The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [$a_o$ is Bohr radius]

The difference between the radii of $3^{\mathrm{rd}}$ and $4^{\text{th }}$ orbits of ${\mathrm{Li}}_{}^{2+}$ is ${\mathrm{\Delta R}}_1$. The difference between the radii of $3^{\mathrm{rd}}$ and $4^{\text{th }}$ orbits of ${\mathrm{He}}^{+}$ is $\Delta {\mathrm{R}}_2.$ Ratio of  $\Delta {\mathrm{R}}_1:\Delta {\mathrm{R}}_2$ is :

The figure below is the plot of potential energy versus internuclear distance $\left(\mathrm{d}\right)$ of ${\mathrm{H}}_2$ molecule in the electronic ground state. The value of the net potential energy ${\mathrm{E}}_0$ (as indicated in the figure) is $-5.24649\times {10}^{\mathrm{n}}$ $\mathrm{kJ} {\mathrm{mol}}^{-1},$ for $\mathrm{d}={\mathrm{d}}_0$ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent, find the value of $\mathrm{n}$ to the nearest integer value.

As reference, the potential energy of $\mathrm{H}$ atom is taken as zero when its electron and the nucleus are infinitely far apart.

Use Avogadro constant as $6.023\times {10}^{23} {\mathrm{mol}}^{-1}.$  Give an answer to the nearest integer value.

According to Bohr's atomic theory:
(A) Kinetic energy of electron is $\propto \frac{{\mathrm{Z}}^2}{{\mathrm{n}}^2}.$
(B) The product of velocity (v) of electron and principal quantum number $\left(\mathrm{n}\right), \text{'}vn\text{'}\propto {\mathrm{Z}}^2.$
(C) Frequency of revolution of electron in an orbit is $\propto \frac{{\mathrm{Z}}^3}{{\mathrm{n}}^3}.$
(D) Coulombic force of attraction on the electron is $\propto \frac{{\mathrm{Z}}^3}{{\mathrm{n}}^4}.$

Choose the most appropriate answer from the options given below: