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

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SUMMARY

The discussion focuses on calculating the Coulomb barrier between a proton and a lithium nucleus using the formula UCoul = kZ1Z2e²/r. The interaction radius was initially miscalculated using atomic rather than nuclear radii, leading to incorrect results. The correct nuclear radius for lithium is 4.8 femtometers (fm) and for a proton is 0.85 fm, resulting in an interaction radius of 5.65 fm. The final calculation yields a Coulomb barrier of approximately 7.66 eV, which is deemed too low for practical applications, indicating a need for careful attention to unit conversions and powers of ten.

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  • Basic algebra for manipulating equations
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eigenmax
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Homework Statement


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).

Homework Equations


The equation is UCoul = kZ1Z2e2/r

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.
 
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You need to consider the nuclear not the atomic radius of lithium.
 
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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.
 
What do you believe to be the correct answer? Please include units.
 
I would think the answer to be around 350keV
 
And in what units is 1.224733x10-13?
 
eV
 
eigenmax said:
eV
Nope. If you use the equation and the numbers that you provided, the answer comes out in Joules.
 
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.
 
  • #10
eigenmax said:
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.
It's more than that. Recheck your powers of 10.
 

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