Physics - Modern Physics Question with Solution | TestHub

The radius of a nucleus, $R$ is related to its atomic number $A$ as:

$R=R_0{A}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

where $R_0$ is the nuclear radius of hydrogen.

Thus, the density of a nucleus is given by:

$d=\frac{\mu A}{{\displaystyle \frac{4}{3}}\pi {\left(R_0{A}^{{\displaystyle \frac{1}{3}}}\right)}^3}=\frac{3\mu }{4\pi R_0^3}=\text{Constant}$ 

(Here, $\mu$ is atomic mass unit)

Hence, the ratio of nuclear density of oxygen to helium nucleus is $1:1$