Question

A near $UV$ photon of $300nm$ is absorbed by a gas and then re-emitted as two photons. One photon is red with wavelength of the second photon is

• A. 1060 nm
• B. 496 nm
• C. 300 nm
• D. 215 nm

Answer 1

Answer: (B)

Energy values are additives.
$E=E_1+E_2$
$\frac{hc}{\lambda }=\frac{hc}{{\lambda }_1}+\frac{hc}{{\lambda }_2}$
or $\frac{1}{\lambda }=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}$
or $\frac{1}{300}=\frac{1}{760}+\frac{1}{{\lambda }_2}$
or $\frac{1}{{\lambda }_2}=\frac{1}{300}-\frac{1}{760}$
On solving $\lambda =495.6nm$
$\approx 496nm$