Comment
Conclusion
Acknowledgements
References
COMMENT
At frequent intervals (biennially in recent times),
the International Union of Pure and Applied Chemistry (IUPAC) publishes
revised tables of recommended atomic-weight values, Ar(E),
for chemical element E. Recent editions of tables include uncertainties,
U[Ar(E)], and refer to the tabulated Ar(E)
values as "standard atomic weights" applicable reliably to
normal terrestrial sources. The latest such IUPAC table is based on
a reevaluation in 1997 (ref. 1). In the table submitted
here (Table
1), we list all recommended values since 1882, but exclude radioactive
elements without stable isotopes (or radio-isotopes with half-lives
comparable to the age of the earth). The values are shown in atomic-number
order (column 1), with the currently recognized chemical symbol of element
E (column 2), and current IUPAC recommended element name (column 3).
A year, column 4, is given only when the Commission recommended for
the element a new atomic-weight value, Ar(E), (column
5) or its uncertainty, U[Ar(E)]1
(column 6; ref. 2). These values remain valid until
the year of another change. No entry made for any element in a year
implies that the last earlier entry is still current and that any later
determinations have not lead the Commission to change the relevant recommended
values. It is the stated policy of the Commission to refrain from such
a change unless that change would result in a significant improvement
in value or its uncertainty.
1In accordance with IUPAC's atomic
weights Commission's statements, we have used for the uncertainty symbol
a capital "U" as recommended in the ISO Guide to the expression of uncertainty
in measurement (ref. 2) to indicate an expanded uncertainty. Although
the Commission has declined to specify the degree of expansion, i.e.
the recommended K value, we believe it is expected to correspond to
at least two standard deviations.
Mononuclidic elements have highly accurate Ar(E)
values that depend only on the numeric value of the atomic mass of the
nuclide. Recommended nuclidic mass values are published in tables (ref.
3) with sponsorship by the International Union of Pure and Applied
Physics.
The element symbol and name for some elements have
changed during the last century, as has the spelling of elements authorized
by international commissions. These changes are summarized in Table
2. It may be noted that in the International Commission report of
1906 it was mentioned that Urbain and Auer had independently proved
that the "old" ytterbium was a mixture of two elements, for
the second of which Urbain had suggested, and the Commission approved,
lutecium. To avoid confusion, the optional name, neoytterbium, for the
other element was recommended. A symbol appears not to have been proposed.
The optional name neoytterbium was not abandoned until 1925.
Table of the values in history
The values for Ar(E) in our table
for years prior to the founding in 1920 of IUPAC are those in International
Critical Tables (ICT) (ref. 4) assembled by G.
P. Baxter, based on the International Atomic Weights Commission values
Ar(E) since that Commission's first substantive report
in 1903 (ref. 5). The Commission membership of
F. W. Clarke (U.S.A.), W. Ostwald (Germany), T. E. Thorpe (Great Britain),
and G. Urbain (France) was designed to be small. It remained the same
up to World War I, but the reports during the war years were no longer
signed by Ostwald.
Early values. Many early determinations
and lists of atomic weights were quoted both as scaled to hydrogen (1)
and to oxygen (16). Since, for most elements, the latter scale related
more directly to the chemical determinations employed, and thus did
not depend on the uncertainty of the Ar(O)/Ar(H)
ratio, the oxygen scale was generally preferred, and are used here without
adjustment. The correction factor for converting atomic weights from
the old chemical Ar(16O) = 16 scale to
the new Ar(12C) = 12 scale is 0.9999625
and would be negligible. For a few early physical determinations of
atomic weights based on Ar(16O) = 16, the
correction factor is 0.99968218 and could not be neglected for 18 values
in our table, namely: for Be in 1949, C (1953), Na (1953), P (1951),
S (1947), In (1955), I (1951), Sm (1955), Gd (1955), Tb (1953), Dy (1955),
Er (1955), Tm (1953), Ta (1953), W (1955), Re (1955), Pt (1955), and
Th (1953). The adjustments made to these 18 values were very small compared
with the changes and uncertainties of the atomic-weight values as discussed
herein.
Prior to 1903, Baxter quotes the values from the American
Chemical Society's Atomic Weights Committee which he himself chaired
after 1912. That Committee was chaired by F. W. Clarke between 1894
and 1912, when it made significant changes (ref. 6)
from Clarke's own 1882 recalculation of the atomic-weight values (ref.
7). The values in that 1882 calculation represented significant
improvements in methods of Ar(E) determination and
their critical analysis. These values are quoted as the starting values
by Baxter in the ICT collection (ref. 4) and also
in the table presented here (Table 1).
For the remaining years before 1903, the reports of
the American Committee on Atomic Weights differed from the subsequent
1903 International Committee reports in the omission of chemical symbols
in the atomic-weight tables. Only the full chemical names were listed.
