Heisenbergs uncertainity principle for an electron

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Homework Help Overview

The discussion revolves around applying the Heisenberg uncertainty principle to determine the smallest region of space in which an electron can be confined, given an uncertainty in its speed.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the uncertainty principle, specifically questioning the interpretation of the given uncertainty in speed as opposed to the speed itself. There are attempts to calculate the confinement size using Dirac's constant and momentum.

Discussion Status

Some participants have provided calculations and expressed uncertainty about their results. There is an ongoing exploration of the correct interpretation of the uncertainty in speed and its implications for calculating momentum.

Contextual Notes

Participants note that the uncertainty in speed is not the same as the speed of the electron, which raises questions about the proper application of the uncertainty principle in this context.

DODGEVIPER13
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Homework Statement


The speed of an electron is measured to within an uncertainty of 2e4 m/s. What is the size of the smallest region of space in which the electron can be confined?


Homework Equations


Diracs Constant=ΔxΔp
p=mv

The Attempt at a Solution


what I did was (Diracs Constant)/mv = Δx, (1.054560653e-34)/((9.109e-31)(2e4))=6nm this is this incorrect but I don't understand why?
 
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DODGEVIPER13 said:

Homework Statement


The speed of an electron is measured to within an uncertainty of 2e4 m/s. What is the size of the smallest region of space in which the electron can be confined?


Homework Equations


Diracs Constant=ΔxΔp
p=mv

The Attempt at a Solution


what I did was (Diracs Constant)/mv = Δx, (1.054560653e-34)/((9.109e-31)(2e4))=6nm this is this incorrect but I don't understand why?
Hi,
I am not sure, I may be wrong.
Use Heisenberg uncertainty principle:
\Delta x \Delta p ≥ \hbar/2.<br />
The given value is not the speed of electron. It is the uncertainty of speed.
Got it?
 
Hi. Not value but only order of value has meaning in this situation. Order of nano meter seems fine. What is the 'correct' answer you have got?
 
Sweet springs the correct answer is 5.8nm what I get is 6nm I know it's so close but it's not what I'm getting. Rajini given the uncertainty of speed how then would I find speed go the electron so I can find p.
 
Ok I'm starting to think I got the right answer after using wolfram I get 5.78 I am starting to think my calculator has some kind of rounding algorithm
 

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