If the wave number of `1^(st)` line of Balmer series of H-atom is 'x' then :

Options

A. Wave number of `1^(st)` line of lyman series of the `He^(+)` ion will be `(108 x)/5`
B. Wave number of `1^(st)` line of lyman series of the `He^(+)` ion will be `(36x)/5`
C. The wave length of `2^(nd)` line of lyman series of H-atom is `5/(32x)`
D. The wave length of `2^(nd)` line of lyman series of H-atom is `(32x)/5`

Answer

A,C

Explanation

`barv=RZ^2(1/n_1^2-1/n_2^2)implies x=R(1/2^2-1/3^2)=(5R)/36`
`barv_1=Rxx2^2(1-1/2^2)=3R=36/5x xx3=(108x)/5`
Wavelength of `2^(nd)` line of lyman series of H-atom
`1/lambda=Rxx1^2(1/1^2-1/3^2)implies 1/lambda=Rxx8/9`
`1/lambda=(36x)/5xx8/9 implies lambda=5/32 x`