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When uncertainty in position and momentu...

When uncertainty in position and momentum are equal, then the uncertainly in velocity is

A

`sqrt((h)/(pi))`

B

`(1)/(2) sqrt((h)/(pi))`

C

`(1)/(2m) sqrt((h)/(pi))`

D

`2m sqrt((h)/(pi))`

Text Solution

Verified by Experts

The correct Answer is:
C
`Delta x = Delta p`
`Delta p^(2) = (h)/(4pi) or Delta p = (1)/(2) sqrt((h)/(pi))`
`m Delta v = (1)/(2) sqrt((h)/(pi)) or, Delta v = (1)/(2m) sqrt((h)/(pi))`
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Knowledge Check

  • If uncertainty in position and velocity are equal then uncertainty in momentum will be:

    A
    `1/2 sqrt((mh)/(pi))`
    B
    `1/2 sqrt((h)/(pi m))`
    C
    `h/(4 pi m)`
    D
    `(nh)/(4pi)`

  • Hiesenberg.s uricertainty principle states that it is impossible to determine simultaneously the position and momentum of a particle. He considered the limits of how precisely we can measure properties of an e^- (or)other microscopic particles like electron. The more accurately we measure the momentum of a particle, less accurately we can determine its position. If uncertainty in measurement of position and momentuin are equal calculate the uncertainty in velocity

    A
    `(Deltap)/(m)`
    B
    `(m)/(Delta p)`
    C
    `mDeltap`
    D
    `1/(m Delta p)`

  • de-Broglie proposed dual nature for electron moving. The wavelength is given by the equations lambda = (h)/(m u) . Later on Heisenburg proposed. The total incertainly uncertainity principle as. If uncertainity in position an momentum of an electron are same, then uncertainty in its velocity can be given by

    A
    `ge sqrt((h)/(4pi m))`
    B
    `ge sqrt((h)/(2m))`
    C
    `ge sqrt((lambda)/(4pi m))`
    D
    `ge (1)/(m) sqrt((h)/(4pi ))`

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