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

$\begin{array}{l}\mathrm{E}=\frac{\mathrm{hc}}{\mathrm{\lambda }}...\left(\mathrm{i}\right)\\ {\mathrm{E}}_1=\frac{\mathrm{hc}}{{\mathrm{\lambda }}_1}....\left(\mathrm{ii}\right)\\ {\mathrm{E}}_2=\frac{\mathrm{hc}}{{\mathrm{\lambda }}_2}....\left(\mathrm{iii}\right)\\ \mathrm{E}={\mathrm{E}}_1+{\mathrm{E}}_2\\ \frac{\mathrm{hC}}{\mathrm{\lambda }}=\mathrm{hc}\left(\frac{1}{{\mathrm{\lambda }}_1}+\frac{1}{{\mathrm{\lambda }}_2}\right)\\ \frac{1}{\mathrm{\lambda }}=\frac{1}{{\mathrm{\lambda }}_1}+\frac{1}{{\mathrm{\lambda }}_2}\\ \frac{1}{\left(300\times {10}^{-9}\right)}=\frac{1}{\left(760\times {10}^{-9}\right)}+\frac{1}{{\mathrm{\lambda }}_2}\\ \frac{1}{{\mathrm{\lambda }}_2}=\left(\frac{1}{300}-\frac{1}{760}\right)\times {10}^{-9}\\ =\left(0.00333-0.00131\right)\times {10}^9=2.02\times {10}^6{\mathrm{m}}^{-1}\end{array}$