The nucleus is the tiny, dense core of the atom. It is made of nucleons — protons (charge $+e$, mass $\approx 1.0073\ \text{u}$) and neutrons (no charge, mass $\approx 1.0087\ \text{u}$). The number of protons is the atomic number $Z$, the total number of nucleons is the mass number $A$, and the number of neutrons is $N = A - Z$. A nucleus is written ${}^{A}_{Z}X$.
- Isotopes: same $Z$, different $A$ (e.g. ${}^{1}_{1}\text{H}$, ${}^{2}_{1}\text{H}$, ${}^{3}_{1}\text{H}$). Same chemistry, different mass.
- Isobars: same $A$, different $Z$ (e.g. ${}^{3}_{1}\text{H}$ and ${}^{3}_{2}\text{He}$).
- Isotones: same number of neutrons $N$ (e.g. ${}^{3}_{1}\text{H}$ and ${}^{4}_{2}\text{He}$, both with $N = 2$).
Experiments show the nuclear radius obeys $R = R_0 A^{1/3}$, where $R_0 = 1.2\ \text{fm} = 1.2 \times 10^{-15}\ \text{m}$. Because volume $\propto R^3 \propto A$, the nuclear volume is proportional to the number of nucleons. This means the nuclear density is essentially the same for all nuclei, an enormous $\rho \approx 2.3 \times 10^{17}\ \text{kg m}^{-3}$ — about $10^{14}$ times the density of water.
A startling fact emerges when nucleons bind: the mass of a nucleus is always less than the sum of the masses of its free nucleons. This shortfall is the mass defect $\Delta m = [Z m_p + (A - Z) m_n] - M_{\text{nucleus}}$. By Einstein's mass-energy relation $E = \Delta m\, c^2$, the missing mass appears as energy released when the nucleus forms. A convenient conversion is $1\ \text{u} = 931.5\ \text{MeV}/c^2$, so $1\ \text{u}$ of mass defect corresponds to $931.5\ \text{MeV}$.
The energy equivalent of the mass defect is the binding energy $E_b = \Delta m\, c^2$ — the energy needed to split the nucleus into its separate nucleons, or equivalently the energy released when it is assembled. More useful for comparing nuclei is the binding energy per nucleon, $\frac{E_b}{A}$, which measures how tightly each nucleon is held.
Plotting $\frac{E_b}{A}$ against $A$ gives the famous binding-energy curve. It rises steeply for light nuclei, reaches a broad peak of about $8.8\ \text{MeV}$ near iron-56, then falls slowly for heavy nuclei to about $7.6\ \text{MeV}$ for uranium. Two consequences follow: very heavy nuclei can release energy by splitting (fission) toward the peak, while very light nuclei can release energy by combining (fusion) toward the peak. Nuclei near iron are the most stable in the universe.