The uncertainties in the velocities of two particles, A and B are 0.05 and 0.02ms−1 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
2
4
0.25
A
2
B
0.25
C
4
D
1
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Solution
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Using the relation,
Δx⋅Δv=h4πm
[Heisenberg' uncertainty principle]
or, Δx=h4πm⋅Δv
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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