26 No. 3
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New Best Estimates of the Values of the Fundamental Constants
by Ian Mills
The so-called fundamental constants of nature have an increasing importance in science today. Fundamental constants refer to the Planck constant h, the Boltzmann constant KB, the elementary charge e, and a number of others listed on the next page. These quantities play a key role in most of the basic relations involved in modern physics and chemistry, and they provide the ultimate standard of reference for all quantitative measurements. For these reasons, the scientists strive to determine the values of these constants with ever greater accuracy in terms of the base units of our system of measurement, such as the kilogram, metre, second, ampere, and kelvin—the base units of the SI, the International System of units. The Consultative Committee for Units (of the International Committee on Weights and Measures, BIPM/CCU) advises the Comité International des Poids et Mesures on defining (or redefining) each of the base units of the SI in terms of the fundamental constants rather than in terms of material artefacts or time intervals related to the rotation of the earth. Today, some, but not all, of the base units of the SI are defined in this way, and we are working on the remainder.
In December 2003, new best estimates of the fundamental constants were released. (Click here for table, pdf file) These are compiled and published with the authority of a CODATA committee that exists for this purpose, but in practice they are produced (on this occasion) by Barry Taylor and Peter Mohr at the U.S. National Institute for Standards and Technology (NIST), in Gaithersburg, MD. These new values displace the 1998 values (also produced by Mohr and Taylor), which have been in use for the last four years. The 1998 values in their turn displaced the 1986 best estimates (which were produced by Cohen and Taylor), which were in use for the 12 years from 1986 to 1998.
As the years go by, scientists determine these constants with ever-greater accuracy. The uncertainties associated with the best estimates of the fundamental constants have mostly been falling by roughly an order of magnitude each 10 years, as new and improved experimental measurements make it possible to determine the constants with ever greater precision. The most interesting constants for chemistry from the new 2002 best estimates, comparing the 1986, 1998, and 2002 values, can be viewed in the accompanying table (pdf file). The complete list is available from the NIST Web site, <http://physics.nist.gov/constants>, and will be published in an archive journal early in 2004.
Determining a set of best estimates of this kind is not simple, because there are numerous theoretical equations relating the constants and there are many different experiments that provide information on one or another of the constants. Thus, they all have to be determined from a single giant least-squares calculation, using all the available data with their uncertainties and all the known theoretical relations. This is why they are only revised at wide intervals. However, Barry Taylor says that they hope to revise them at more frequent intervals from now on, perhaps every three or four years. There is also a table of correlation coefficients among the various values on the NIST Web site.
Note that a few of these constants are exact (have zero uncertainty), because of the way that the units are defined. Thus, the metre is now defined in such a way as to make the speed of light c0 exact, and the ampere is defined in such a way as to make the magnetic constant
µ0 (the permeability of free space) exact. The relation
e0µ0 = 1/c02 then implies that the electric constant e0 (the permittivity of free space) is also exact.
As an example of the relations that we believe to hold between the constants, the Boltzmann constant, k, the gas constant, R, and the Avogadro constant, NA, are related by the equation: R = NA k. Although these three constants might be independently determined by different methods, there would be no sense in adopting values that did not fit this relation.
A more complicated relation is that between the Planck constant, h, and the Avogadro constant, NA:
where c0 is the speed of light in vacuum, Ar(e) is the relative electron mass (on the atomic mass scale, referred to m(12C)/12), Mu is equal to 1 g/mol (the standard molar mass),
a is the fine structure constant, and R8 is the Rydberg constant. Because the best measurements of the Avogadro constant and the Planck have a relative standard uncertainty of about 10-7, whereas all the other constants in this relation are either exact or are known to about 10-9, we require the best estimates of h and NA to satisfy this relation within their mutual uncertainties. Unfortunately recent measurements of the value of h (from Watt balance experiments) and NA (from the X-ray crystal density experiment) are not quite consistent within the uncertainty budget estimated for each value, and this has led to an increase in the uncertainty of these two constants since the 1998 appraisal (which is exceptional!). There is then a consequent increase in the estimated uncertainties of several other constants.
These constants are described as the 2002 best estimates, although the values have only just been released in December 2003, because the cut-off date for data included in the analysis was 31 December 2002.
The NIST Web site: http://physics.nist.gov/constants
Mohr and Taylor, J. Phys. Chem. Ref. Data 28, pp 1715–1852 (1999); also in Rev. Mod. Phys. 72, pp 351–495, No 2, April 2000 (which is essentially the same paper) ; these two papers describe the 1998 best estimates, but they contain a lot of useful information.
See also the SI Brochure 7th edition 1998, ed. Mills and Quinn, available from the BIPM Web site <www.bipm.org/en/
publications/brochure>, for information on the definition of the SI base units. The brochure is also available as a printed book (ISBN 92-822-2154-7), which can be ordered from the BIPM Web site.
Ian M. Mills <[email protected]> is professor of chemistry at the University of Reading; since 1996, he is the IUPAC representative on the International Committee on Weights and Measures/Consultative Committee on Units.
last modified 27 April 2004.
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