The frequency of light emitted for the transition `n = 4` to `n =2` of `He^+` is equal to the transition in `H` atom corresponding to which of the following ?

Options

A. `n = 2` to `n = 1`
B. `n = 3` to `n = 2`
C. `n = 4` to `n = 3`
D. `n = 3` to `n = 1`

Answer

A

Explanation

`v(H) = v (He^+)`
`RZ^2 (1/(n_1^2) - 1/(n_2^2))_(H) = RZ^2 (1/(n_1^2) - 1/(n_2^2))_(He^+)`
`1/(n_1^2) - 1/(n_2^2) = 4(1/4 - 1/16)`
`1/(n_1^2) - 1/(n_2^2) = 1 - 1/4 = 3/4`
`:. n_1 = 1 and n_2 = 2`.