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Nuclei and nuclear size scales

An atomic nucleus contains positively charged protons and electrically neutral neutrons, collectively called nucleons. For an isotope with proton number $Z$, neutron number $N$ and mass number $A=Z+N$, these numbers specify the nuclear composition.

Nuclear radii are approximately described by

$$R=r_0A^{1/3},$$

with $r_0\approx1.2,\mathrm{fm}$. Because volume scales as $R^3\propto A$, this relation implies that nuclear matter has roughly constant density across a wide range of nuclei.

For example, a nucleus with $A=64$ has

$$R\approx1.2\times64^{1/3},\mathrm{fm} =1.2\times4,\mathrm{fm} \approx4.8,\mathrm{fm}.$$

These scales are about $10^5$ times smaller than typical atomic radii.

The attractive strong nuclear interaction binds nucleons at short range, while electrostatic repulsion acts between protons. Their competition, together with the quantum nature of protons and neutrons, determines which nuclear configurations can form stable or long-lived bound states.

Atomic mass is dominated by the nucleus, but a bound nucleus has slightly less mass than its separated nucleons. That mass defect reflects nuclear binding energy and provides the next quantitative step in understanding nuclear stability.

Nuclear structure therefore operates on a scale and through interactions very different from ordinary chemical bonding, even though both ultimately influence measured atomic masses.