The mass of a particle is 10−10g and its radius is 2×10−4cm. If its velocity is 10−6cm sec−1 with 0.0001% uncertainty in measurement,the uncertainty in its position is :
A
5.2×10−8m
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B
5.2×10−7m
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C
5.2×10−6m
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D
5.2×10−9m
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Solution
The correct option is A5.2×10−8m m=10−10g=10−13kg ΔV=6.0001 of V V=10−6cm/s=10−8m/s ΔV=0001100×10−8=10−14m/s Uncertainty in momentum =Δp=mΔV=10−13×10−14=10−23m/s According to uncertainty principle we get Δx=Δp=n4n Δx=n4n×1Δp =6.6×10−344×3.14×1027