The value of `(n_2 + n_1)` and `(n_2^2 - n_1^2)` for `He^+` ion in atomic spectrum are 4 and 8 respectively . The wavelength of emitted photon when electron jump from `n_2 ` to `n_1 ` is

Options

A. `(32)/(9) R_H`
B. `(9)/(32) R_H`
C. `(9)/(32) R_H)`
D. `(32)/(9) R_H)`

Answer

C

Explanation

`(n_2^2 - n_1^2)/(n_2 + n_1) = 8/4`
`implies ((n_2 - n_1)(n_2 + n_1))/((n_2 + n_1)) = (n_2 + n_1) = 2`
`therefore n_2 = 3 , n_1 = 1 implies bar(upsilon) = Z^2 R[1/(n_1^2)- 1/(n_2^2)]`
`=(2)^2 R (1/((1)^2) - 1/((3)^2))= (32R)/(9) , lambda =(9)/(32R)`