Question

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

• A. $2.02 \times10^{6}m^{-1}$
• B. $3.02 \times 10^{6} m^{- 1}$
• C. $1.02 \times 10^{6} m^{- 1}$
• D. $2.2 \times 10^{6} m^{-1}$

Answer 1

Answer: (A)

$E= \frac{hc}{\lambda} \ldots\left(i\right)$
$E_{1} =\frac{hc}{\lambda_{1}} \ldots\left(ii\right) $
$E_{2} =\frac{hc}{\lambda_{2}} \ldots\left(iii\right) $
$E=E_{1}+E_{2}=hc \left(\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}\right)$
$\frac{1}{\lambda}=\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}$
$ \frac{1}{\left(300\times10^{-9}\right)}=\frac{1}{\left(760\times10^{-9}\right)}+\frac{1}{\lambda_{2}}$
$ \frac{1}{\lambda_{2}} =\left(\frac{1}{300}-\frac{1}{760}\right)\times10^{9} $
$=\left(0.00333 -0.00131\right)\times10^{9} =202 \times10^{6} m^{-1}$