What is Binding Energy Formula?
The formula for calculating the binding energy (BE) of a nucleus is given by:
BE = [Z × mp + (A – Z) × mn – m] × c2
Where,
- BE represents the binding energy of the nucleus
- Z is the number of protons (atomic number) in the nucleus
- mp is the mass of a proton [1.00728 atomic mass units]
- A is the total number of nucleons (protons + neutrons) in the nucleus
- mn is the mass of a neutron [1.00867 amu]
- m represents the actual mass of the nucleus
- c is the speed of light [3.00 x 108 m/s]
In the formula, the terms (Z × mp) and ((A – Z) × mn) represent the total mass of all the protons and neutrons in the nucleus, respectively. The term m represents the actual mass of the nucleus, which may be slightly different from the sum of the individual masses due to the mass defect.
Other Formula of Binding Energy
Another formula that can be used to calculate the binding energy is:
E = mc2
Where,
- E is the Energy
- m is the Mass
- c is the Speed of Light
E = mc2 is one of the most famous equations in physics and is derived from Einstein’s theory of special relativity. In the context of binding energy, we know that the nuclei of any atom are composed of protons and neutrons which are held by strong nuclear forces. The total mass of a nucleus is slightly less than the sum of the masses of its individual nucleons when they are at rest (measured independently outside the nucleus). This missing mass is known as the mass defect (Δm).
Thus the above formula can be written as:
Eb = Δmc2
Where Eb is the binding energy.
For example, the mass defect of an atom of deuterium is 0.0023884, thus its binding energy from the above formula came out to be nearly equal to 2.23 MeV. This implies that the energy required to disintegrate an atom of deuterium is 2.23 MeV.
Note: This equation is also known as mass-energy equivalence, as this shows that mass and energy are interchangeable.
Read more about Mass Energy Equivalence.
Binding Energy
Binding energy is a fundamental concept in the field of physics, particularly in the study of atomic and nuclear systems. Binding Energy is defined as the energy required to hold together the constituents of a system, such as the particles within an atomic nucleus or the electrons surrounding an atomic nucleus. Understanding binding energy is crucial for comprehending the stability, structure, and behaviour of atoms, molecules, and nuclei.
Binding energy specifically refers to the amount of energy needed to disassemble a nucleus into its individual protons and neutrons. The binding energy of nuclei is a positive value because every nucleus needs net energy to isolate them into neutrons and protons. Binding Energy is applicable to atoms and ions bound together in crystals.