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

[eigenmax]

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 U_Coul = 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]

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

 

[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.

 

[kuruman]

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

 

[eigenmax]

I would think the answer to be around 350keV

 

[kuruman]

And in what units is 1.224733x10^-13?

 

[eigenmax]

eV

 

[kuruman]

eV

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

 

[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.

 

[kuruman]

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.