If the radius of a nucleus with mass number $125$ is $1.5 \text{ fermi}$, then the radius of a nucleus with mass number $64$ is: (in $\text{ fermi}$)

Highly energetic electrons are bombarded on a target of an element containing $30$ neutrons. The ratio of the radius of the nucleus to that of a Helium nucleus is $14^{1/3}$. The atomic number of the nucleus will be

The volume of a nucleus is directly proportional to

The mass number of $He$ is $4$ and that for sulphur is $32$. The radius of the sulphur nucleus is larger than that of the helium nucleus by a factor of:

An element consists of a mixture of three isotopes $A$, $B$, and $C$ of masses $m_1$, $m_2$, and $m_3$ respectively. If the relative abundances of the three isotopes $A$, $B$, and $C$ are in the ratio $2:3:5$, the average mass of the element is:

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