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A protons Min KE

  • #1

Homework Statement



A proton is confined in a uranium nucleus of radius 7.41 fm. Determine the proton's minimum kinetic energy K less than or equal to delta K according to the uncertainty principle if the proton is well approximated by a Gaussian wave packet confined by the nuclear diameter.


Homework Equations



change in momentum * change in x is greater than or equal to h(bar)/2
I don't know



The Attempt at a Solution



I found the minimum change in momentum but can't seem to relate that to the minimum KE. I tried change KE= change in p*c but that was wrong.
since it is confined by the diameter do I times the radius by 2? Thats how I did it.

dx=14.82E-15 m
h(bar)/2=1.0546E-34/2=5.273E-35
5.273E-35/14.82E-15= 3.54E-21
3.54E-21*3E8= 1.0674E-12 J

But this is wrong and I don't have a clue as to why. Can someone help me out please?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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618
First of all, try to put units on ALL of your quantities, ok? Otherwise, people can only guess what '3.54E-21' might be supposed to stand for. Having said that, it looks like you got delta(p) ok. But I am completely unable to guess what the '3E8' in the last line might be. How do you go from momentum to energy?
 
  • #3
Dick
Science Advisor
Homework Helper
26,258
618
Oh, I get it. You really are using p*c=E!!! That only holds for massless particles. The proton is hardly massless.
 

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