Question

A photon of energy 10.2 eV corresponds to light of wavelength ${\lambda }_0$. Due to an electron transition from x =2 to x = 1 in a hydrogen atom, light of wavelength A is emitted. If we take into account the recoil of the atom when the photon is emitted, then :

• A. $\lambda <{\lambda }_0$
• B. $\lambda >{\lambda }_0$
• C. $\lambda ={\lambda }_0$
• D. None of these

Answer 1

The correct option is B $\lambda >{\lambda }_0$

Without recoil of atom
$\frac{hc}{{\lambda }_0}=10.2eV$
With recoil of atom
$\underset{\cdot }{\to }=\underset{m}{\underset{\cdot }{\leftarrow }}+m\to \frac{h}{\lambda }$
$\frac{hc}{\lambda }+\frac{1}{2}m{v}^2=10.2$
$\frac{hc}{\lambda }<\frac{hc}{{\lambda }_0}$
$\therefore {\lambda }_0<\lambda$