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Homework Help: Minimum kinetic energy

  1. Apr 13, 2010 #1
    36. A proton is confined in a uranium nucleus of radius 8 x 10^-15 m. Determine the proton's minimum kinetic energy according to the uncertainty principle if the proton is confined to a one-dimensional box that has length equal to the nuclear diameter.

    What's wrong with my equation and value I used for L^2?

    362.jpg
     
  2. jcsd
  3. Apr 13, 2010 #2
    You defined [tex]L = 2\Delta x[/tex] so that means L should be the diameter and not the radius of the nucleus.
     
  4. Apr 13, 2010 #3
    Son of a... It does say diameter. :rolleyes: And so delta-x is the radius.

    Where did the 8 come from?
     
    Last edited: Apr 13, 2010
  5. Apr 13, 2010 #4
    I think the 8 came from if you pulled the 2 from 2*r out of the square it would be 4. And then you would have 2*4 = 8.
     
  6. Apr 13, 2010 #5
    But the 1.6 x 10^-5 nm = 2r, so that term is already squared. She has 8*m*d^2, not 2*m*(2r)^2 which would be 8*m*r^2.

    The definition of delta-x is arbitrary, right? But it has to make sense in the context of the wave function. It seems that delta-x = L/2 is a common definition.
     
    Last edited: Apr 13, 2010
  7. Apr 13, 2010 #6
    I think your grader just corrected it twice. Not thinking that you would interpret at as a single correction.
     
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