$\frac{1}{\lambda( H )}= R (1)^2\left[\frac{1}{ n _1^2}-\frac{1}{ n _2^2}\right]$

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

Given $\lambda( H )=\lambda\left( He ^{+}\right)$

$R (1)^2\left[\frac{1}{ n _1^2}-\frac{1}{ n _2^2}\right]= R (4)\left[\frac{1}{2^2}-\frac{1}{4^2}\right]$

$\frac{1}{ n _1^2}-\frac{1}{ n _2^2}=\frac{1}{1^2}-\frac{1}{2^2}$

On comparing $n _1=1$ and $n _2=2$