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

Explanation

In the case of `He^(+)` spectrum of Balmer transition (n=4 to n=2),
`overline(v)=(1)/(lamda)=Rz^(2)((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))=Rxx(2)^(2)xx((1)/(2^(2))-(1)/(4^(2)))=(3R)/(4)`
For hydrogen spectrum, `overline(v)=(1)/(lamda)=(1)/(R)(((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))=(3R)/(4)`
`therefore (1)/(n_(1)^(2))-(1)/(n_(2)^(2))=(3)/(4)`, this is possible if `n_(1)=1 and n_(2)=2`, i.e., the transition is from n=2 to n=1.