The ratio of the density of oxygen nucleus (O 816) and helium...

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

$R = {R}_{0}A\dfrac{1}{3}$

where ${R}_{0}$ is the nuclear radius of hydrogen.

Thus, the density of a nucleus is given by:

$d = \dfrac{\muA}{\dfrac{4}{3}\pi{\left({R}_{0}{A}^{\dfrac{1}{3}}\right)}^{3}} = \dfrac{3\mu}{4\pi{R}_{0}^{3}} = \text{Constant}$

(Here, $\mu$ is atomic mass unit)

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