Question

When the momentum of a photon is changed by an amount $p^{\prime }$ then the corresponding change in the de-Broglie wavelength is found to be $0.20$%. Then, the original momentum of the photon was

• A. $300p^{\prime }$
  
• B. $500p^{\prime }$
  
• C. $400p^{\prime }$
• D. $100p^{\prime }$

Answer 1

The correct option is B $500p^{\prime }$

As, we know de-Broglie wavelength,

$\lambda =\frac{h}{p}$

$\therefore \lambda \propto \frac{1}{p}$

$\Rightarrow \frac{\Delta p}{p}=-\frac{\Delta \lambda }{\lambda }\therefore \left|\frac{\Delta p}{p}\right|=\left|\frac{\Delta \lambda }{\lambda }\right|$

$\Rightarrow \frac{p^{\prime }}{p}=\frac{0.20}{100}=\frac{1}{500}$

or, $p=500p^{\prime }$