 # Binding Energy

The energy that is necessary to split the nucleus of an atom into its components namely: neutrons and protons or collectively known as the nucleons. The binding energy of nuclei is a positive value because every nuclei need net energy to isolate them into every neutron and proton.

## Mass Defect

The nuclear binding energy holds a significant difference between the nucleus actual mass and its expected mass depending on the sum of the masses of isolated components.

Since energy and mass are related based on the following equation:

$E=mc^{2}$

Where c is the speed of light. In nuclei, the binding energy is so high that it holds the considerable amount of mass.

The actual mass is less than the sum of individual masses of the constituent neutrons and protons in every situation because energy is ejected when the nucleus is created. This energy consists of mass which is ejected from the total mass of the original components and called as mass defect. This the mass is missing in the final nucleus and describes the energy liberated when the nucleus is made.

Mass defect is determined as the difference between the atomic mass observed (Mo) and expected by the combined masses of its protons (mp, every proton has a mass of 1.00728 AMU) and neutrons (mn, 1.00867 AMU).

$M_{d}=(m_{n}+m_{p})-m_{o}$

### Nuclear Binding Energy

Once the mass defect is calculated, nuclear binding energy can be determined by converting mass to energy by applying E=mc2. When this energy is calculated which is of joules for a nucleus, you can scale it into per-mole quantities and per-nucleon. You need to multiply by Avogadro’s number to convert into joules/mole and divide by the number of nucleons to convert to joules per nucleon.

Nuclear binding energy is also applied to situations where the nucleus splits into fragments that consist of more than one nucleon wherein, the binding energies of the fragments can be either negative or positive based on the position of the parent nucleus on the nuclear binding energy curve. When heavy nuclei split or if the new binding energy is known when the light nuclei fuses, either of these processes results in liberation of binding energy. Binding energy is also applied in determining whether fusion or fission will be favorable. For elements which are lighter than iron-56, the fusion releases energy since the nuclear binding energy rises with the hike in mass. Elements which are heavier than iron-56 release energy on fission, since the lighter elements consist of higher binding energy. Hence, there exists a peak at iron-56 according to the nuclear binding energy curve.