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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
(a) According to Heisenberg's uncertainty principle
`Deltax.Deltap=(h)/(4pi)`
Given, `Deltax=Deltap " " (Delta x`=uncertainty in position)
`(Delta p)^(2)=(h)/(4pi) " " (Deltap=mxxDelta v)`
`m^(2) Deltav^(2)=(h)/(4pi) " " `m=mass
`Delta v^(2)= (h)/(m^(2) 4pi) rArr Deltav=(1)/(2m) sqrt((h)/(pi)) " "` (`Deltav`=uncertainty in velocity)
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