Mass-Energy and Nuclear Binding Energy

  • The mass of a nucleus is always less than the mass of constituent nucleons in their free state. This difference is called MASS DEFECT, (Δm).
  • The energy equivalent to mass defect is called the BINDING ENERGY OF NUCLEUS, BE.
  • BE = [ZMp + (A − Z) Mn – M] 931.5 MeV.
  • Binding energy of a nucleus is given by,
    BE = (Δm)C2 Joules (Δm is in Kg)
    BE = (Δm) 931.5 MeV (Δm is in amu)
  • Average Binding energy = \tt \frac{BE}{A}
  • Binding fraction or average binding energy is a measure of stability of nucleus.
  • Mass defect per nucleon is called PACKING FRACTION. \tt PF = \frac{M-A}{A} = \frac{\Delta m}{A}
  • If packing fraction is positive, nucleus is unstable.
    If packing fraction is negative, nucleus is stable.
  • With increase in mass number A, B.E per nucleon increases rapidly, reaches a maximum value and then decreases slowly.
  • Average Binding energy is maximum for 26Fe56 and it is 8.7 MeV.
  • For deuteron, the average binding energy is about 1 MeV.
  • Average Binding energy is low for both light and heavy nuclei.
  • The average binding energy for helium is about 7 MeV.
  • The binding energy per nucleon for iron is maximum at 8.7 MeV and is the most stable and will undergo neither fission nor fusion.

Part1: View the Topic in this Video from 0:13 to 3:08

Part2: View the Topic in this Video from 5:20 to 11:38

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1. Mass defect (Δm) : Δm = Sum of masses of nucleons − Mass of nucleus
=\left\{Z_{m_{p}} + (A - Z)m_{n}\right\} - M = \left\{Zm_{p} + Zm_{c} + (A - Z)m_{n}\right\} - M'

2. Mass defect per nucleon is called packing fraction.
Packing fraction (f) = \frac{\Delta m}{A} = \frac{M - A}{A}, where M = Mass of nucleus, A = Mass number.

3. Binding energy per nucleon : The average energy required to release a nucleon from the nucleus is called binding energy per nucleon.
Binding energy per nucleon =\tt \frac{Total \ binding \ energy}{Mass \ number (i.e. total \ number \ of \ nucleons)} = \frac{\Delta m \times 931}{A} \frac{MeV}{Nucleon}