Explanation

(d) The wavelength of different spectral lines of Lyman series is given by
$\frac{1}{\lambda} = R_{H}\left\lbrack \frac{1}{1^{2}} - \frac{1}{n^{2}} \right\rbrack$; where $n = 2,\ 3,\ 4,\ldots..$
For shortest wavelength, $n = \infty$
$\therefore\frac{1}{\lambda} = \frac{R_{H}}{1}$
Or $\lambda = \frac{1}{R_{H}} = \frac{1}{109678cm^{- 1}}$
$= 9.117 \times 10^{- 6}cm = 9.117 \times 10^{- 8}m$
$= 911.7 \times 10^{- 10}m = 911.7\mathring{\mathrm{A}}$