Problem 26.
An alpha particle with kinetic energy 10 MeV makes a headon collision with a lead nucleus at rest. What is the distance of closest approach of the two particles? (Assume that the lead nucleus remains stationary and that it may be treated as a point charge. The atomic number of lead is 82. The alpha particle is a helium nucleus, with atomic number 2.)
Solution
In this problem we need to use energy conservation. The initial energy (kinetic energy of alpha particle) should be equal to the final energy, which is the potential energy of interaction of alpha particle and a lead nucleus. Then
We know the initial energy:
We know the charge of the particles:
Then we can find the shortest distance:
