What transition in `He^(o+)` ion shall have the same wave number as the first line in Balmer series of H atom ?

Options

A. `3to2`
B. `6to4`
C. `5to3`
D. `7to5`

Answer

B

Explanation

`barv_H=Rz^2(1/n_1^2-1/n_2^2),z=1,n_1=2,n_2=3` for first line in Balmer series of H spectrum
i.e., `barv_H=R(1)(1/4-1/9)=(R5)/36`
To have the same wave no, for `He^(+)` ion
Here z=2
Hence multiply `n_1` and `n_2` values of H atom with the value of z so that corresponding values of `n_1` and `n_2` in `He^+` ion are `n_1=4` and `n_2=6`
`barv_(He)=R.[1/16-1/36]=R.4[(9-4)/144]`
`=R.4 5/14= R 5/36`