Show that the density of a nucleus is independent of its mass number. Why are lighter nuclei more stable than heavier nuclei?

Reason for more stability of lighter nuclei∵ Density of nucleus \(\displaystyle =\frac{\text { Mass of nucleons }}{\text { Volume }}\) \(\displaystyle =\frac{\mathrm{mA}}{\dfrac{4}{3} \pi \mathrm{R}^{3}}\) where \(\displaystyle \mathrm{R}=\mathrm{R}_{0}(\mathrm{~A})^{1 / 3}\) \(\displaystyle =\frac{\mathrm{mA}}{\dfrac{4}{3} \pi\left(\mathrm{R}_{0}\right)^{1 / 3} \mathrm{~A}}=\frac{\mathrm{m}}{\dfrac{4}{3} \pi \mathrm{R}_{0}{ }^{3}}\) Reason: Due to neutron - proton ratio