Atomic And Nuclear Size

NCERT gives the empirical nuclear radius relation $R=R_0{A}^{1/3}$, where $A$ is the mass number and $R_0\approx 1.2$ fm is a constant, reflecting the near-constant density of nuclear matter. Because nucleons are essentially incompressible and packed together, the volume grows in proportion to $A$, so the radius grows as the cube root of $A$. For $A=125$, the cube root is $\sqrt[3]{125}=5$, giving $R=1.2\times 5=6.0$ fm. The value 1.2 fm is wrong because it is $R_0$ itself, the radius for a single nucleon ($A=1$). The value 3.0 fm is wrong because it uses roughly $A^{1/3}$ for a lighter nucleus and misapplies the constant. The value 12.0 fm is wrong because it doubles the correct answer, as if the cube root were 10 rather than 5. As stated in NCERT Class 12, Chapter 13 (Nuclei), this cube-root law implies that nuclear density is essentially the same for all nuclei, since volume, proportional to $R^3$, rises in step with the number of nucleons. This constant density is a hallmark of the short-range, saturating nature of the strong nuclear force, which binds each nucleon mainly to its immediate neighbours. A magnitude check confirms a few femtometres is the expected size scale for a medium-mass nucleus, tens of thousands of times smaller than the roughly 0.1 nm atomic dimensions.