A photon of wavelength `300` nm is absorbed by a gas and then reemitted as two photons. One photon is red with wavelength of `760` nm. The wave number of the second photon will be.

Options

A. `2.02 xx 10^6 m^-1`
B. `3.02 xx 10^6 m^-1`
C. `1.02 xx 10^6 m^-1`
D. `2.2 xx 10^6 m^-1`

Answer

A

Explanation

(a) `E = (hc)/(lamda)` …(i)
`E_1 = (hc)/(lamda_1)` ….(ii)
`E_2 = (hc)/(lamda_2)`…(iii)
`E = E_1 + E_2 = hc((1)/(lamda_1) + (1)/(lamda_2))`
`(1)/(lamda) = (1)/(lamda_1)+(1)/(lamda_2)`
`(1)/((300 xx 10^-9)) = (1)/((760 xx 10^-9)) +(1)/(lamda_2)`
`(1)/(lamda_2) = ((1)/(300) - (1)/(760)) xx 10^9`
=`(0.00333 - 0.00131) xx 10^9 = 2.02 xx 10^6 m^-1`.