Question

Explain the terms mass defect and binding energy. How are they related?

Answer 1

Atomic nuclei consist of protons and neutrons (collectively called nucleons). The total mass of a nucleus is always less than the sum of the masses of its individual nucleons. This difference gives rise to the ideas of mass defect and binding energy.

1. Mass Defect: Mass defect is the difference between the combined mass of all free nucleons and the actual mass of the nucleus.
Δm = `(Zm_p + Nm_n) − M_"nucleus"`

2. Binding Energy: Binding energy is the energy required to completely separate a nucleus into its individual nucleons. It is a measure of the nuclear stability of a nucleus.

1. Higher binding energy means the nucleus is more stable.
2. Lower binding energy means the nucleus is less stable and easier to break apart.

Relation Between Mass Defect and Binding Energy:

• The mass defect is directly related to binding energy through Einstein’s mass-energy equivalence principle (E = mc²).
• The energy equivalent of the mass defect is what we call the binding energy:
  Binding energy = Δmc²
• If the mass defect is measured in atomic mass units (u), then it can be converted into MeV (Mega electron volts):
  1u = 931.5 MeV

Thus, the missing mass (mass defect) in the nucleus is transformed into binding energy, which holds the nucleus together.