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Question: A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of he...

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

A

H

B

H1/2H^{1/2}

C

H0H^{0}

D

H−1/2H^{- 1/2}

Answer

H−1/2H^{- 1/2}

Explanation

Solution

: Velocity acquired by a particle while falling from a height H is

v=2gHv = \sqrt{2gH}……. (i)

As λ=hmv=hm2gH\lambda = \frac{h}{mv} = \frac{h}{m\sqrt{2gH}} (using (i))

Or λ∝1H\lambda \propto \frac{1}{\sqrt{H}}