Nuclear Radius

Scattering experiments establish that nuclear radius grows with mass number as $R=R_0{A}^{1/3}$, where $R_0=1.2$ fm is an empirical constant; the cube-root dependence reflects that nuclear volume is proportional to the number of nucleons. For $A=125$, the cube root is $A^{1/3}=125^{1/3}=5$, so $R=1.2\times 5=6.0$ fm. The value 1.2 fm is simply $R_0$ and ignores the mass-number factor. The value 150 fm wrongly multiplies $R_0$ by $A$ itself instead of by $A^{1/3}$. The value 2.4 fm corresponds to $A=8$ (cube root 2) and uses the wrong mass number. This matches the NCERT empirical nuclear-size relation. A plausibility check confirms the radius is of the order of a few femtometres, the correct scale for medium-mass nuclei, and grows much more slowly than the mass number, consistent with the cube-root law.