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)`

Explanation

Velocity of a body falling from a hight H is given by
`" "v=sqrt(2gH)`
We know that de-broglie wavelength
`" "lamda=(h)/(mv)=(h)/(msqrt2gH)implies=(h)/(msqrt(2g)sqrt(H))`
Here `(h)/(msqrt(2g))` is a constant `phi` say 'K'.
So `" "lamda=K(1)/(sqrtH)implieslamdaprop(1)/(sqrtH)`
`implies" "lamdapropH^(-1//2)`