Question

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

• A. 759 nm
• B. 857 nm
• C. 957 nm
• D. 657 nm

Answer 1

Answer: (A)

759 nm

Energy of observed photon = Sum of energies of two emitted photons
$E_3=E_1+E_2$

$\Rightarrow \frac{1}{{\lambda }_3}=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}$

$\Rightarrow \frac{1}{300}=\frac{1}{496}+\frac{1}{{\lambda }_2}$

$\Rightarrow \frac{1}{{\lambda }_2}=\frac{1}{300}-\frac{1}{496}$

$\Rightarrow {\lambda }_2=\frac{300\times 496}{196}$

$\Rightarrow {\lambda }_2=759.2nm$