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Uncertainty principle and an electron

  1. Jan 3, 2006 #1
    question is:
    use the uncertainty principle to show that if an electron were confined inside and atomic nucleus, diameter of [tex]2 x 10^{-15}m[/tex], it would have to be moving relativistically i.e. more than 0.1c.
    what i have done is the following:
    [tex] \Delta x \Delta p = \frac{\hbar}{2}[/tex]
    then i set [tex]\Delta x = 2 x 10^{-15}[/tex] and solved for [tex]\Delta p[/tex]

    from this i dont know how to solve for the speed, i considered replacing [tex]\Delta p[/tex] with [tex]\gamma m\Delta v[/tex] but this doesnt seem to work with the gamma in there.
    what is a better way to solve this?
  2. jcsd
  3. Jan 3, 2006 #2


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    Must you actually solve for the speed? [it can be done, since you can write [tex]\gamma[/tex] in terms of v... but do you need to?]
    While v>0.1c may characterize "relativistic", is there another way?
  4. Jan 3, 2006 #3
    this was the hint that was given, that relativistic speeds were > 0.1c, but if you could give me a hint on comparing something else it would be appreciated.
  5. Jan 3, 2006 #4


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    What is the corresponding inequality for [tex]\gamma[/tex]?
  6. Jan 3, 2006 #5
    i dont know of anything similar, but gamma will be less than or equal to 1. is this close to the right track?
  7. Jan 4, 2006 #6
    Find [itex] \frac{\gamma v}{c}[/itex] (= [itex]\frac{\Delta p}{mc}[/itex])

    Squre both sides and solve for v/c.
  8. Jan 4, 2006 #7
    v < c
    Therefore, gamma > 1
    Last edited: Jan 4, 2006
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