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. `6 to 4`
C. `5 to 3`
D. `4 to 2`

Answer

B

Explanation

For H atom , first Balmer line in series is
`E_(3) - E_(2) = (-E_(1)(H))/((3)^(2)) + (E_(1)(H))/((2)^(2)) =(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) xx2^(2) |(16-36)/(16xx36)|`
` = (4 xx 20)/(36 xx 16) E_(1)(H) = (5E_(1)(H))/(36)`