Answer: Splitting the Atom“Splitting” an atom in the

Chapter , Problem 11P

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Problem 11P

Splitting the Atom

“Splitting” an atom in the process of nuclear fission releases a great deal of energy. If all the atoms in 1 kg of  undergo nuclear fission, will be released, equal to the energy from burning of coal. What is the source of this energy? Surprisingly, the energy from this nuclear disintegration ultimately comes from the electric potential of the positive charges that make up the nucleus.

The protons in a nucleus exert repulsive forces on each other, but this force is less than the short-range attractive nuclear force. If a nucleus breaks into two smaller nuclei, the nuclear force will hold each of the fragments together, but it won’t bind the two positively charged fragments to each other. This is illustrated in Figure VII.1. The two fragments feel a strong repulsive electrostatic force. The charges are large and the distance is small (roughly equal to the sum of the radius of each of the fragments), so the force—and thus the potential energy—is quite large.

In a fission reaction, a neutron causes a nucleus of  to split into two smaller nuclei; a typical reaction is

Right after the nucleus splits, with only the electric force now acting on the two fragments, the electrostatic potential energy of the two fragments is

This is the energy that will be released, transformed into kinetic energy, when the fragments fly apart. If we use reasonable estimates for the radii of the two fragments, we compute a value for the energy that is close to the experimentally observed value of 200 MeV for the energy released in the fission reaction. The energy released in this nuclear reaction is actually electric potential energy.

Suppose the original nucleus is at rest in the fission reaction noted above. If we neglect the kinetic energy of the neutrons, after the two fragments fly apart,

A. The Br nucleus has more kinetic energy.

B. The La nucleus has more kinetic energy.

C. The kinetic energy of the Br nucleus equals that of the La nucleus.