Nuclear Binding Energy

As per the atomic structure, an atom is made up of protons, neutrons and electrons. Ideally the mass of an atom should be the sum total of the mass of its constituent protons and neutrons (the mass of electrons is negligible), but it has been found that the sum total of the mass of protons and neutrons is higher than that of the nucleus. Physicists call this missing mass or energy as binding energy. In other words, binding energy can be defined as the energy needed to break down the nucleus into number of free unbound neutrons and protons or inversely it is the energy required to hold the nucleus of an atom together. Nuclear binding energy is measured in kJ/mole of nuclei or MeV/nucleon.

According to the Einstein's theory of relativity
E = mc²
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) c²
where Δm is the difference between calculated mass and actual mass.

Apart from the formula mentioned above, there is another simpler way to calculate the nuclear binding energy of chemical elements. Let us take an example to illustrate this.

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
Nuclear binding energy per nucleon is defined as the average energy needed to remove each nucleon.

Nuclear Binding Energy per Nucleon =

Nuclear Binding Energy Number 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.

Nuclear binding energy is an important topic as far as research in the field of nuclear power is concerned. In the 20th century, most of the countries spent huge amounts of money funding research on nuclear physics, but 21st century has thrown different challenges in front of the global community, one of the most important of those being safeguarding nuclear power from falling into the hands of terrorists. While most eminent scientists have stressed on the fact that nuclear energy can be used to generate power, most countries want to tap this energy for defense purposes. In the end, we can only hope that nuclear energy is used for progressive purposes as the benefits of using nuclear power for domestic purposes are immense.