1. What is nuclear binding energy?
The energy that is required to break the carbon
atom into smaller nuclei by breaking the nuclear
force is called nuclear binding energy.
Definition – To split the nucleus of an atom into
smaller or lighter nuclei or its nucleons forming an
individual mass of proton and neutron, some
amount of energy is required, and that energy is
called nuclear binding energy.
You should know,
The total of the masses of protons and neutrons is
always less than the mass of nuclei.
2. BINDING ENERGY PER NUCLEONS
The difference between nuclear attraction and
disruptive energy is the binding energy per
nucleon. For calculating the binding energy per
nucleon, we have to convert mass to energy by
using a formula which is given by Einstein.
E = mc2
Where E is the binding energy of the nucleus
c is the speed of light in a vacuum
m is the mass difference.
This formula is called the binding energy per
nucleon formula.
NOTE – Mass must be taken in kg.
3. VARIATION OF BINDING ENERGY
WITH MASS NUMBER
The binding energy is constant for atomic numbers
but it varies with atomic masses of elements. Also,
the binding energy is less for both light and heavy
nuclei.
By this, we understand that,
1) To produce binding energy per nucleon the
force should be attractive and sufficiently strong.
2) The binding energy is less for heavy and light
nuclei because their nucleus is of short range.
3) If the nucleus is at a distance more than the
nuclear force from the particular nucleons then it
will not show any kind of influence on binding
energy.
4) Nucleons having a maximum range of nuclear
force then its binding energy will be proportional to
that.
4. VARIATION OF BINDING ENERGY
WITH MASS NUMBER
Let’s understand the variation of binding energy
with mass number.
To understand the variation of binding energy with
mass number, we need to draw a graph between
these two parameters. By this, we understand that,
1.To produce binding energy per nucleon, the
force should be attractive and sufficiently strong.
2.The binding energy is less for heavy and light
nuclei because their nucleus is short-range.
3.If the nucleus is at a distance more than the
nuclear force from the particular nucleons, it will
not influence binding energy.
4.Nucleons having a maximum range of nuclear
force, their binding energy will be proportional.
5. Let’s take an example to understand this concept
in a better way,
Note – The fused heavier nuclei have more
binding energy when compared to the lighter
nuclei. This means that the final nucleus is more
tightly bound than the initial one.
In simple words, when mass increases, the
binding energy per nucleon decreases.
6. STABILITY OF ELEMENTS BASED
ON THE BINDING ENERGY PER
NUCLEON
Two major factors determine nuclear stability. The
neutron/proton ratio is one, while the total number
of nucleons in the nucleus is the other.
Those elements that have greater mass defect
and have higher binding energy are considered to
be more stable.
As a result, nuclear stability is proportional to
nuclear binding energy.
Example- Iron – 56 has more binding energy value
thus the nucleus of iron is most efficiently bounded
and is most stable.
7. MASS DEFECT
given equation describes the relationship between
energy and mass:
E = mc2
The speed of light is denoted by c. The binding
energy of nuclei is so great that they can hold a lot
of mass.
Because energy is released when the nucleus is
produced, the actual mass is always smaller than
the sum of the atomic masses of the nucleons.
This energy is made up of mass, called mass
defect since it is exerted from the overall mass of
the initial atom. This mass is absent from the final
proton and neutron, the energy released during
nuclear reactions.
8. 𝚫M = (Zmp + Nmn) – MA
M – mass defect
MA – the mass of the nucleus
mp – mass of a proton (1.00728 amu)
mn – the mass of a neutron (1.00867 amu)
Z – number of protons
N – number of neutrons
Binding Energy Calculation
Binding energy calculation can be done in the
following way:
Binding Energy = mass defect x c2
where c = speed of light in vacuum
c = 2.9979 x 108 m/s.
Binding Energy is expressed in terms of
MeV’s/nucleon or kJ/mole of nuclei.
9. Conclusion
From all of the above, we conclude. We learned
that binding energy is the energy that is required to
split the heavier nucleus of an atom into a smaller
one by forming the mass of their proton and
neutron. As we studied above, the higher the
number of nucleons, the higher will be the binding
energy. This energy also defines the stability of
atoms. The atom will be more stable if the binding
energy is higher. The energy from fusion and
fission is used to generate electric power in
several industries. By the Einstein formula which is
E = mc2, we can determine the nuclear binding
energy.
