The ground state energy of hydrogen atom is -13.6 eV . When its...

Key Idea : Excitation energy is defined as the energy required to take the electron from ground level orbit to any higher order orbit (ie, $n=2,3,4 \ldots)$. Given, ground state energy of hydrogen atom E_1=-13.6 $\mathrm{eV}$Energy of electron in first excited state (ie, $n=2$ ) E_2=-$\frac{13.6}{(2)^2} \mathrm{eV}Therefore, excitation energy$$\begin{aligned}\Delta E & =E_2-E_1 \\ & =-\frac{13.6}{4}-(-13.6) \\ & =-3.4+13.6=10.2 \mathrm{eV} \end{aligned}$$