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If uncertainty in position and momentum ...

If uncertainty in position and momentum are equal then uncertainty in velocity is.

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
According to Heienberg's uncertainty principle,
`(Deltax) (Deltap_(x)) ge (h)/(4pi)`
If `(Deltax) = (Deltap_(x))`
then `(Deltap_(x))^(2) ge (h)/(4pi)`
or `Deltap_(x) ge sqrt((h)/(4pi)) (1)` ltbrlt Since `p = mv`, we have
`Deltap_(x) = mDeltav_(x)`
Substitution of Eq. `(2)` in Eq. `(1)` gives
`Deltav_(x) ge (1)/(m) sqrt((h)/(4pi))`
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