A gas absorbs a photon of `310nm` and emits three photons. If energy of emitted photons is in the raio `1:2:1` then select correct statement(s) :

Options

A. The wave length of emitted photons is in the ratio `1: 2:1`
B. The wave length of emitted photons is in the ratio `2:1:2`
C. The wave length of emitted photons is in the ratio `1240 nm`.
D. The wavelength of least energatic photon is `1310 nm`.

Answer

B, C

Explanation

`E_(1) = (12400)/(lambda_(1)) :. (E_(1))/(E_(2)) = (lambda_(1))/(lambda_(2)) = (1)/(2) rArr lambda_(1) = 2lambda_(2)`
`E_(2) = (12400)/(lambda_(2))`
`E = (12400)/(3100) = 2 ((12400)/(lambda_(1))) + (12400)/(lambda_(2))`
`:. (12400)/(3100) = 2((12400)/(lambda_(1))) + ((12400)/(lambda_((1)/(2))))`
`(12400)/(3100) = 4 ((12400)/(lambda_((1)/(2))))`
`lambda_(1) = 4 xx 3100 Å`
`= 12400Å`
`= 1240 nm`