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Question
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to ______.
Options
`H`
`H^(1/2)`
`H^0`
`H^(-1/2)`
Solution
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to `underline(H^(-1/2))`.
Explanation:
According to de-Broglie a moving material particle sometimes acts as a wave and sometimes as a particle.
The wave associated with a moving particle is called matter wave or de-Broglie wave and it propagates in the form of wave packets with the group velocity. According to de-Broglie theory, the wavelength of de-Broglie wave is given by `H = v = sqrt(2gH)`
We know that de-Broglie wavelength `λ = h/p`
`λ = h/(mv) = h/(msqrt(2gH)`
h, m and g are constant
∴ `h/(msqrt(2g)` is constant ⇒ `λ oo 1/sqrt(H)` ⇒ `λ oo H^(-1/2)`
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