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Heisenburg Uncertainty Principle - Seems like an easy question?

  1. Apr 27, 2012 #1
    Heisenburg Uncertainty Principle - Seems like an easy question??

    1. The problem statement, all variables and given/known data
    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.


    2. Relevant 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


    3. 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.
     
  2. jcsd
  3. Apr 27, 2012 #2

    jambaugh

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    Science Advisor
    Gold Member

    Re: Heisenburg Uncertainty Principle - Seems like an easy question??

    The more precise form of the HUP is:
    [tex] \Delta x \Delta p \ge \frac{\hbar}{2}[/tex]
    (wikipedia:Plank's Constant)
    That will give you a factor of 1/4 pi in your answers.
     
  4. Apr 27, 2012 #3
    Re: Heisenburg Uncertainty Principle - Seems like an easy question??

    What makes you think you've made an error?
     
  5. Apr 29, 2012 #4
    Re: Heisenburg Uncertainty Principle - Seems like an easy question??

    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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