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

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) H1/2 (C) H0 (D) H-1/2

Tardigrade Admin · Accepted Answer

Velocity acquired by a particle while falling from a height H is v =√2gH ...(i) As λ = (h/mv) = (h/m√2gH) (Using (i) or λ propto(1/√H)

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

$H$

$H^{1/2}$

$H^{0}$

$H^{- 1/2}$

Velocity acquired by a particle while falling from a height $H$ is
$v = 2 g H ... (i)$
As $λ = \frac{h}{m v} = \frac{h}{m 2 g H}$ (Using $(i)$
or $λ \propto \frac{1}{H}$

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

H

H1/2

H0

H−1/2

Velocity acquired by a particle while falling from a height H is v=2gH​...(i) As λ=mvh​=m2gH​h​ (Using (i) or λ∝H​1​

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

$H$

$H^{1/2}$

$H^{0}$

$H^{- 1/2}$

Velocity acquired by a particle while falling from a height $H$ is
$v = 2 g H ... (i)$
As $λ = \frac{h}{m v} = \frac{h}{m 2 g H}$ (Using $(i)$
or $λ \propto \frac{1}{H}$