Energy required for exciting the hydrogen atom in the ground state to orbit \(n\) is given by

\(E=E_{n}-E_{1}\)

i.e.\(12.1 =  - \frac{{13.6}}{{{n^2}}} - \left( {\frac{{ - 13.6}}{{{1^2}}}} \right)\) \( =  - \frac{{13.6}}{{{n^2}}} + 13.6\)

or, \(-1.5=\frac{-13.6}{n^{2}}\) or, \(n^{2}=\frac{13.6}{1.5}=9\) or, \(n=3\)

Number of spectral lines emitted

\(=\frac{n(n-1)}{2}=\frac{3 \times 2}{2}=3\)