$STATEMENT-1$: The plot of atomic number ( $\mathrm{y}$-axis) versus number of neutrons ( $\mathrm{x}$-axis) for stable nuclei shows a curvature towards $x$-axis from the line of $45^{\circ}$ slope as the atomic number is increased. and  $STATEMENT-2$: Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons and neutrons in heavier nuclides.

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?

Why do stable nuclei never have more protons than neutrons ? 

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

The sodium nucleus $_{11}^{23}Na$ contains