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Homework Help: How to calculate the Coulomb barrier between a proton and a lithium nucleus

  1. Jan 1, 2018 #1
    1. The problem statement, all variables and given/known data
    How to calculate the Coulomb barrier between a proton and a lithium nucleus. The variable is r (interaction radius). The known data is Z1, Z2, k (Coulomb constant), and e (elementary charge).

    2. Relevant equations
    The equation is UCoul = kZ1Z2e2/r

    3. The attempt at a solution
    I used the sum of lithium's atomic radius and the radius of a proton as the interaction radius. I got 1.5200084x10-10m. I plugged in all the numbers and got 4.552437x10-18 as my Coulomb barrier, which I think is incorrect.
     
  2. jcsd
  3. Jan 1, 2018 #2

    kuruman

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    You need to consider the nuclear not the atomic radius of lithium.
     
  4. Jan 2, 2018 #3
    Ok, thanks. The nuclear radius of lithium is 4.8fm and the radius of a proton is 0.85fm. That gives an interaction radius of 5.65fm, or 5.65x10-15. Plugging in the new numbers gives 1.224733x10-13, which is still incorrect.
     
  5. Jan 2, 2018 #4

    kuruman

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    What do you believe to be the correct answer? Please include units.
     
  6. Jan 2, 2018 #5
    I would think the answer to be around 350keV
     
  7. Jan 2, 2018 #6

    kuruman

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    And in what units is 1.224733x10-13?
     
  8. Jan 4, 2018 #7
  9. Jan 4, 2018 #8

    kuruman

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    Nope. If you use the equation and the numbers that you provided, the answer comes out in Joules.
     
  10. Jan 4, 2018 #9
    Oh, ok. Sorry. That comes out to be 7.66eV. That seems awfully low. One can't run a proton accelerator on 7.66 volts.
     
  11. Jan 7, 2018 #10

    kuruman

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    It's more than that. Recheck your powers of 10.
     
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