Question

A near $UV$ photon of $300 \,nm$ 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} $
$\frac{h c}{\lambda} =\frac{h c}{\lambda_{1}}+\frac{h c}{\lambda_{2}}$
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 =495.6 \,nm $
$ \approx 496 \,nm $