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

Options

A. `7 to 5`
B. `5 to 3`
C. `6 to 4`
D. `4 to 2`

Answer

C

Explanation

For H atom first Balmer line in the series is
`E_3 - E_2 = (E_1(H))/(9) - (E_1(H))/(4) = (5E_1(H))/(36)`
For `He^(+)` ion (Z = 2)
`E_6 - E_4 = (-E_1(H) xx 2^2)/(6^2) - (E_1(H) xx 2^2)/(4^2)`
`= -E_1 (H) xx 2^2 ((16-36)/(16 xx 36))`
`= (4 xx 20)/(16 xx 36)E_1(H) = (5E_1(H))/(36)`.