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Question

The uncertainties in the velocities of two particles, A and B are 0.05 and 0.02 ms1 respectively. The mass of B is five times to that of the mass of A.
What is the ratio of uncertainties ΔxAΔxB in their positions?

  1. 1
  2. 2
  3. 4
  4. 0.25

A
2
B
0.25
C
4
D
1
Solution
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Using the relation,

ΔxΔv=h4πm

[Heisenberg' uncertainty principle]

or, Δx=h4πmΔv

Thus, ΔxA=h4π×0.05×m ....(i)

ΔxB=h4π×0.02×5m ....(ii)

Dividing (i) by (ii), we get

ΔxAΔxB=0.02×50.05=105 = 2

Hence, the correct option is A

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