(b) $E = 13.6\left\lbrack \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right\rbrack$. For highest energy in Balmer series
$n_{1} = 2$ and $n_{2} = \infty \Rightarrow E = 13.6\left\lbrack \frac{1}{(2)^{2}} - \frac{1}{(\infty)^{2}} \right\rbrack = 3.4\ eV$