All about mass defect and binding energy

One of the most critical problems in physics is the mass defect and binding energy in solids — that is, the missing mass that comes from the breaking of bonds. The mass defect governs the size of the crystal and its density and the binding energy affects the energy required to compress it. The mass defect can be predicted from the first principles, but it is hard to measure because it depends on the geometry of the crystal. With accurate measurements, it can be used to determine the sizes of all the structures. The use of binding energy or mass defect, is a method used to create heat, light and/or electrical energy. 

Mass defect

A mass defect is an error in mathematics, physics or astronomy that causes the mass of an object to differ from that expected by chance when the object is tested as usual. The mass defect in the standard model of particle physics is a systematic deviation from the predictions of the theory for the masses of particles that describe the observed world. The deviation is a result of how the standard model of particle physics has to be extended to deal with the high energy behaviours of particles. The Standard Model, as it stands, is not a good model of nature. For example, an error in a formula that calculates the mass of an object causes it to be heavier than it should be, which violates the rule that mass and energy are conserved.

Mass Defect Formula

The mass defect is the difference between the nucleus’s total mass and the mass of its protons and nucleons.

Δm = [Z(m_p + m_e) + (A – Z)m_n] – m_atom

Here, 

∆m is the Mass Defect

m_p is the mass of the proton ( 1.007277 amu)

m_e is the mass of an electron (1.000548597 amu)

m_n is the mass of neutron (1.008665 amu)

m_atom is the mass of the nuclide

Z is the atomic number

A is the mass number

Binding Energy

The energy required to separate a particle from a bunch of particles or disperse all the bunch’s particles by applying force is called binding energy. In simple terms, the binding energy is the smallest amount of energy capable of removing an electron from an atom. This energy can disassemble a unit into its subunits. The binding energy is used for splitting the atomic nucleus into its constituent neutrons and protons. Binding energy is equal to the work done on the nucleus to oppose the binding forces of the nucleons to pull them apart.

Binding Energy Per Nucleon

Binding Energy per nucleon (B/N) is a fundamental quantity that measures the interaction of nuclear forces between the nucleons (proton, neutron and muon) within a nucleus. B/N is the quantity that, in the absence of interaction, shows the net force between the nucleons and therefore, is the extent to the change in the binding energy of the nucleons when the nucleons are given a small separation (the nuclear force is feeble). This energy is based on the energy of the nucleus when it is deformed and does not account for the binding energy of the deformed nucleus. Binding energy per nucleon (B/N) is defined as the product of the binding energy, which indicates the energy stored in an atom and the nucleon mass number.

Relation between Mass Defect and Binding Energy

This is how the binding energy and mass defect are related:

∆E = ∆mc²

where ∆E is the binding energy

∆m is the mass defect

c is the speed of light.

The binding energy is directly proportional to the mass defect. Since a hydrogen atom has only one nucleon and no proton, its binding energy and mass defect are zero.

During the formation of a nucleus, energy is released. This energy contains mass which gets subtracted from the total mass of the original nucleus. This is why, whenever we calculate the actual mass of the components, we also need to consider that the mass of the overall package is always less than that of the individual components. This leads to mass defect.

Conclusion

The mass defect in the standard model of particle physics is a systematic deviation from the predictions of the theory for the masses of particles that describe the observed world.  The Standard Model, as it stands, is not a good model of nature. For example, an error in a formula that calculates the mass of an object causes it to be heavier than it should be, which violates the rule that mass and energy are conserved. Binding energy is the smallest amount of energy capable of removing an electron from an atom. Binding Energy per nucleon (B/N) is a fundamental quantity that measures the interaction of nuclear forces between the nucleons (proton, neutron and muon) within a nucleus.