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Question

A golf ball has a mass of 40 g, and a speed of 45 m/s.
If the speed can be measured within accuracy of 2% , calculate the uncertainty in the position.

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Solution

According to Heisenberg uncertainty principle,

Δx.Δv=h4πm

Δx=uncertainty in position

Δv=uncertainty in velocity

h=planck's constant

m=mass of particle.

Uncertaintyin the position:

Given:Mass of golf ball=40 g

Speed of golf ball=45m/s

accuracy in speed=2%

The uncertainty in the speed is 2%,i.e.,Δv=45×2100=0.9ms1

According to Heisenberg uncertainty principle,

Δx.Δv=h4πm

Δx=h4πmΔv

Δx=6.626×1034Js4×3.14×(40g×103kg g1)×(0.9 ms1)

This is nearly 1018 times smaller than the diameter of a typical atomic nucleus. As we know, for large particles,the uncertainty principle sets no meaningful limit to the precision of measurements.

Final Answer: uncertainty in position is 1.46×1033m













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