More conservation of energy
Now that we know about electric potential energy, we can revisit our old friend, the law of conservation of energy. It’s basically the same as before: start out with
then rearrange for the unknown quantity and substitute everything else.
An alpha particle with a charge of 3.2 × 10−19 C moving at 1.0 × 106 m/s from infinity approaches a gold nucleus whose charge is 1.3 × 10−17 C. How close does the alpha particle get?
We by substituting the energy formulae into the equation given above:
The particle will stop moving when it gets to the closest point, so we make zero. It starts at infinity, and one over infinity, for our purposes, is zero, so that gets rid of another term. We are left with
Solving for final radius, we have
and working that out gives us the answer, 1.1 × 10−11 m.