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Setting up an Uncertainty Problem

  1. Nov 2, 2016 #1
    1. The problem statement, all variables and given/known data
    A proton is known to lie within the nucleus of a gold atom. The radius of a gold nucleus is approximately 6 fm. What is the minimum uncertainty in the proton’s velocity [you may treat the problem as one-dimensional and you should express your answer as a fraction of c].

    2. Relevant equations
    ΔxΔp ≥ ħ/2

    3. The attempt at a solution
    I think I got this, but Chegg is showing up weird inconsistent answers. I just want to make sure my logic is sound:

    So since we can treat this one dimensionally, we know that the proton lies within a 6fm range. For simplicity, we can (in our imaginations) draw a 6 fm line and put a point on the center. On that center, our uncertainty of the position of the proton is ± 3 fm. So our Δx should be 3fm instead of 6 fm!

    The rest of the work is rather simple, I just want to make sure I'm setting this up properly.
     
  2. jcsd
  3. Nov 2, 2016 #2

    TSny

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    The 6 fm represents the radius of the nucleus.
     
  4. Nov 2, 2016 #3
    Not very helpful. I think my work shows that I understand this.
     
  5. Nov 2, 2016 #4

    haruspex

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    No, it shows you thought the 6fm was a diameter.
     
  6. Nov 3, 2016 #5

    kuruman

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    Not that it would make a difference to this order of magnitude calculation, but if someone gave me a proton in a one-dimensional box that extends, say, from zero to 12 fm and asked "where is the proton?", I would say "somewhere between zero and 12 fm". So in such situations, I consider the position uncertainty to be the entire range in which the particle can be without me knowing any better.
     
  7. Nov 3, 2016 #6
    You're 100% right. Thanks for that!
     
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