fraction

The passage around this formula

The second primary method shares almost nothing with the first except its answer. The X-ray crystal density route determines the mass of a nearly perfect single-crystal silicon sphere by counting the atoms in it. With eight atoms per cubic unit cell of lattice parameter a, the atom count follows from the macroscopic sphere volume, and the sphere mass follows from the count [ 4 ] : $N = \frac{8\,V_{\mathrm s}}{a^{3}}, \qquad m_{\mathrm s} = N\, m({}^{28}\mathrm{Si}) = h\,N \left( \frac{m({}^{28}\mathrm{Si})}{h} \right)$. The ratio of the silicon-28 atomic mass to h is a constant of nature known to high accuracy, so with h fixed the sphere becomes a primary mass standard [ 4 ] . The mise en pratique notes that the second equality is not exact — the total binding energy of the crystal reduces the right-hand side…

Read this part in the article →