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

Options

A. `n_(1) = 1` "to" `n_(2) = 2`
B. `n_(1) = 2 "to" n_(2) = 4`
C. `n_(1) = 1 "to" n_(2) = 3`
D. `n_(1) = 2 "to" n_(2) = 3`

Answer

A

Explanation

`barv _(H_2^o+) = (1)/(lambda_(H_2^o+)) = R ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`.....(i)
`barv _(He^o+) = (1)/(lambda_(H^o+)) = RZ^(2)((1)/(2^(2)) - (1)/(4^(2)))`
`= R xx 4 ((1)/(4) - (1)/(16))`
`=- R xx ((4)/(4)- (4)/(16)) = R xx (1 - (1)/(4))`.....(ii)
Compairing equation (i) and (ii)
`:. (1)/(n_(1)^(2)) = ,n_(1) = 1`
`(1)/(n_(2)^(2)) = (1)/(4) , n_(2) = 2`