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  4. If the kinetic energy of a free electron doubles, it’s de-Broglie wavelength changes by the factor

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Q. If the kinetic energy of a free electron doubles, it’s de-Broglie wavelength changes by the factor

VITEEEVITEEE 2019

Solution:

de-Broglie wavelength,
$\lambda=\frac{h}{p}=\frac{h}{\sqrt{2.m.\left(K.E\right)}}$
$\therefore \lambda\,\propto \frac{1}{\sqrt{K.E}}$
If K.E is doubled, then de-Broglie wavelength becomes $\frac{\lambda}{\sqrt{2}}$