Determining the Avogadro Constant from Electrical Measurements

It is now possible to obtain indirect values of the Avogadro constant N A having comparatively small combined standard uncertainties by appropriately combining the values of a number of other fundamental physical constants. These constants, whose values in several important cases can be obtained from electrical measurements, include the Rydberg, fine-structure, Josephson, von Klitzing, Planck, and Faraday constants, the molar mass of the proton, the proton-electron mass ratio, and the shielded proton gyromagnetic ratio. This paper gives the expressions that relate N A to these other fundamental constants and the values of N A that can be obtained from these expressions using the currently available data. It also briefly discusses the prospects of obtaining an indirect value of N A with a combined standard uncertainty that is small enough to allow the redefinition of the kilogram.