The nucleus

A nucleus is made of protons and neutrons, together called nucleons.

• Atomic number Z = number of protons.
• Neutron number N = number of neutrons.
• Mass number A = Z + N, the total number of nucleons.

A nucleus is written ᴬ_Z X, for example ¹⁶₈O.

Families of nuclei:

Isotopes have the same chemistry (same electrons) but different masses.

Nuclear masses are tiny, so we use the atomic mass unit u, defined as 1/12 of the mass of a carbon-12 atom: 1 u ≈ 1.66 × 10⁻²⁷ kg. A proton or a neutron is about 1 u.

Size: experiments show the radius grows as the cube root of A:

R = R₀ A^(1/3), with R₀ ≈ 1.2 fm (1 fm = 10⁻¹⁵ m).

Example: ¹⁶O has R = 1.2 × 16^(1/3) ≈ 1.2 × 2.5 = 3.0 fm. A nucleus with 8 times as many nucleons is only twice as wide.

Since volume grows as R³, which grows as A, the volume is proportional to the number of nucleons. So every nucleus has the same density, about 2.3 × 10¹⁷ kg/m³: nucleons pack together like marbles in a bag. A teaspoon of nuclear matter would weigh a billion tonnes.

Nuclear force: protons repel each other strongly, so something stronger must hold the nucleus together. The nuclear force is very strong, short-ranged (a few fm only), and pulls protons and neutrons alike.