• Tags: nucleus, protons, neutrons, size
• Difficulty: Foundation

The nucleus contains protons (charge +e, mass 1.00728 u) and neutrons (charge 0, mass 1.00866 u), collectively called nucleons. The atomic number Z = number of protons, neutron number N = A - Z, where A = mass number = total nucleons. Isotopes: same Z, different A (e.g., C-12, C-13, C-14 — all carbon). Isobars: same A, different Z (e.g., C-14 and N-14). Isotones: same N, different Z (e.g., C-13 with N=7 and N-14 with N=7). Nuclear radius follows the empirical formula R = $R_0$ * A^$\frac{1}{3}$, where $R_0$ = 1.2 fm. This means nuclear volume V = $\frac{4}{3}$pi$R^3$ is proportional to A. Since mass is also proportional to A, nuclear density rho = 3$\frac{m_p}{4*pi*R_0^3}$ ≈ 2.3 x 10^17 kg/$m^3$, independent of A. This extraordinary density (a teaspoon of nuclear matter would weigh ~5 billion tonnes) is the same for all nuclei.