Kilogram - Proposed Future Definitions - Atom-counting Approaches - Carbon-12

Carbon-12

Though not offering a practical realization, this definition would precisely define the magnitude of the kilogram in terms of a certain number of carbon‑12 atoms. Carbon‑12 (12C) is an isotope of carbon. The mole is currently defined as “the quantity of entities (elementary particles like atoms or molecules) equal to the number of atoms in 12 grams of carbon‑12.” Thus, the current definition of the mole requires that 1000⁄₁₂ (83⅓) moles of 12C has a mass of precisely one kilogram. The number of atoms in a mole, a quantity known as the Avogadro constant, is experimentally determined, and the current best estimate of its value is 6.02214129(27)×1023 entities per mole. This new definition of the kilogram proposed to fix the Avogadro constant at precisely 6.02214X×10^23 with the kilogram being defined as “the mass equal to that of 1000⁄₁₂ · 6.02214X×10^23 atoms of 12C.”

The accuracy of the measured value of the Avogadro constant is currently limited by the uncertainty in the value of the Planck constant—a measure relating the energy of photons to their frequency. That relative standard uncertainty has been 50 parts per billion (ppb) since 2006. By fixing the Avogadro constant, the practical effect of this proposal would be that the uncertainty in the mass of a 12C atom—and the magnitude of the kilogram—could be no better than the current 50 ppb uncertainty in the Planck constant. Under this proposal, the magnitude of the kilogram would be subject to future refinement as improved measurements of the value of the Planck constant become available; electronic realizations of the kilogram would be recalibrated as required. Conversely, an electronic definition of the kilogram (see Electronic approaches, below), which would precisely fix the Planck constant, would continue to allow 83⅓ moles of 12C to have a mass of precisely one kilogram but the number of atoms comprising a mole (the Avogadro constant) would continue to be subject to future refinement.

A variation on a 12C-based definition proposes to define the Avogadro constant as being precisely 84,446,8893 (≈6.02214162×1023) atoms. An imaginary realization of a 12-gram mass prototype would be a cube of 12C atoms measuring precisely 84,446,889 atoms across on a side. With this proposal, the kilogram would be defined as “the mass equal to 84,446,8893 × 83⅓ atoms of 12C.”