Uncertainty principle and an electron

  • #1
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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?
thanks
 

Answers and Replies

  • #2
robphy
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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?
 
  • #3
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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.
 
  • #4
robphy
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What is the corresponding inequality for [tex]\gamma[/tex]?
 
  • #5
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i dont know of anything similar, but gamma will be less than or equal to 1. is this close to the right track?
 
  • #6
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Find [itex] \frac{\gamma v}{c}[/itex] (= [itex]\frac{\Delta p}{mc}[/itex])

Squre both sides and solve for v/c.
 
  • #7
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gamma will be less than or equal to 1.
v < c
Therefore, gamma > 1
 
Last edited:

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