Calculate the radius, volume and density of any nucleus using the empirical formula R = R₀ × A^(1/3).
The nuclear radius follows the empirical formula R = R₀ × A^(1/3), where R₀ is approximately 1.2 to 1.3 femtometres (10⁻¹⁵ m) and A is the mass number. This relationship implies that nuclear volume is directly proportional to the number of nucleons, meaning all nuclei have roughly the same density — about 2.3 × 10¹⁷ kg/m³. This extraordinary density is what makes neutron stars so extreme: they are essentially giant nuclei.
The cube-root dependence on A is a key signature of the liquid drop model. Just like adding more water to a drop increases its radius as the cube root of volume, adding more nucleons to a nucleus increases its radius as the cube root of A. This proportionality breaks down slightly for very light nuclei and near the drip lines, but holds well across most of the nuclear chart.