Force between particles in nucleus

[tomwilliam]

Homework Statement

The nucleus of a zinc atom has 30 protons and 35 neutrons, and a diameter of 4.00 x 10^-13 m.
What is the minimum repulsive electrostatic force between two protons in the nucleus.

Homework Equations

The Attempt at a Solution

Not sure how to approach this. I understand that the minimum force will be when these protons are furthest apart. How do I calculate the maximum distance between the protons in the nucleus?
Using Electrostatic Force = -DeltaPotentialEnergy/distance?

I can calculate the spherical area of the nucleus, and calculate the number density of the protons, but I don't see how this helps. I could use ElectricalPotentialEnegy = q1q2/(4pi perm0 r) and use the known charge of a proton, but I still have two unknowns (r and Potential Energy).
Any ideas?
Thanks

 

[Redbelly98]

You seem to be overthinking this problem.

Imagine two particles are confined to be within a sphere of diameter D. How far apart can the two particles get?

 

[tomwilliam]

Well, I see what you're saying for two particles. But if two protons in the zinc nucleus experience a repulsive force as a result of being at either end (maximum distance apart), then what about the repulsive force as a result of all of the other protons? How can I just ignore that?

 

[tomwilliam]

Forget it - I've just realized that the question is only asking for the force between the two protons in question...
Thanks for your help.