Binding energy in the atomic nucleus[edit | edit source]

Binding energy is the energy needed to separate an atomic nucleus into its seperate protons and neutrons (nucleons). It is a key concept in nuclear physics, as it explains why nuclei are stable and how energy is released in nuclear reactions.

Definition[edit | edit source]

We can define nuclear binding energy as either the energy to disassemble a nucleus or the energy released during assembly.

It is calculated using Einstein’s mass–energy equivalence:

E = Δm · c²

where:

E = binding energy (MeV)

Δm = mass defect

c = speed of light (≈ 3.00 × 10⁸ m/s)

Mass Defect[edit | edit source]

Mass defect is the difference between:

the sum of the masses of all protons and neutrons
the actual mass of the nucleus

It can be calculated using the formula:

Δm = Z · mₚ + N · mₙ − mₙᵤcₗₑᵤₛ

where:

Δm = mass defect
Z = number of protons
N = number of neutrons
mₚ = mass of a proton
mₙ = mass of a neutron
mₙᵤcₗₑᵤₛ = mass of the nucleus

This difference exists because some of the mass is converted into energy when the nucleus forms. This energy is the binding energy.

For example, if you add up the masses of individual nucleons, the result is always slightly larger than the mass of the nucleus. The “missing” mass has been converted into energy that holds the nucleus together.

Physical Meaning[edit | edit source]

Binding energy determines how strongly nucleons are held together by the strong nuclear force. The stronger the binding energy, the more stable the nucleus is.

To compare the different sizes of the nuclei, you can use the binding energy per nucleon:

Binding energy per nucleon = total binding energy / number of nucleons

This value is useful because it allows comparison between light and heavy nuclei.

Binding Energy Curve[edit | edit source]

When plotting binding energy per nucleon against mass number, a characteristic curve appears:

it increases quickly for light nuclei
it reaches a maximum around iron (Fe) and nickel (Ni)
it slowly decreases for heavier nuclei

This explains two important processes:

Nuclear fusion (light nuclei combine → energy released)

Nuclear fission (heavy nuclei split → energy released)

In both cases, energy is released because the products have a higher binding energy per nucleon than the original nuclei.

Example[edit | edit source]

An example is the helium-4 nucleus (²He⁴):

It consists of 2 protons and 2 neutrons
The sum of their individual masses is greater than the actual nuclear mass
The difference corresponds to the binding energy

This is why helium-4 is a very stable nucleus.

Applications[edit | edit source]

Binding energy plays an important role in:

nuclear power plants (fission reactions)

energy production in stars (fusion reactions)

radioactive decay

nuclear medicine and radiation physics

Summary[edit | edit source]

Binding energy is the energy that holds the nucleus together. It comes from the conversion of mass into energy and determines the stability of atomic nuclei. The concept is essential for understanding both natural processes in stars and technological applications such as nuclear energy.