The ground state energy of hydrogen atom is -13.6 eV. The energy needed to ionize hydrogen atom from its second excited state will be 

Second excited state is 3rd energy level.
Energy of hydrogen atom at any level ‘n’ is given by $\frac{-13.6}{{\mathrm{n}}^2}\mathrm{eV}$
the, 3rd level has energy,
$=\frac{-13.6}{9}=-1.51\mathrm{eV}.$
So, ionization energy needed is 1.51 eV.