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

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1. Jan 1, 2018

### eigenmax

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. Jan 1, 2018

### kuruman

You need to consider the nuclear not the atomic radius of lithium.

3. Jan 2, 2018

### eigenmax

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.

4. Jan 2, 2018

### kuruman

What do you believe to be the correct answer? Please include units.

5. Jan 2, 2018

### eigenmax

I would think the answer to be around 350keV

6. Jan 2, 2018

### kuruman

And in what units is 1.224733x10-13?

7. Jan 4, 2018

eV

8. Jan 4, 2018

### kuruman

Nope. If you use the equation and the numbers that you provided, the answer comes out in Joules.

9. Jan 4, 2018

### eigenmax

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. Jan 7, 2018

### kuruman

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