31

Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs

[28.08, 30.97 [32.05, [35.44, 39.95 39.10 40.08 44.96 47.87 50.94 52.00 54.94 55.85 58.93 58.69 63.55 65.38 69.72 72.63 74.92 78.97 [79.90, 83.80 85.47 87.62 88.91 91.22 92.91 95.95

28.09]

28.09

32.08] 35.46]

32.06 35.45

79.91]

Table 2. continued

56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

79.90

101.1 102.9 106.4 107.9 112.4 114.8 118.7 121.8 127.6 126.9 131.3 132.9

E

Element Name barium lanthanum cerium praseodymium neodymium promethiumc samarium europium gadolinium terbium dysprosium holmium erbium thulium ytterbium lutetium hafnium tantalum tungsten rhenium osmium iridium platinum gold mercury thallium lead bismuthc poloniumc astatinec radonc franciumc radiumc actiniumc thoriumc protactiniumc uraniumc neptuniumc plutoniumc americiumc curiumc berkeliumc californiumc einsteiniumc fermiumc mendeleviumc nobeliumc lawrenciumc rutherfordiumc dubniumc seaborgiumc bohriumc hassiumc meitneriumc darmstadtiumc roentgeniumc coperniciumc

Symbol Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf Db Sg Bh Hs Mt Ds Rg Cn

Standard Atomic Weight


137.3 138.9 140.1 140.9 144.2 150.4 152.0 157.3 158.9 162.5 164.9 167.3 168.9 173.0 175.0 178.5 180.9 183.8 186.2 190.2 192.2 195.1 197.0 200.6 [204.3, 204.4] 207.2 209.0

204.4

232.0 231.0 238.0



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Table 2. continued Atomic Number 113 114 115 116 117 118

Element Name nihoniumc fleroviumc moscoviumc livermoriumc tennessinec oganessonc

Symbol

Standard Atomic Weight


Nh Fl Mc Lv Ts Og

See ref 24, which provides Microsoft Excel and Word files as educational resources. bScaled to an atomic weight of 12 for carbon-12 (12C), where 12C is a neutral atom in its nuclear and electronic ground state, having the result that atomic weight values are dimensionless. The atomic weights of many elements are not invariant, but depend on the origin and treatment of the material. The standard atomic weights apply to elements of natural terrestrial origin. Although the atomic weights of some elements in some naturally occurring materials may differ from given values because of a variation in the mole fractions of an element’s stable isotopes, the last significant figure of each tabulated value is considered reliable to ±1 except for zinc, which is ±2. For 12 of these elements, both a conventional atomic weight and an atomic weight interval are given with the symbol [a, b] to denote the set of atomic weight values in normal materials; thus, a ≤ atomic weight ≤ b. For lithium, the conventional atomic weight is only three digits because of the large variation found in lithium-bearing reagents. cElement has no stable isotopes, only radioactive isotopes, and an atomic weight cannot be determined. However, four such elements (Bi, Th, Pa, and U) do have a characteristic terrestrial isotopic composition, and for these a standard atomic weight is tabulated. a

carbon, nitrogen, oxygen, magnesium, silicon, sulfur, chlorine, bromine, and thallium. For these 12 elements, the standard atomic weight is given as an atomic weight interval with the symbol [a, b] to denote the set of atomic weight values in normal materials;6 thus, a ≤ atomic weight value ≤ b. Symbols a and b denote the lower and upper bounds of the interval [a, b], respectively. CIAAW recognized that some users of atomic weight data only need typical values for the 12 elements having interval atomic weight values, such as for trade and

Figure 3. U.S. Geological Survey research diver holds 16.5-in (42-cm)long core of calcite (DH-11) immediately after removal at a depth of 30 m below the water table, Devils Hole,10 Nevada, June 24, 1987. DH-11 yielded a remarkable climatic record.9 Coring rack is visible below scuba tank. Reprinted with permission from ref 13.

Figure 2. Variation in atomic weight of hydrogen in river waters across the continental United States. Adapted with permission from ref 12. Copyright 2001 John Wiley and Sons. Blue color indicates waters most depleted in 2H (resulting in lower atomic weight of hydrogen), and brown indicates those most enriched in 2H (resulting in higher atomic weight of hydrogen). F



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Figure 4. Atomic weight of oxygen in a vein calcite core (CaCO3) from Devils Hole,10 Nevada, is a proxy for sea surface temperature off of southern California between 4.5 and 160 thousand years ago. Data from ref 14. Higher atomic weight values of oxygen in CaCO3 indicate higher sea surface temperatures, and lower atomic weight values of oxygen in CaCO3 indicate lower sea surface temperatures.

