JEE Main & Advanced Physics Nuclear Physics And Radioactivity Size of Nucleus

(1) Nuclear radius : Experimental results indicates that the nuclear radius is proportional to \[{{A}^{1/3}}\], where A is the mass number of nucleus i.e. \[R\propto {{A}^{1/3}}\]\[\Rightarrow \]\[R={{R}_{0}}{{A}^{1/3}}\], where \[{{R}_{0}}=1.2\times {{10}^{-15}}\,m=1.2\,\,fm\].

(2) Nuclear volume : The volume of nucleus is given by \[V=\frac{4}{3}\pi \,{{R}^{3}}=\frac{4}{3}\pi \,R_{0}^{3}A\,\,\Rightarrow V\propto A\]

(3) Nuclear density : Mass per unit volume of a nucleus is called nuclear density.

\[\text{Nuclear density}\,\text{(}\rho \,\text{) }=\,\frac{\text{Mass of nucleus}}{\text{Volume of nucleus}}=\frac{mA}{\frac{4}{3}\pi \,{{({{R}_{0}}{{A}^{1/3}})}^{3}}}\]

where m = Average of mass of a nucleon (= mass of proton + mass of neutron \[=1.66\times {{10}^{-27}}\,kg\]) and \[mA=\]Mass of nucleus

\[\Rightarrow \]\[\rho =\frac{3m}{4\pi R_{0}^{3}}=2.38\times {{10}^{17}}kg/{{m}^{3}}\]