# A photon of 300nm is observed by a gas and then re-emits two photons. One re-emitted photon has wavelength 496nm, the wavelength of second re-emitted photon is

$(a)\;759nm\qquad(b)\;857nm\qquad(c)\;957nm\qquad(d)\;657nm$

$E_{\text{photon absorbed}}=E_1+E_2$(energy released)
$\large\frac{hC}{\lambda}=\frac{hC}{\lambda_1}+\frac{hC}{\lambda_2}$
$\Rightarrow\large\frac{1}{\lambda}=\frac{1}{\lambda_1}+\frac{1}{\lambda_2}$
$\Rightarrow\large\frac{1}{300\;nm}=\frac{1}{496\;nm}+\frac{1}{\lambda_2}$
$\therefore\lambda_2 = \Large\frac{496\times300}{496-300}$$\;nm=759.183\;nm$
Hence (a) is the correct answer.
edited Mar 19, 2014