Question

A near ultraviolet photon of $300nm$ is absorbed by a gas and then remitted as two photons. One photon is red with wavelength of $760nm$. What would be the wave number of the second photon?

Answer 1

Energy absorbed $=$ Sum of energy of two quanta
$\frac{hc}{300\times {10}^{-9}}=\frac{hc}{760\times {10}^{-9}}+\frac{hc}{\lambda \times {10}^{-9}}$
On solving, we get,
$\overline{v}\left(wavenumber\right)=\frac{1}{\lambda }=2.02\times {10}^{-3}{m}^{-1}$.