Heisenburg Uncertainty Principle - Seems like an easy question?

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Homework Help Overview

The discussion revolves around the Heisenberg Uncertainty Principle, specifically calculating the minimum uncertainty in velocity for a boulder, a proton, and an electron given a specific uncertainty in position. The original poster presents their calculations and results for each case.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the uncertainty principle using the formula Δv = h / (Δx * m) for different masses. Some participants question the accuracy of the results and suggest considering significant digits and the more precise form of the uncertainty principle.

Discussion Status

The discussion is ongoing, with participants exploring the calculations and addressing potential errors. There is acknowledgment of the need for precision in significant digits, and some guidance has been offered regarding the use of a more precise form of the uncertainty principle.

Contextual Notes

Participants note that the calculations may be sensitive to significant digits, which could affect the acceptance of the answers in the context of the problem.

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Heisenberg Uncertainty Principle - Seems like an easy question??

Homework Statement


The position of a 900 kg boulder's center of mass has been determined to within an uncertainty of 1.0 nm. (a) What is the minimum uncertainty in the boulder's velocity? (b) Repeat the calculation, but for a proton with the same uncertainty in position. (c) Repeat the calculation, but for an electron with the same uncertainty in position.


Homework Equations


Δx*Δp ~ h
Assuming that there is no uncertainty in the measurement of mass,
Δx*mΔv = h
where Δv is the uncertainty in the measurement of velocity.
Δv = h / Δx *m

h = 6.6256 *10^-34 J-s
m = 900 kg for boulder
mp = 1.6725*10^-27 kg for proton
me = 9.1*10^-31 kg for electron.
Δx = 1.0*10^-9 m


The Attempt at a Solution


I did each of these the same way. Plugged in the variables using this equation:
Δv = h / (Δx *m)
The answers I got are:
a. 7.36*10^-28 m/s
b. 396.7 m/s
c. 7.28*10^5 m/s

I'm hoping I've made a silly error somewhere, but I've been unable to find it.
 
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The more precise form of the HUP is:
\Delta x \Delta p \ge \frac{\hbar}{2}
(wikipedia:Plank's Constant)
That will give you a factor of 1/4 pi in your answers.
 


What makes you think you've made an error?
 


Thanks for the help.
I used the link from jambaugh and that equation helped. I got a, but it still won't accept b&c. It is really picky about significant digits.
 

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