The frequency of light emitted for the transition n = 4 to n = 2 of $H{e}^{+}$  is equal to the transition in H atom corresponding to which of the following?                                                                 

$v=R{Z}^2(\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2})$

$ForH{e}^{+},Z=2,n_1=2,n_2=4$

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

$=4R\left[\frac{3}{16}\right]\mathrm{.......}\left(i\right)$

$=\frac{3R}{4}$

For H, Z = 1 as the frequency of light emitted for the transition n = 4 to n =2 of  $H{e}^{+}$ is equal to the transition in H – atom corresponds to n = 2 to n = 1

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

$=R\left[\frac{3}{4}\right]=\frac{3R}{4}$