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The mass of a particle is 10-10 g. If its velocity is 10-6 cm sec-1 with 0.0001% uncertainty in measurement, the uncertainty in its position is

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Asked on December 26, 2019 by

Maanu Spandana

The mass of a particle is 10

−10

g and its radius is 2×10

−4

cm. If its velocity is 10−6cm sec

−1

with 0.0001% uncertainty in measurement,the uncertainty in its position is :

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ANSWER

m=10

−10

g=10

−13

kg

ΔV=6.0001% of V

V=10

−6

cm/s=10

−8

m/s

ΔV=

100

0001

×10

−8

=10

−14

m/s

Uncertainty in momentum =Δp=mΔV=10

−13

×10

−14

=10

−23

m/s

According to uncertainty principle we get

Δx=Δp=

4n

n

Δx=

4n

n

×

Δp

1

=

4×3.14×10

27

6.6×10

−34

=5.2×10

−8