Question

A gas absorbs a photon of $355$ nm and emits at two wavelengths. If one of the emissions is at $680$ nm, then find the wavelength of the other in nm.

Answer 1

Answer: 743

Energy of absorbed photon = Sum of the energies of emitted photon
$\frac{hc}{\lambda }=\frac{hc}{{\lambda }_1}+\frac{hc}{{\lambda }_2}$
or $\frac{1}{\lambda }=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}$
$\frac{1}{355\times 10^{-9}}=\frac{1}{680\times 10^{-9}}+\frac{1}{\lambda }$
$\frac{1}{{\lambda }_2}=\frac{1}{355\times 10^{-9}}-\frac{1}{680\times 10^{-9}}=1.346\times 10^6$
or ${\lambda }_2=11.346\times 10^6=743\times 10^{-9}$ m
$=743$ nm