Explanation

(c)
Applying Rydberg formula,
$\overline{v} - \frac{1}{\lambda} = R_{H}\left\lbrack \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right\rbrack cm^{- 1}$
For the first line in Lyman series,
$n_{1} = 1\ and\ n_{2} = 2$
$So,\ \overline{v} = 109678\left\lbrack \frac{1}{1^{2}} - \frac{1}{2^{2}} \right\rbrack = \frac{109678 \times 3}{4}$
$\ \ \ \ \ \ = 82258.5cm^{- 1}$