The volume of a nucleus is proportional to ........ (where,$A$ is the mass number of the nucleus).

The radius of the nucleus of ${ }_{13}^{27} Al$ is $\qquad$ . (Given: $R_{0}=1.2 \text{ fm}$)

As compared to a $^{12}C$ atom,a $^{14}C$ atom has:

$A$ nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2:1$. After disintegration,they will move:

$A$ nucleus disintegrates into two smaller parts,which have their velocities in the ratio $3: 2$. The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$. The value of '$x$' is:

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.