A neutron moving with some kinetic energy collides head-on with a stationary helium ion $\left(H{e}^{+}\right)$ in its ground state. The minimum kinetic energy of neutron so that the collision can be inelastic, is

Consider a hydrogen like atoms which are in $n^{\mathrm{th}}$ excited state and their energy is given by 

$E_n=\frac{-13.6}{n^2}{Z}^2$

In the emission spectra of this atom the most energetic photons have energy, $E_{\max }=117.5 \mathrm{eV}$ and least energetic photon have energy, $E_{\min }=2.75 \mathrm{eV}.$ Find the atomic number of the atom.