Question

A ball rebounds elastically from the floor. What doesthis situation share with the ideas of momentum conservation discussed in connection with pair production?

Short answer

In pair production, the higher mass nucleus alters the momentum of the incoming photon significantly during the collision but absorbs negligible kinetic energies during the collision. Hence, the laws of energy and momentum conservations hold.

Step-by-step solution

Concept used

Pair production is a phenomenon in which a photon of sufficiently high energy interacting with a matter forms an electron and positron in the vicinity of a nucleus. The laws of energy and momentum conservations hold only in the vicinity of the nucleus.

Energy conservation

When a ball hits the floor and rebounds back elastically,,there is a negligible loss of kinetic energy of the ball. So, the initial kinetic energy of the ball is the same as the final kinetic energy. The momentum of the floor upon collision is comparable to the momentum of the falling ball. But, the kinetic energy transferred by the ball to the floor is negligible due to a huge difference in the mass of the ball and the floor. Hence, the laws of energy conservation and momentum conservation hold.

Conservation of momentum

Now, when a photon having very high energy interacts with the matter, an electron and a positron are produced with equal momentum and kinetic energies. The nucleus behaving like the floor absorbs negligible kinetic energy from the incoming photon, which acts like the falling ball. So, the initial energy of the photon is equal to the combined energies of the electron and positron. Also, the higher mass nucleus significantly alters the momentum of the photon and thus, momentum is also conserved.