The spectral line obtained in the spectrum of $H{e}^{+}$ ion when the transition takes place between two levels whose sum is 4 and difference is 2. given $R=109677c{m}^{-1}$   

Suppose the transition takes place between levels $n_1$ and $n_2$   
given $n_1+n_2=4$  ______   (1)
          $n_2+n_1=2$ _______ (2)
From (1) and (2) we get $n_1=1\&n_2=3$   
$\frac{1}{\lambda }=Z^{2}R[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$ 
For $H{e}^{+},Z=2$  
$\frac{1}{\lambda }=2^2\times 109677[\frac{1}{1^2}-\frac{1}{3^2}]c{m}^{-1}$ 
$\lambda =2.56\times {10}^{-6}cm\approx 3\times {10}^{-6}$