A light of wavelength `12818 Å` is emitted when the electron of a hydrogen atom drops from fifth to third quantum level. Find the wavelength of the photon emitted when electron falls from third to ground level.

Answer

`102.5 nm`

Explanation

`1/lambda = R (1/(n_1^2)- 1/(n_2^2))`
For sjpectral line of electron jump from `n = 5` to `n = 3`
`1/(1281.8) = R (1/(3^2) - 1/(5^2)) = R(16/225) " " …..(i)`
For spectral line of electron jump from `n = 3` to `n = 1`
`1/lambda = R(1/(1^2) - 1/(3^2)) = R(8/9) " " .....(ii)`
Dividing (i) by (ii)
`lambda/(1281.8) = 16/225 xx 9/8`
or `" " lambda = (16 xx 9)/(225 xx 8) xx 1281.8 = 102.5 nm`.