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

Explanation

`(1)/(lambda)=bar(v) = RZ^(2)((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
For Balmer Series `( 4 rarr2)` transition, `(1)/(lambda) = R.Z^(2)((1)/(2^(2))-(1)/(4^(2)))`
`= (Rxx 4 xx 12)/( 4 xx 16) = ( 3R)/( 4)`
For Hydrogen Spectrum, `(1)/(lambda)= R.1^(@)((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
`implies (3R)/(4) = R((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
`implies (1)/(n_(1)^(2))-(1)/(n_(2)^(2))=(3)/(4)` `n_(2) = 2, n_(1)=1` =[From hit and trial method]
For ` 2 rarr 1` transition. `(1)/(n_(1)^(2))-(1)/(n_(2)^(2))=(1)/(1^(2))-(1)/(2^(2)) -1-(1)/(4)=(3)/(4)`