Question

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

• A. $2.02\times 10^6{m}^{-1}$
• 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)

$E=\frac{hc}{\lambda }\dots \left(i\right)$
$E_1=\frac{hc}{{\lambda }_1}\dots \left(ii\right)$
$E_2=\frac{hc}{{\lambda }_2}\dots \left(iii\right)$
$E=E_1+E_2=hc\left(\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}\right)$
$\frac{1}{\lambda }=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}$
$\frac{1}{\left(300\times 10^{-9}\right)}=\frac{1}{\left(760\times 10^{-9}\right)}+\frac{1}{{\lambda }_2}$
$\frac{1}{{\lambda }_2}=\left(\frac{1}{300}-\frac{1}{760}\right)\times 10^9$
$=\left(0.00333-0.00131\right)\times 10^9=202\times 10^6{m}^{-1}$