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College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

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BuyFindarrow_forward

College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

The velocity of a proton in an accelerator is known to an accuracy of 0.250% of the speed of light. (This could be small compared with its velocity.) What is the smallest possible uncertainty in its position?

To determine

The smallest possible uncertainty in the position of proton.

Explanation

Given info:

Uncertainty in velocity of proton is,Δv=0.25%ofc.

Formula used:

The Heisenberg's Uncertainty principle can be expressed mathematically as,

ΔxΔph4π

Calculation:

The uncertainty in momentum can be given as,

Δp=mΔv

The smallest uncertainty in the position of electron will be,

ΔxΔp=h4πΔxmΔv=h4πΔx=h4πmΔv

Substituting the given values in the above equation, we get

Δx=6.626×1034Js4×3

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