An Exact Value for Avogadro’s Number

Ronald F. Fox and Theodore P. Hill in American Scientist:

Avogadro’s number, N A , is the fundamental physical constant that links the macroscopic physical world of objects that we can see and feel with the submicroscopic, invisible world of atoms. In theory, N A specifies the exact number of atoms in a palm-sized specimen of a physical element such as carbon or silicon.

The name honors the Italian mathematical physicist Amedeo Avogadro (1776-1856), who proposed that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. Long after Avogadro’s death, the concept of the mole was introduced, and it was experimentally observed that one mole (the molecular weight in grams) of any substance contains the same number of molecules. This number is Avogadro’s number, although he knew nothing of moles or the eponymous number itself.

Today, Avogadro’s number is formally defined to be the number of carbon-12 atoms in 12 grams of unbound carbon-12 in its rest-energy electronic state. The current state of the art estimates the value of N A , not based on experiments using carbon-12, but by using x-ray diffraction in crystal silicon lattices in the shape of a sphere or by a watt-balance method. According to the National Institute of Standards and Technology (NIST), the current accepted value for N A is:

N A = (6.0221415 ± 0.0000010) × 1023

This definition of N A and the current experiments to estimate it, however, both rely on the precise definition of a gram. Originally the mass of one cubic centimeter of water at exactly 3.98 degrees Celsius and atmospheric pressure, for the past 117 years the definition of one gram has been one-thousandth of the mass of “Le Gran K,” a single precious platinum-iridium cylinder stored in a vault in Sèvres, France. The problem is that the mass of Le Gran K is known to be unstable in time. Periodic cleanings and calibration measurements result in abrasion of platinum-iridium and accretion of cleaning chemicals.

These changes cannot be measured exactly, simply because there is no “perfect” reference against which to measure them—Le Gran K is always exactly one kilogram, by definition. It is estimated that Le Gran K may have changed about 50 micrograms—that is, roughly by about 150 quadrillion (1.5 × 1017) atoms—since it was constructed. This implies that by current measurement conventions, the mass of a single atom of carbon-12 is changing in time, whereas modern theory postulates that it remain constant.

More here.