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

## 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.

kuruman
Homework Helper
Gold Member
You need to consider the nuclear not the atomic radius of lithium.

• Dr. Courtney
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.

kuruman
Homework Helper
Gold Member
What do you believe to be the correct answer? Please include units.

I would think the answer to be around 350keV

kuruman
Homework Helper
Gold Member
And in what units is 1.224733x10-13?

eV

kuruman
Homework Helper
Gold Member
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.

kuruman