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  4. A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to

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Q. A particle is dropped from a height $H$. The de Broglie wavelength of the particle as a function of height is proportional to

Solution:

Velocity acquired by a particle while falling from a height $H$ is
$V=\sqrt{2 g H}\,\,\,....(i)$
As $\lambda=\frac{h}{m v}=\frac{h}{m \sqrt{2 g H}}$ (Using (i))
$\Lambda \alpha \frac{1}{\sqrt{H}}$