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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

Dual Nature of Radiation and Matter

Solution:

Velocity acquired by a particle while falling from a height $H$ is, $v=\sqrt{2 gH }$
$\lambda=\frac{h}{m v}=\frac{h}{m \sqrt{2 g H}} \text { or } \lambda \propto H^{-\frac{1}{2}}$