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Question

The uncertainty in the position of an object weighing 40 g is ±103 m. Calculate the uncertainty in its velocity.

A
1.32×1030 m/s
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B
2.63×1029 m/s
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C
0.55×1030 m/s
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D
4.55×1029 m/s
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Solution

The correct option is A 1.32×1030 m/s
From Heisenberg’s uncertainty principle,
Δx. (Δp) ≥ h4π
Δx.m.(Δv)h4π
Where, h = Planck’s constant
Δx = uncertainty in position = 103 m
Δv = uncertainty in velocity
m = mass of the bullet in kilograms = 40×103 kg
So, Δvh4πΔxm ....(1)

Putting up the values in eq. (1)
Δv6.6×10344×3.14×103×40×103Δv1.313×1030 m/s

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