The distance between two nucleons for which the potential energy is minimum,is (in $fm$)

The ratio of mass densities of nuclei of $^{40}Ca$ and $^{16}O$ is close to

The volume of a nucleus is directly proportional to

Mass numbers of two nuclei are in the ratio of $4: 3$. Their nuclear densities will be in the ratio of

In a periodic table,the average atomic mass of magnesium is given as $24.312 \; u$. This average value is based on their relative natural abundance on Earth. The three isotopes and their masses are $_{12}^{24} Mg \; (23.98504 \; u)$,$_{12}^{25} Mg \; (24.98584 \; u)$,and $_{12}^{26} Mg \; (25.98259 \; u)$. The natural abundance of $_{12}^{24} Mg$ is $78.99 \%$. Calculate the abundances of the other two isotopes.

The unit of length convenient on the nuclear scale is a fermi: $1 \; f = 10^{-15} \; m$. Nuclear sizes obey roughly the following empirical relation: $r = r_{0} A^{1/3}$,where $r$ is the radius of the nucleus,$A$ is its mass number,and $r_{0}$ is a constant equal to about $1.2 \; f$. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of a sodium nucleus.