(a) $E\ = \ - \ Z^{2}\frac{13.6}{n^{2}}eV$
For first excited state,
$\ \ \ \ \ \ \ \ \ \ E_{2}\ = \ - 3^{2} \times \frac{13.6}{4}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ - 30.6\ eV$
Ionisation energy for first excited state of $Li^{2 +}$ is 30.6 eV.