The difference between excitation energy and binding energy of electron in a ${\mathrm{He}}^{+}$ ion is 42.31 eV. The energy quantum number of the excited state is 

$E_0=$Energy of electron in the ground state 

$=-13.6Z^{2}eV$

E = Energy in excited state $=-\frac{13.6Z^2}{n^2}eV$

Binding energy in the excited state $=+\frac{13.6Z^2}{n^2}eV$

Excitation energy $=-\frac{13.6Z^2}{n^2}-(-13.6Z^2)eV=13.6Z^2(1-\frac{1}{n^2})eV$

$\therefore$ Difference $=13.6Z^2(1-\frac{1}{n^2})-13.6\frac{Z^2}{n^2}=13.6Z^2(1-\frac{2}{n^2})eV$

$\begin{array}{l}\therefore 13.6\times 2^2\times (1-\frac{2}{n^2})=42.31\\ \Rightarrow n=3\end{array}$