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  4. When the momentum of a photon is changed by an amount p′ , the corresponding change in the de-Broglie wavelength is found to be 0.2 % . Then, the original momentum of the photon was

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Q. When the momentum of a photon is changed by an amount $ p′$ , the corresponding change in the de-Broglie wavelength is found to be $0.2\%$ . Then, the original momentum of the photon was

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Solution:

$\because \, \lambda =\frac{h}{p}$
$\therefore \, \, \lambda \propto \frac{1}{p}$
$\Rightarrow \, \frac{\Delta p}{p}= \, -\frac{\Delta \lambda }{\lambda }$
$\therefore \, \, \left|\frac{\Delta p}{p}\right|=\left|\frac{\Delta \lambda }{\lambda }\right|$
$\Rightarrow \, \frac{p'}{p}=\frac{0.20}{100}=\frac{1}{500}$
$\Rightarrow \, p=500\,p'$