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Question

The uncertainity in position for a dust particle (m=1011g ;diameter=104cm and velocity=1011cm/s) will be: ( The error in measurement of velocity is 1%)
  1. 5.27×107cm
  2. 5.27×106cm
  3. 5.27×104cm
  4. 5.27×105cm

A
5.27×104cm
B
5.27×105cm
C
5.27×106cm
D
5.27×107cm
Solution
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Δx = uncertainty in position
Heisenberg uncertainty equation is Δx(mΔv)=h/4π

Δv = 1% eroor in the velocity = 1×1011/100×102=1015 m = 1014
1015×1014×Δx=6.626×10344π

Δx=6.6261054π m1

or Δv=0.527×105
Δv=5.27×104

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