Explanation

(c) For Paschen series $\overline{v} = \frac{1}{\lambda} = R\left\lbrack \frac{1}{3^{2}} - \frac{1}{n^{2}} \right\rbrack;n = 4,\ 5,\ 6\ldots$
For first member of Paschen series $n = 4$
$\frac{1}{\lambda_{1}} = R\left\lbrack \frac{1}{3^{2}} - \frac{1}{4^{2}} \right\rbrack \Rightarrow \frac{1}{\lambda_{1}} = \frac{7R}{144}$
$\Rightarrow R = \frac{144}{7\lambda_{1}} = \frac{144}{7 \times 18800 \times 10^{- 10}} = 1.1 \times 10^{7}$
For shortest wave length $n = \infty$
So, $\frac{1}{\lambda} = R\left\lbrack \frac{1}{3^{2}} - \frac{1}{\infty^{2}} \right\rbrack = \frac{R}{9}$
$\Rightarrow \lambda = \frac{9}{R} = \frac{9}{1.1 \times 10^{7}} = 8.225 \times 10^{7}m = 8225\ \mathring{\mathrm{A}}$