Question

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. H^1/2

c. H⁰

d. H^-1/2

Answer 1

As we know de Broglie wave length is given by
$$\begin{gathered} \lambda =\frac{h}{p}=\frac{h}{mv} \\ andvelocityofparticle\left(v\right)atbelowheightH,ifitisfreefallingisgivenby \\ v=\sqrt{2gH} \\ Thus\lambda =\frac{h}{mv}=\frac{h}{\sqrt{2gH}},so\lambda isproportionalto{H}^{-\frac{1}{2}} \end{gathered}$$