Nuclear Binding Energy

To understand Nuclear Binding Energy, we first need to understand what binding energy is. Whenever in a system of particles, the particles are to be separated from one another, the energy required for separation is known as Binding energy.

Binding Energy is usually distinguished at the following levels:

1.   At the Atomic Level- Atomic energy is required to separate an atom into electron and nucleus. It is commonly known as Ionization energy.

2.   At the Molecular Level- In a chemical reaction, when a molecule separates into bonds, the energy required is Molecular Binding Energy.

3.   At the Nuclear Level- The energy required to separate parts of a nucleus (protons and neutrons) is Nuclear Binding Energy.

Nuclear Binding Energy Meaning

In the subatomic nuclei of an atom, whenever a neutron and proton have to separate from each other, the amount of energy required for getting them separated is known as Nuclear Binding Energy, or when to say, the protons and neutrons are combined into a single nucleus the energy liberated this can also be called as Nuclear Binding Energy.

Now that nuclear binding energy’s meaning is clear, we see that the binding energy of a stable nucleus is always a positive number as the nucleus must gain energy for nucleons to move apart from one another.

Mass of Nucleus and Nuclear Binding Energy

The total mass of a nucleus is always lesser than the separate mass of neutrons and protons. The difference between the two can be calculated as Nuclear Binding Energy, and the missing mass is called a “Mass Defect”. Einstein’s relationship [E=m.c2] states that energy is proportional to the mass difference, where “E” stands for Nuclear Binding energy, “m” stands for the difference in mass and “c” stands for the speed of light, where speed of light is a universal constant.

During the nuclear separation or fission, some portion of the mass of the nucleus gets converted into energy. The mass is removed from the total mass of the particle, and it gets missing in the nucleus. This is called a mass defect. The Nuclear Binding Energies are enormous and are at least a million times more than the electron binding energies of an atom.

Nuclear Binding Energy Examples

When we study nuclear binding energy examples, we take a hydrogen 2- nucleus consisting of a proton and neutron each. The hydrogen 2- nucleus can be separated by supplying 2.23 million electron volts (MeV). Conversely, whenever a slowly moving proton and neutron combine with each other to form a Hydrogen 2 nucleus 2.23 million electron volts (MeV) are liberated in the form of gamma radiation.

Determining the Mass Defect

The difference between the mass of the nucleus and the mass of nucleons is called the “Mass Defect”.

We need to know three important things to calculate Mass Defect:

·  The perfect mass of the nucleus,

·  The nucleus’s composition (i.e. the number of protons and neutrons),

·  Individual masses of protons and neutrons,

To calculate Mass Defect

• Add masses of each proton and neutron that make up the nucleus,

• Now subtract the mass of the nucleus from the above-calculated mass of each proton and neutron

Example: Let us find out the mass defect of a copper-63 nucleus

if the actual mass of a copper-63 nucleus is 62.91367 amu.

·  Firstly, determine the composition of the copper-63 nucleus and then find the cumulative mass of its components, i.e. its proton and neutron.

The nucleus of a Copper atom has 29 protons, and copper-63 also has (63 – 29) 34 neutrons.

The mass of a proton is 1.00728 amu, and a neutron is 1.00867 amu.

Thus, the combined mass is calculated:

29 protons(1.00728 amu/proton) + 34 neutrons(1.00867 amu/neutron)

or

63.50590 amu

 Calculate the mass defect-

Dm = 63.50590 amu – 62.91367 amu = 0.59223 amu

How To Calculate Nuclear Binding Energy?

Calculating Nuclear Binding Energy Involves the Following Steps:

1.   Determining the mass defect

2.   Conversion of Mass defect into energy

3.   Expressing the nuclear binding energy as energy per mole of atoms or as energy per nucleon.

Furthermore, Nuclear Binding Energy can be calculated using Einstein’s Energy Equation, [E=m.c2] where “E” stands for Nuclear Binding energy, “m” stands for the difference in mass and “c” stands for the speed of light, where speed of light is universally constant.

Conclusion

In short, the energy required to separate neutrons and protons in a nucleus or, conversely the energy liberated from the combination of neutrons and protons is known as Nuclear Binding Energy. Many factors are necessary to calculate the exact binding energy required for nuclear fission or fusion. Knowing the exact mass defect and mass of neutrons and protons constitutes an integral part of determining the nuclear binding energy.