# Nuclear Binding Energy

Nuclear binding energy is an important topic in the field of nuclear physics. As non-renewable sources of energy are getting replenished, the world is looking at nuclear energy to satisfy its power needs.

Rahul Pandita

*E = mc*

^{2}where

*E*is the energy,

*m*is the mass, and

*c*is the speed of light in vacuum.

From this equation, we can deduce the nuclear binding energy equation, BE

*BE = (Δm) c*

^{2}where Δm is the difference between calculated mass and actual mass.

Apart from the formula mentioned above, there is another simpler way to calculate it.

Lithium -7 is made up of 3 protons and 4 neutrons.

The mass of Lithium -7 is 7.0160 AMU

*(atomic mass unit)*

The mass of 3 protons is 3 is 3 × 1.0073 = 3.0219 AMU

The mass of 4 neutrons is 4 × 1.0087 = 4.0348 AMU

The mass of constituents of the nucleus = 3.0219 + 4.0348 = 7.0567 AMU

The mass defect = 0.0407 AMU

The nuclear binding energy of Lithium-7 = 0.0407 × 931 = 37.891 MEV

Nuclear Binding Energy Per Nucleon

It is defined as the average energy needed to remove each nucleon.

There is a relation between the binding energy per nucleon and the stability of the nucleus. That is, the higher the binding energy per nucleon, the more stable is the nucleus. According to the nuclear binding energy table, iron has the highest binding energy per nucleon. Nuclei with smaller mass than iron have lower binding energy per nucleon.

Nuclear Binding Energy per Nucleon = |
Nuclear Binding EnergyNumber of Nucleons |

There is a relation between the binding energy per nucleon and the stability of the nucleus. That is, the higher the binding energy per nucleon, the more stable is the nucleus. According to the nuclear binding energy table, iron has the highest binding energy per nucleon. Nuclei with smaller mass than iron have lower binding energy per nucleon.

Nuclear Binding Energy Curve

Elements from Hydrogen to Sodium have increasing binding energy per nucleon. Elements are more stable from magnesium to xenon and then even though atomic mass increases, the binding energy per nucleon decreases. The binding energy of nucleons is in millions of electron volts. One of the important analysis of the binding energy curve is that elements having atomic mass higher than iron, have unstable nuclei, hence, they emit energy by nuclear fission. On the other hand, elements with atomic masses lower than iron yield energy by nuclear fusion.

Nuclear Fusion and Nuclear Fission

If two light nuclei are forced together, they will combine to make a nucleus and this process will either release or absorb energy. In nuclear fission, heavy unstable nuclei, disintegrate, producing free neutrons and protons. Both of these yield enormous amounts of energy.