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

Explanation

`bar(v)_(Be^(3+)) = (1)/(lamda_(H)) = R ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2))) and bar(v)_(He^(+)) = (1)/(lamda_(He^(+))) = (1)/(lamda_(He^(+))) = RZ_(He^(+))^(2) ((1)/(2^(2)) - (1)/(4^(2)))`
Since, `(1)/(lamda_(H)) = (1)/(lamda_(He^(+)))` (given), therefore, `((1)/(n_(1)^(2))- (1)/(n_(2)^(2))) = 2^(2) ((1)/(4) - (1)/(16)) = (3)/(4)`
`rArr n_(1) =1 and n_(2) = 2`