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.
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