Helium and argon, though listed from 1882, were not given Ar
values in the American reports until 1901, the year in which neon, krypton,
and xenon first appeared in the tables but also without values (refs.
5 & 8).
Minor questions of interpretation. Where Baxter's
ICT 1925 values disagree slightly with the IUPAC Commission's 1925 report
(ref. 9), we have chosen to select the latter,
interpreting the ICT values to be applicable until, but not including,
1925. There are very small discrepancies (usually only in the inclusion
or exclusion of a final zero) between the ICT values and some national
reprintings of the International Atomic Weights Commission's Ar(E)
values. For our table, we have adopted the ICT values. Baxter also had
to make some interpretive decisions on the applicable year of a report.
The so-called 1920/21 international report (ref.10),
for example, was first published in July 1920 (in Britain) and in September
1920 (in the U.S.A.), whereas a slightly differing international report
for 1921 was issued later (ref. 11).
We are not concerned with a few more important differences
between Ar(E) values in the American and independent
German Commission on Atomic Weights (ref.12) as
well as those in the short-lived British (ref. 13),
Spanish (ref.14) and Swiss (ref.15)
committees. Following Baxter's lead, only the internationally recommended
values are given in our table after 1903.
Estimated uncertainties. In recent years, the
IUPAC Atomic-Weight Tables have given uncertainty estimates to all Ar(E)
values, but prior to 1969 the majority of the values did not carry a
quoted uncertainty. Where not recorded, we have entered such expanded
uncertainty values based on general statements of the reliability to
be expected from recommended values. Any such assignment of uncertainties
is necessarily open to doubt. From statements made by those who performed
earlier atomic-weight measurements, we have the impression that the
published data were intended to be truncated to such an extent that
these scientists felt confident to the last given digit. Our initial
fear was that we were overestimating the intended, but unstated uncertainties,
by uniformly giving U[Ar(E)] equal 3 in the
last quoted digit. The only exception we have made is for estimates
of Clarke's original 1882 Ar(E) values, which we estimated
to �0.10 because Clarke explained (ref. 7) that
he had quoted all Ar(E) values to two decimals even
though he thought they were not all reliable to that accuracy. Readers
may find one or two U[Ar(E)] values of very
early Ar(E) values grossly excessive, such as Ar(C)
= 12 � 3, until it is remembered that the author did not give any decimal
figures because he had considerable doubt of the carbon valency of 4
rather than 2 based on CO, cyanates, and lingering doubts on benzene.
As the reader will see in Table 1, the assigned uncertainties,
in the light of the analysis presented here, were in fact underestimated.
Is it not typical of all experimental scientists that, unaware of unknown
error sources and unable to assess the effects of unlikely but large
sources, their uncertainties tend to be too low?
Deviations from 1997 values and reliability index.
Deviations D[Ar(E)] are given in column 7.
They are the differences of the given year's Ar(E)
from the latest (1997) standard Ar(E) value, here
assumed to be equal to ideal "error-free" values for judging
the reliability of earlier recommended values. The 1997 values are the
commissions's current best knowledge of the atomic weights and represent
the closest available approach to the hypothetical "error-free"
values. The deviations from the 1997 values, therefore, yield estimated
errors for the earlier values. With probably very few exceptions, and
certainly for the 19 mononuclidic elements, these current Ar(E)
values are surely much nearer their hypothetical error-free values.
D[Ar(E)] yields especially reliable estimates
of errors for early Ar(E) values when they were based
mostly on chemical, as opposed to physical (now mass-spectrometric)
determinations. The quotient D[Ar(E)]/U[Ar(E)]
in column 8 is a retrospective measure of the reliability of the originally
recommended value judged by its own assigned uncertainty (ref.
16). The bias is determined by subtracting the mean D[Ar(E)]/U[Ar(E)]
value from all other of these fractional values. The mean value of 0.31756
in column 8 is quite small relative to many individual values and represents
a general bias of all values, which we subtracted from all values for
judging retrospectively the reliability of individual atomic-weight
values. For that purpose we calculated a "reliability index"
of atomic-weight values, d, in relation to their uncertainty
estimations or assignments (ref. 16), such that:
d = (n-1)-1/2
. { S [D[Ar(E)]]2/[U[Ar(E)]]2}-1/2
where n is the number of values of D[Ar(E)]/U[Ar(E)].
A well-evaluated data set should have d < 1. The value of
d calculated for all the data on which the reliability could
be assessed is large, namely 9.63. That value is calculated from n =
718, which equals the total number of entries, 802, diminished by the
last quoted values of each of the 84 elements listed.
There is a positive bias of the values in column 8
of Table 1, the ratios of differences from present-day values divided
by the original uncertainty. The algebraic sum of all values, which
ideally should be zero, is +227.696. The mean value of the bias is +227.696/(718-1)
= +0.31356. This is a fraction of the initial uncertainty that is by
no means negligible. The corresponding figures for the values between
1969 and 1997 are 0.606 and 0.606/(194-68-1) = 0.004848, and are very
much smaller. We wonder whether data prior to 1969 might suffer from
unsuspected contamination in atomic-weight determinations.
