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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

Suppose the velocity of an electron in an atom is known to an accuracy of 2.0 × 10 3 m/s (reasonably accurate compared with orbital velocities). What is the electron's minimum uncertainty in position, and how does this compare with the approximate 0.1-nm size of the atom?

To determine

The minimum uncertainty in position of an electron and the comparison of the value of uncertainty in position with the approximate0.1-nmsize of the atom.

Explanation

Given info:

Uncertainty in velocity is,Î”v=2.0Ã—103â€‰m/s.

Formula used:

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

Î”xâ‹…Î”pâ‰¥h4Ï€

Calculation:

The uncertainty in momentum can be calculated as,

Î”p=mÎ”v

The smallest uncertainty in the position of electron will be,

Î”xâ‹…Î”p=h4Ï€Î”xâ‹…mÎ”v=h4Ï€Î”x=h4Ï€mÎ”v

Substituting the given values in the above equation, we get

Î”x=6.626Ã—10âˆ’34Jâ‹…s4Ã—227Ã—9.11Ã—10âˆ’31kgÃ—2.0Ã—103m/s=6.626Ã—10âˆ’34Jâ‹…s229

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