a
\(\mathrm{E}=\frac{\mathrm{hc}}{\lambda} \Rightarrow \lambda=\frac{\mathrm{hc}}{\mathrm{E}}=\frac{6.62 \times 10^{-34} \times 3 \times 10^{8}}{12.5 \times 1.6 \times 10^{-19}}\)

\(=993 \mathrm{A}^{\circ}\)

\(\frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{\mathrm{n}_{1}^{2}}-\frac{1}{\mathrm{n}_{2}^{2}}\right)\)

(where Rydberg constant, \(\mathrm{R}=1.097 \times 10^{7}\) )

\(\frac{1}{993 \times 10^{-10}}=1.097 \times 10^{7}\left(\frac{1}{1^{2}}-\frac{1}{n_{2}^{2}}\right)\)

Solving we get \(n_{2}=3\)

Spectral lines

Total number of spectral lines \(=3\)

Two lines in Lyman series for \(n_{1}=1, n_{2}=2\) and \(\mathrm{n}_{1}=1, \mathrm{n}_{2}=3\) and one in Balmer series for \(n_{1}=2, n_{2}=3\)