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

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 $n_2 = 2.$