$A_0/2$ atoms of $X\left(g\right)$ are converted into $X^{+}\left(g\right)$ by absorbing energy $E_1$. $A_0/2$ of $X^{+}\left(g\right)$ are converted into $X^{-}\left(g\right)$ with the release of energy, $E_2$. Hence the ionisation energy and the electron affinity of $X\left(g\right)$ are repectively _____ and _______.

The correct option is B $\frac{2E_1}{A_0},\frac{2(E_2-E_1)}{A_0}$
$X\left(g\right)\to X^{+}\left(g\right)$
Here amount of energy released is ionisation potential.
For $\frac{A_o}{2}$ absorbed energy =$\frac{A_o}{2}I.E=E_1$
$I.E=\frac{2E_1}{A_o}$
Energy released in the conversion of $Xto{X}^{+}$ will be ionisation energy
Energy released in the conversion of $Xto{X}^{-}$ will be electron affinity.
$E_2=IE\times \frac{A_o}{2}+E.A\frac{A_o}{2}$
$E.A=\frac{2(E_2-E_1)}{A_o}$