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

Options

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

Answer

D

Explanation

For `He^(+) , " " 1/(lambda) = Z^2R (1/(n_1^2) - 1/(n_2^2))`
`1/lambda = 2^2 R (1/(2^2) - 1/(4^2)) = (3R)/4`
For H atom, `1/lambda = R(1/(n_1^2) - 1/(n_2^2)) = (3R)/4`
or `" " 1/(n_1^2) 1/(n_2^2) = 3/4`
`:. n_1 = 1, n_2 = 2`.