What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition `n=4` to `n=2` of `He^(+)` spectrum ?

Explanation

For `He^(+)` ion
`(1)/(lamda)=Z^(2)R[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]`
`=(2)^(2)R[(1)/(2^(2))-(1)/(4^(2))]=(3R)/(4)`
For hydrogen atom,
`(1)/(lamda)=R[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]`
So, `(3R)/(4)=R[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]`
or `(1)/(n_(1)^(2))-(1)/(n_(2)^(2))=(3)/(4)`
i.e., `n_(1)=1 and n_(2)=2`.