commerce. For these purposes, CIAAW provides conventional atomic weight values, and we have abridged these values to four significant figures (last column of Table 2), except for lithium which was abridged by CIAAW to three significant figures (6.94) because the four significant figure value of 6.940 is too precise and did not encompass naturally occurring materials, which include chemical reagents.6 The variation in atomic weight in normal materials owing to natural isotopic fractionation is useful in a wide variety of scientific fields. For example, hydrogen isotopes in water are fractionated by evaporation and precipitation processes, leading to a variation in the atomic weight of hydrogen in river water (Figure 2). These variations in hydrogen isotopic composition (and atomic weight) are used in hydrology and environmental science for identifying and tracing water sources and for investigating groundwater−surface water interaction, and for a host of other uses. Concomitantly, variations in the atomic weight of oxygen in precipitation and groundwater are reflected in the atomic weight of oxygen of calcite (CaCO3) precipitated from groundwater over the last several hundred thousand years.9 Figure 3 shows a calcite core drilled from Devils Hole,10 a cave in southern Nevada. Increasing sea surface temperatures give rise to higher abundances of 18O (higher atomic weights of oxygen) in precipitation and groundwater, and to CaCO3

precipitating from these groundwaters, including calcite precipitated at Devils Hole (Figure 4). Decreasing sea surface temperatures give rise to lower abundances of 18O (lower atomic weights of oxygen) in precipitation, groundwater, and Devils Hole calcite (Figure 4), and these variations are of substantial interest in the study of paleoclimatology and climate change. Even elements with higher atomic numbers can display substantial isotopic fractionation.11 Influence of Variations of Mole Fractions

Variations in mole fractions of stable and radioactive isotopes in normal materials give rise to the variabilities observed in atomic weights of many elements. While the atomic weight of an element can be determined in any material, the standard atomic weight represents the atomic weight of an element in all normal terrestrial materials. All stable (nonradioactive) isotopes and 36 radioactive isotopes, which have half-lives greater than 32,500 years (e.g., for protactinium) and sufficiently large mole fractions that they are listed in IUPAC’s Table of Isotopic Compositions of the Elements,3 contribute to the determination of the standard atomic weights, giving rise to expanded uncertainties in many elements having two or more stable isotopes (or radioactive isotopes that are listed in IUPAC’s Table of Isotopic Compositions of the Elements3). G



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Despite regular improvements in analytical instrumentation, the ranges in mole fractions of isotopes in normal materials prevent more precise values of standard atomic weight from being determined for many elements, for example, argon, nickel, copper, zinc, selenium, strontium, and lead.1 Uncertainties of standard atomic weights are also examined and reported regularly by CIAAW. Readers interested in more details should refer to the full text of CIAAW reports and the careful annotations conveyed in the footnotes (see Meija et al.,1 Wieser and Coplen,6 and Coplen and Holden21).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.6b00510. Glossary of terms in bold font in this article (PDF, DOCX)

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AUTHOR INFORMATION

Corresponding Authors

Rounded Values to Four Significant Figures

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected].

Forty years ago, the first Table of Atomic Weights to Four Significant Figures, based on the 1975 values, was developed under guidance of the Commission and published by the IUPAC Committee on Teaching of Chemistry.16 In more recent years, similar tabulations were also published in the IUPAC scientific journal, Pure and Applied Chemistry, along with detailed CIAAW biennial reviews. The Commission recognized that the details and number of significant digits reported in the full Table of Standard Atomic Weights (e.g., up to nine digits for aluminium (aluminum) or fluorine, or even 10 digits for caesium (cesium)) exceed the need and interests of many users. The abridged table was also published with the expectation that subsequent changes would be minimal. As a retrospective review of such changes, we present in Table 1 the four-digit standard atomic weight values (either published or deduced) over time for elements from hydrogen through uranium since the seminal 1961 report by A. E. Cameron and E. Wichers.4 This report was the first element-byelement review of all of the standard atomic weight values by the Commission, and it corresponded with changing the atomic mass standard from oxygen-16 to carbon-12. From examination of Table 1, one can see that the expectation of minimal changes in standard atomic weight values was a valid prediction.22 Except for six elements (lithium, boron, sulfur, titanium, nickel, and germanium), the four-digit standard atomic weight values have not changed over five decades by more than one digit in the last place. For three of these elements (lithium, boron, and sulfur), the differences are due to recognition of natural isotopic fractionation in normal materials. The improvements in the others, titanium, nickel, and germanium, are due to the use of isotope-ratio mass spectrometry to determine improved mole fractions of isotopes and more accurate values of atomic weight.23 Reviewing the values reported in the 2013 table1 triggered updates to the four-digit standard atomic weight values of selenium and molybdenum. The recent 2015 CIAAW evaluation2 triggered an additional update for the element ytterbium. In these cases, the revisions are due to improved measurements using multicollector inductively coupled plasma mass spectrometry. In its most recent report, CIAAW did not publish a Table of the Standard Atomic Weights abridged to four significant digits and decided in 2015 to discontinue publishing tables abridged to four significant digits. With Table 2, we present for the first time a table containing both standard and conventional atomic weights abridged to four significant digits. This table, which is available as pdf, Microsoft Word, and Microsoft Excel files, 24 enables educators to select atomic weight interval values for discussions of variations in atomic weights of many elements, as well as to provide students with conventional atomic weight values for classroom calculations.

ORCID

Tyler B. Coplen: 0000-0003-4884-6008 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The comments of Dr. Isaac Winograd (U.S. Geological Survey, retired), Ms. Kerri Miller (University of Calgary, Canada), Prof. Peter Atkins (Lincoln College, U.K.), Prof. Ian Mills (University of Reading, U.K.), Prof. Peter Mahaffy (The King’s University, Edmonton, Canada), and Ms. Jacqueline Benefield (U.S. Geological Survey) are appreciated and substantially improved this manuscript. The support of the U.S. Geological Survey National Research Program made this report possible. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

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REFERENCES

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Clarifying Atomic Weights: A 2016 Four-Figure Table of Standard

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