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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{2gH} \quad...\left(i\right) $
As $\lambda = \frac{h}{mv} = \frac{h}{m\sqrt{2gH}} $ (Using $(i)$
or $\lambda \propto\frac{1}{\sqrt{H}}$