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

Explanation

`bar(v)_(H_(2))=1/lambdaRZ^(2)(1/n_(1)^(2)-1/n_(2^(2)))`
`=R(1/n_(1)^(2)-1/n_(2)^(2))(Z=1 "for" H_(2)^(+)) ...(1)`
`bar(v)_(He^(o+))=1/lambdaRZ^(2)(1/2^(2)-1/4^(2))(Z=2 "for" He^(+))`
`=Rxx(4/4-4/16) ...(2)`
Compare (1) and (2)
`R(1/n_(1)^(2)-1/n_(2)^(2))=R(4/4-4/16)`
`:. 1/n_(1)^(2)=4/4=1`
`n_(1)^(2)=1, n_(1)=1`
`1/n_(2)^(2)=4/16=1/4`
`n_(2)^(2)=4, n_(2)=2`
`(n_(1)=1, n_(2)=2)`