Counting a mole of silicon atoms

Counting a mole of silicon atoms. Avogadro’s number, N _A, links the microscopic and macroscopic worlds by specifying how many individuals make up a mole. Now an international team of metrologists has obtained N _A with an unprecedented precision of 30 parts per billion. The result: N _A = 6.02214078(18) × 10²³. The idea behind the new experiment is simple. A sample from a crystalline silicon-28 boule, shown in the figure, was subjected to x-ray interferometry, which yielded the volume of the 8-atom Si unit cell. Other bits of the boule were painstakingly fabricated into spheres whose volumes and masses were carefully measured. The spherical volume divided by the unit-cell volume gives the number of Si atoms; the mass gives the number of moles. Voilà, atoms per mole. The devil, of course, is in the details. The team needed to measure and account for such flaws as pointlike defects in the

boule and surface oxidation on the spheres. Furthermore, uncertainty in the isotopic composition of the silicon translates into an uncertainty in the mass of a mole. Indeed, questions of isotopic composition plagued earlier, similar experiments. In their most recent determination, the researchers worked with a crystal that was highly enriched in ²⁸Si and applied an innovative suite of mass spectrometry techniques to measure the minute remainders of ²⁹Si and ³⁰Si. The new N _A does more than tweak the size of a mole; in combination with other precision experiments, it will be used by metrologists to refine the values of several other fundamental constants. ( B. Andreas et al., Phys. Rev. Lett. 1079-7114 PRLTAO, in press.)