# Homework Help: Nuclear Model - Expression for Total Energy [Modern Physics]

1. Apr 18, 2010

### twotaileddemon

1. The problem statement, all variables and given/known data

Derive an expression for the total energy required to asemble a sphere of charge corresponding to a nucleus of atomic number Z and radius R. Assume the nucleus is a sphere of uniform volume charge density $$\rho$$

2. Relevant equations

$$\rho$$ = mass / volume = 3Am / 4*pi*R3

3. The attempt at a solution

I know the solution is U = 3k * (Ze)2 / 5R, so I need to work on deriving this.

I also know that when an alpha particle collides with the nucleus, the initial kinetic energy is equal to the electrical potential energy of the system and is given by
.5mv2 = kq1q2/r = k(2e)(Ze)/d where d = 4kZe2 / mv2

Not sure how this helps though, but it seems to be in a relevant section in the textbook. There is also info on the binding energy, but it doesn't seem applicable in this case.

Any tips on how to approach the problem, please?

2. Apr 18, 2010

### Matterwave

Have you ever learned of the gravitational analog? Wherein the gravitational potential energy of a sphere of mass M and radius R is -3/5GM^2/R?

You can apply that analog perfectly to this case.

If you haven't seen that. Consider a spherical shell (infinitessimal thickness), what is the potential energy of this shell? How would I go about adding up all these spherical shells to form a sphere?

3. Apr 18, 2010

### twotaileddemon

I think I remember learning about that in a different course, let me check my notes and I'll get back to you. Thanks for the tip!

EDIT 4/19: I was able to figure out how to derive the proof. Thank you!

Last edited: Apr 19, 2010