If $S$ is the surface area of a nucleus of mass number $A$, then

When a $U^{238}$ nucleus,initially at rest,decays by emitting an alpha particle with speed $u$,what will be the recoil velocity of the residual nucleus?

The size of the nucleus is of the order of:

$(a)$ Two stable isotopes of lithium $_{3}^{6} Li$ and $_{3}^{7} Li$ have respective abundances of $7.5 \%$ and $92.5 \%$. These isotopes have masses $6.01512 \; u$ and $7.01600 \; u$,respectively. Find the atomic mass of lithium.
$(b)$ Boron has two stable isotopes,$_{5}^{10} B$ and $_{5}^{11} B$. Their respective masses are $10.01294 \; u$ and $11.00931 \; u$,and the atomic mass of boron is $10.811 \; u$. Find the abundances of $_{5}^{10} B$ and $_{5}^{11} B$.

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

If the nucleus ${}_{13}^{27}Al$ has a nuclear radius of about $3.6 \, fm$,then ${}_{52}^{125}Te$ would have its radius approximately as .......$fm$.