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Question

Uncertainity in position is twice the uncertainity in momentum uncertainity in velocity is :

A
hπ
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B
12mh2π
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C
122mh
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D
h4π
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Solution

The correct option is B 12mh2π
From Heisenberg’s uncertainty principle,
Δx.Δph4π
(or) Δx.m.(Δv)h4π
where h = Planck’s constant
Δx = uncertainty in position
Δv = uncertainty in velocity
Δp = uncertainty in momentum
m = mass of a particle

Given: Δx=2Δp
Putting the values, we get
2Δp.(Δp)h4π=2(Δp)2
We know that, Δp=mΔv
Δv=12mh2π

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