#### CHAPTER 13 NUCLEUS

Nuclear force

The force acting inside the nucleus or acting between nucleons is called nuclear force. Nuclear force is the strongest forces in nature. It is

• very short range attractive force.

• non-central, non-conservative force.

• neither gravitational nor electrostatic force.

• independent of charge.

• 100 times that of electrostatic force and 1038 times that of gravitational force.

Nuclear binding energy

The minimum energy required to separate the nucleons up to an infinite distance from the nucleus, is called nuclear binding energy.

Binding energy per nucleon

• The binding energy per nucleon, Ebn, is practically constant, i.e. practically independent of the atomic number for nuclei of middle mass number (30 < A < 170).

• It is maximum, about 8.75 MeV, for A = 56 and has a value of 7.6 MeV for A = 238.

• Ebn is lower for both light nuclei (A < 30) and heavy nuclei (A > 170).

Properties of binding force and binding energy

1. The force is attractive and sufficiently strong to produce a binding energy of a few MeV per nucleon.

2. The constancy of the binding energy in the range 30 < A < 170 is due to the fact that the nuclear force is short-ranged. Let us consider a particular nucleon inside a sufficiently large nucleus. It will be under the influence of only some of its neighbours, which come within the range of the nuclear force. If any other nucleon is at a distance more than the range of the nuclear force from the particular nucleon it will have no influence on the binding energy of the nucleon under consideration. If a nucleon can have a maximum of p neighbours within the range of nuclear force, its binding energy would be proportional to p. Let the binding energy of the nucleus be pk, where k is a constant having the dimensions of energy. If we increase A by adding nucleons they will not change the binding energy of a nucleon inside. Since most of the nucleons in a large nucleus reside inside it and not on the surface, the change in binding energy per nucleon would be small. The binding energy per nucleon is a constant and is approximately equal to pk.

The property that a given nucleon influences only nucleons close to it is referred to as saturation property of the nuclear force.

3. A very heavy nucleus, say A = 240, has lower binding energy per nucleon compared to that of a nucleus with A = 120. Thus if a nucleus A = 240 breaks into two A = 120 nuclei, nucleons get more tightly bound. This implies energy would be released in the process. This is the principle of energy production through fission.

4. If we consider two very light nuclei (A ≈ 10) joining to form a heavier nucleus. The binding energy per nucleon of the fused heavier nuclei is more than the binding energy per nucleon of the lighter nuclei. This means that the final system is more tightly bound than the initial system. Again energy would be released in such a process of fusion.

PE is positive (or the force is repulsive) for r < ro

PE is negative (or the force is attractive) for r > ro