## Wednesday, February 4, 2015

### Mass Defect and Binding Energy of Nucleus

Mass defect

The mass of the total nucleons is little bit more than the mass of the nucleus. This difference in the mass is called mass effect. Between the protons there is a strong force of the repulsion because of their positive charges. To overcome this repulsion and to keep them together, they need some energy. They cannot get the energy from the outside so a portion of the mass is sacrificed and that mass is converted into energy to keep the nucleons together. This sacrificed the mass could be called as mass defect.

Binding energy

The energy that is corresponding to mass defect is called binding energy. This energy keeps the nucleons together therefore nucleus will be having its stability. If there is no mass defect, then there won’t be any binding energy and hence nucleons cannot be together.

Anyway mass defect is not the exact measure of stability of the nucleus. Similarly even the binding energy is not the exact measure of the stability of a nucleus. It is not the binding energy, but the binding energy per nucleons is a measure of the stability of the nucleus. This binding energy per nucleon is called binding fraction. If binding energy per nucleons is more, then the nucleus will be more stable.

We can write the equations for mass defect, binding energy and the binding energy per nucleon as shown below.

Binding energy curve

We can draw a graph taking the mass number on x-axis and the binding energy per nucleon on y-axis. This graph is drawn for all the existing elements of the periodic table and it is observed that with the increase of the mass member, binding energy per nucleon is also increasing up to some extent. Within this region itself there are specific elements like helium, carbon and oxygen that are having exceptionally highly binding energy per nucleon. It means that there are more stable than the neighboring elements.

It is noticed that up to the iron, with respect to the increase of mass number binding energy per nucleon is also increasing. Beyond iron with the increase of the mass number binding energy per nucleon slowly starts decreasing and by the time uranium is reached, it reaches to its minimum value. It means to say that uranium is the most unstable element because of its less binding energy per nucleon.

In the case of the uranium, there is more number of the protons inside the nucleus and between them there does a strong repulsive force exist. This makes the nucleus unstable and to get the stability, it emits some elements from the nucleus. This kind of emission is called radioactivity.

Problem and solution

The following problem we are expected to calculate mass defect, binding energy and binding energy per nucleon of an Alpha particle? In the problem mass of the proton and neutron are given as shown below.

We know that the mass defect is nothing but the difference in the mass of the total nucleons to the mass of nucleus. It can be identified that an Alpha particle will have two protons and two neutrons. By substituting the appropriate data we can get the answer as shown below.

Nuclear forces

There are three kinds of basic forces in the nature. They are gravitational forces, electromagnetic forces and nuclear forces. Among the existing forces gravitational forces are the weakest forces, electromagnetic forces are much stronger than the gravitational forces and the nuclear forces are the strongest forces.

Both gravitational and electric forces are long-range forces whereas nuclear forces a short-range force. The nuclear force acts only between the nucleons of a given nucleus.
Gravitational forces are always attractive whereas electromagnetic forces either attractive are repulsive. Nuclear forces by default are attractive in nature.

Nuclear forces are charge independent forces. It means the force of attraction between the protons, neutrons and between the proton and neutron is same.

Nuclear forces are spin dependent forces. If two nucleons are having the parallel spin between them, there is a better force of attraction and vice versa.

Nuclear forces are non-central forces and there is no simple mathematical formula to express them.