Consider the following statements :

$A.$ Atoms of each element emit characterstics spectrum.

$B.$ According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.

$C.$ The density of nuclear matter depends on the size of the nucleus.

$D.$ A free neutron is stable but a free proton decay is possible.

$E.$ Radioactivity is an indication of the instability of nuclei.

Choose the correct answer from the options given below 

Which of the following is true for a sample of isotope containing ${U^{235}}$ and ${U^{238}}$

The ratio of the density of oxygen nucleus $\left({ }_8^{16} O \right)$ and helium nucleus $\left({ }_2^4 He \right)$ is

Consider the following statements ( $X$ and $Y$ stand for two different elements):

$(I)$ ${ }_{32}^{65} X$ and ${ }_{33}^{65} Y$ are isotopes.

$(II)$ ${ }_{42}^{86} X$ and ${ }_{42}^{85} Y$ are isotopes.

$(III)$ ${ }_{85}^{174} X$ and ${ }_{88}^{177} Y$ have the same number of neutrons.

$(IV)$ ${ }_{92}^{235} X$ and ${ }_{94}^{235} Y$ are isobars.

Which of the above statements are correct?

The radius of a nucleus of mass number $64$ is $4.8$ fermi. Then the mass number of another nucleus having radius of $4$ fermi is $\frac{1000}{x}$, where $x$ is______.