The figure shows a graph between $\ln \left|\frac{{\mathrm{A}}_{\mathrm{n}}}{{\mathrm{A}}_1}\right|$ and $\ln \left|\mathrm{n}\right|$, where ${\mathrm{A}}_{\mathrm{n}}$ is the area enclosed by the ${\mathrm{n}}^{\mathrm{th}}$ orbit in a hydrogen-like atom. The correct curve which represents this relation is,

 

Consider a hydrogen-like atom whose energy in ${\mathrm{n}}^{\mathrm{th}}$ excited state is given by ${\mathrm{E}}_{\mathrm{n}}=-\frac{13.6{\mathrm{Z}}^2}{{\mathrm{n}}^2}$. When this excited atom makes a transition from the excited to the ground state, the most energetic photons have energy ${\mathrm{E}}_{\max }=52.2224 \mathrm{eV}$ and least energetic photons have energy ${\mathrm{E}}_{\min }=1.224 \mathrm{eV}.$ The atomic number of the atom is