Voltage required for penetration of an unknown element

[grantaere]

Homework Statement

An unknown element has a nucleus with charge 14.00 e and a radius of about 3.60×10-15 m. How much voltage must be used to accelerate a proton (radius 1.20×10-15 m) so that is has sufficient energy to just penetrate the unknown element?
Assume that the potential is that for point charges.

Homework Equations

V = kQ/r

The Attempt at a Solution

I tried calculating the two potential differences caused by the incoming proton and the positively charged atom, then adding them separately, but it seems that this isn't the right answer/ right approach.
V = (8.99e9*(14*(1.6e-19))/3.6e-15) + (8.99e9(1.6e-19)/1.2e-15) = 6.79e6 V
Any pointers would be very much appreciated!

 

[Bystander]

You are looking for the amount of energy (work) to bring two charges into contact. What is the force between two charges?

 

[grantaere]

So then I should use F=fqQ/r^2 to find the force between the two charges when they meet? I did that (and got 6.71E-13N) -- so then I can find the acceleration, but I'm still not sure how value this would be used to calculate voltage?

 

[Bystander]

Just wanted to know if you were familiar with the general Coulomb repulsion/attraction. The problem statement has apparently done the integration for the work, but omitted one of the charges, perhaps to give you a potential (rather than work) in terms of volts per unit charge. Hint enough?

 

[grantaere]

Oh, I got the answer now. I forgot that the calculation for potential difference only involves the charge acting on the proton, and doesn't involve the charge of the proton itself. Thanks for your help!