Which transition in the hydrogen atomic spectrum will have the same wavelength as the transition, `n = 4 " to " n = 2` of `He^(+)` spectrum?

Options

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

Answer

D

Explanation

`1/lambda =Z^2 * R_H[1/(n_1^2)-1/(n_2^2)]`
For `He^(+) , 1/lambda =2^2 * R_H [1/2^2 -1/4^2]=4xx3/16 R_H = 3/4 R_H`
For `H, 1/lambda =1^2 * R_H [1/1^2 - 1/2^2]=3/4 R_H`
Hence, for hydrogen, it is the transition corresponding to `n = 2 " to " n = 1`.