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

Options

A. H
B. `H^(1//2)`
C. `H^(0)`
D. `H^(-1//2)`

Answer

D

Explanation

Velocity of a body falling from a height H is given by
`v= sqrt(2gH)`
We know that de-Broglie wavelength
`lamda=h/(mv)=h/(msqrt(2gH))implies h/(msqrt(2g)sqrtH)`
Here, `h/(msqrt2g)` is a constant say . K.
So, `lamda=K1/(sqrtH)implies lamdaprop 1/(sqrtH)implies lamda prop H^(-1//2)`