Question

A photon of $400\text{nm}$ is absorbed by a gas molecule and then the molecule re-emits two photons. One re-emitted photon has wavelength $500\text{nm}$. Assuming that there is no change in the energy of molecules, the wavelength of second re-emitted photon is:

• A. $100\text{nm}$
• B. $2000\text{nm}$
• C. $1000\text{nm}$
• D. $1500\text{nm}$

Answer 1

The correct option is B $2000\text{nm}$

$E=E_1+E_2$
where $E_1$ and $E_2$ is the Energy of photon 1 and photon 2 and $E=\frac{hc}{\lambda }$
$\Rightarrow \frac{hc}{\lambda }=\frac{hc}{{\lambda }_1}+\frac{hc}{{\lambda }_2}$
or $\frac{1}{\lambda }=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}$

$\Rightarrow \frac{1}{400}=\frac{1}{500}+\frac{1}{{\lambda }_2}$
On solving,
$\Rightarrow {\lambda }_2=2000\text{nm}$