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CISCEISC (Science) ISC Class 12
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Syllabus

Overview: Mass-Energy Equivalence : Nuclear Binding Energy

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Estimated time: 12 minutes
CISCE: Class 12

Key Points: Mass-Energy Relation

  • Before Einstein, mass and energy were considered separate and independently conserved quantities.
  • Einstein showed that mass and energy are related by the equation
    E = mc2
    called Einstein’s mass–energy relation.
  • A small loss of mass produces a large amount of energy because c2 is very large.
  • Conservation of mass and conservation of energy are unified into a single law of conservation of mass–energy.
CISCE: Class 12

Definition: Pair Production

When an energetic γ-ray photon falls on a heavy substance, it is absorbed by some nucleus of the substance and its energy gives rise to the production of an electron and a positron. This phenomenon, in which energy is converted into mass, is called 'pair-production'.

CISCE: Class 12

Definition: Pair Annihilation

Whenever an electron and a positron come very close to each other, they annihilate each other by combining together and two y photons (energy) are produced. This phenomenon, in which mass is converted into energy, is called 'pair-annihilation'.

CISCE: Class 12

Definition: Mass Defect

The difference between the sum of the masses of the nucleons constituting a nucleus and the rest-mass of the nucleus is called ‘mass defect'.

CISCE: Class 12

Definition: Binding Energy

The binding energy (BE) of a nucleus is defined as the minimum energy required to separate its nucleons and place them at rest at infinite distance apart.

CISCE: Class 12

Formula: Binding Energy Formula

\[E_{b}=\left[Zm_{\mathrm{H}}+(A-Z)m_{n}-m(_{Z}X^{A})\right]c^{2}\]

CISCE: Class 12

Definition: Binding Energy per Nucleon

Binding energy per nucleon is defined as the average energy required to remove a nucleon from the nucleus to infinite distance. Higher the binding energy per nucleon, greater is the stability of the nucleus.

CISCE: Class 12

Key Points: Binding Energy Curve

  • The binding energy curve is a plot of average binding energy per nucleon versus mass number (A).
  • The curve has a maximum around A = 50 to 80 (about 8.5 MeV per nucleon); hence, nuclei like Fe⁵⁶ are the most stable.
  • For very heavy nuclei (A > 80), the binding energy per nucleon decreases, so such nuclei, such as uranium, are less stable and may be radioactive.
  • For very light nuclei (A < 20), the binding energy per nucleon is also low, so they are comparatively less stable.
  • Energy is released when heavy nuclei split (nuclear fission) or when light nuclei combine (nuclear fusion) because the binding energy per nucleon increases in both cases.
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