d
For \(He^+\) ion, \(\frac{1}{\lambda } = {Z^2}R\left[ {\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}}} \right]\)

\({(2)^2}R\left[ {\frac{1}{{{2^2}}} - \frac{1}{{{4^2}}}} \right] = \frac{{3R}}{4}\)

For hydrogen atoms, \(\frac{1}{\lambda } = R\left[ {\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}}} \right]\)

\(\frac{{3R}}{4} = R\left[ {\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}}} \right]\,\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}} = \frac{3}{4}\)

\(n_1 = 1\) and \(n_2 = 2.\)