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An Exact Value for Avogadro's Number

Untangling this constant from Le Gran K could provide a new definition of the gram

Ronald Fox, Theodore Hill

Replacing the Kilogram Standard

Le Système International d'Unites (SI), the organization that oversees measurements and standards that have been officially recognized and adopted by nearly all countries, identifies exactly seven basic units. These official units and their standards of measurement are length (meter), mass (kilogram), time (second), electrical current (ampere), thermodynamic temperature (kelvin), amount of substance (mole) and luminous intensity (candela).

Of these basic seven, which are assumed to be mutually independent, the kilogram is the only unit that is still defined in terms of a physical artifact. Not only is this definition inelegant, but it is also labor-intensive compared with the fundamental and universal definitions of the other units. Maintaining and preserving Le Gran K—cleaning and calibrating and compensating for lost platinum-iridium atoms and adsorbed contaminants—requires intensive labor and expense. This labor is duplicated scores of times around the world, where many national bureaus of standards maintain their own replicas of Le Gran K. These subordinate lesser Ks also require periodic re-calibration with the French K and with their own subordinate scale users. For these reasons, there has been considerable effort to design a method that will eliminate the need for this final SI artifact.

Using N A * carbon-12 atoms to define 12 grams is one such solution. The two main candidates for an alternative definition of the kilogram, the silicon-lattice method and the watt-balance method, are both experimental in nature, and thus, as with the Le Gran K definition, change in time depending on the state of the art of the laboratory equipment used in the experiments.

The proposal to use N A * also offers a distinct advantage in reducing experimental errors. Using today's methods for determining Avogadro's number requires two experiments, usually far apart in time and space: first, calibrating the scales (at the laboratory, often not in France) with Le Gran K in France; and second, running the N A experiment. The resulting best current approximation to N A thus compounds the errors from both experiments. Precisely the same experiments that are used to determine N A , when viewed from the perspective of a known fixed value (say N A *) for Avogadro's number, would now simply measure 1 gram.

For example, running the experiment with the crystal silicon sphere mentioned above would proceed in exactly the same manner as before. The total number of atoms in the sphere would be estimated the same way, but now N A * would determine the mass of the sphere, and weighing the sphere with scales would now be calibrating the scale, not vice versa.

In conclusion, adopting this natural value N A * for Avogadro's number would be elegant and easy and would have far-reaching and important consequences experimentally, theoretically and economically. Above all, it would eliminate forever the dependence of SI physical units on manmade objects.

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