For values since 1969 (n = 111), we find d =
0.45, indicating a desirable high degree of reliability of IUPAC's evaluation
of more recent Ar(E) values. It must be remembered
that by neglecting the remaining and unknown errors in the 1997 values,
we have biased the reliability index in favor of the assessment of recent
changes in Ar(E) values. Nevertheless, it is remarkable
that the d = 0.45 value for the reliability of recently recommended
Ar(E) values agrees with that in reference (ref. )
in which the reliability was assessed by a different retrospective method.
That method, though inferior to the method used in this paper, was free
from the bias due to the remaining uncertainties in the current Ar(E)
values.
CONCLUSION
We have assembled more than a century's historic record
of internationally recognized atomic-weight values and their uncertainties.
Comparison of older with current best values leads to a retrospective
analysis of this carefully evaluated data set. The self-discipline by
the relevant IUPAC Commission of estimating uncertainties since 1969
appears to have contributed to improved reliability, by about an order
of magnitude, as quantified by a previously proposed numerical index
measure. This conclusion is convincing and not dependent on details
of the analysis. For instance, one could weight each tabulated entry
by the number of years of its validity, or one could discard all data
within ten years of the present because they are too close to current
values to provide adequate retrospection. The ultimate conclusion would
remain unchanged.
ACKNOWLEDGEMENTS
The authors sincerely thank other past and present
members of the international atomic-weights commissions, especially
Prof. John de Laeter. The interchange of ideas has been constructive
and personally enjoyable. Despite diverging opinions and interest, a
remarkable consensus was always reached. Over the many years in which
we have served as Commission secretary, we are unaware of any significant
challenge of the recommended values in, surely, the most widely used
data set for science, technology, and commerce. Dr. H. H. Ku's intensive
review of our manuscript and comments have clarified the text significantly.
Ms. Shalini Mohleji is commended for extensive library work and extensive
data tabulation efforts. The encouragement and active support of the
U.S. Geological Survey is viewed with gratitude as continuation of an
historical interest, established by its erstwhile chief chemist, Frank
W. Clarke. For more than forty years, before the United States was recognized
as a major center for basic science, Clarke maintained a universally
acclaimed world leadership in the field of atomic weights.
REFERENCES
1. R. D. Vocke, "Atomic Weights
of the Elements 1997", Pure Appl. Chem., in preparation.
2. ISO, "Guide to the Uncertainty
in Measurement," International Organization for Standardiza-tion, Engl.
Ed. (1993).
3. G. Audi and A. H. Wapstra, Nucl.
Phys. A565, 1-65 (1993).
4. "International Critical Tables,"
U.S. National Research Council, 1, 43-45 (1926).
5. Report of the International
Committee on Atomic Weights, J. Am. Chem. Soc. 25, 1-5 (1903).
6. F. W. Clarke, J. Am. Chem. Soc.
16, 179-193 (1894).
7. F. W. Clarke, "The Constants
of Nature, Part 5. Recalculation of the Atomic Weights," Smithsonian
Misc. Publ. 441 i-xiv, 1-259 (1882).
8. Sixth Report of the American
Chemical Society Committee on Atomic Weights, J. Am. Chem. Soc. 21,
200-214 (1898).
9. IUPAC, "2nd Report of the International
Commission of Chemical Elements, IUPAC, 1925," J. Am. Chem. Soc. 47,
597-601 (1925).
10. F. W. Clarke, T. E Thorpe,
and G. Urbain, J. Am. Chem. Soc. 42, 1761-1764 (1920).
11. F. W. Clarke, T. E Thorpe,
and G. Urbain, J. Am. Chem. Soc. 43, 1751-1753 (1921).
12. "Ninth Report of the German
Commission on Atomic Weights," Chem. Berichte 62B, I (1929).
13. "Report by the Subcommittee
on Atomic Weights of the Council of the Chemical Society of Great Britain,"
J. Chem. Soc. (London), [no volume no.], 216-218 (1929).
14. "Report of the Spanish Committee
on Atomic Weights," Anales Soc. Espa�. F�s. Qu�m. 20, 25-33 (1922).
15. "Report by the Swiss Committee
on Atomic Weights," Helv. Chim. Acta 4, 449-458 (1921).
16. P. De Bi�vre, H. H. Ku, and
H. S. Peiser, J. Phys. Chem. Ref. Data 23, 509-513 (1994)
Ref. History
of the recommended atomic-weight values from 1882 to 1997: a comparison
of differences from current values to the estimated uncertainties of
earlier values, Pure Appl. Chem., Vol. 70, No. 1, pp. 237-257,
1998.
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Comment - Conclusion
- Acknowledgements - References