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^(o+) , n_(1) = 2` and `n_(2) = 4` and `Z = 2`
`Thus (1)/(lambda) = R_(H)Z^(2)[(1)/(Z^(2)) - (1)/(4^(2))]`
`= R_(H) xx 4 [(1)/(Z^(2)) - (1)/(4^(2))]`
`for H, (1)/(lambda) = Z^(2)R_(H)[(1)/(n_(1)^(2)) - (1)/(n_(2)^(2))] = R_(H) xx 1 [(1)/(n_(1)^(2)) - (1)/(n_(2)^(2))]`
Since `lambda` is same
`4[(1)/(Z^(2)) - (1)/(4^(2))] = [(1)/(n_(1)^(2)) - (1)/(n_(2)^(2))]`
`rArr[(4)/(4) - (4)/(16)] = [(1)/(n_(1)^(2)) - (1)/(n_(2)^(2))]`
`rArr[(1)/(1^(2)) - (1)/(2^(2))] = [(1)/(n_(1)^(2)) - (1)/(n_(2)^(2))]`
` :. n_(1) = 1 nad n_(2) = 2`