A particle is droped 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 attained by the particle after falling from a height H is
`v=sqrt(2gH)`
Where g = acceleration due to gravity
The de Brolige wavelength is given by
`lamda=h//p=h/(mv)=h/(msqrt2gH)`
Where m is the mass and p is the momentum of particle
`:.lamdaprop1/sqrtH" or "lamdapropH^(-1//2)`