Packing fraction and binding energy both decide the stability. Which of the following statements supports it? 

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  1. Higher packing fraction, lower binding energy
  2. Same packing fraction and binding energy
  3. Lower packing fraction, lower binding energy
  4. Lower packing fraction, higher binding energy

Answer (Detailed Solution Below)

Option 4 : Lower packing fraction, higher binding energy
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Concept:

Packing fraction:

  • It is defined as the mass per unit nucleon.
  • Formula, packing fraction = Δ m/A where Δ m = change in mass, A = nucleon
  • A negative packing fraction indicates the stability of the nucleus thus, a large binding energy and vice versa.

Binding energy:

  • The amount of energy required to separate a particle from a system of particles or to disperse all the particles of the system.
  • Binding energy is especially applicable to subatomic particles in atomic nuclei, to electrons bound to nuclei in atoms, and to atoms and ions bound together in crystals.
  • Formula, Δ E = Δ mc2 where Δ E = binding energy, Δm = change in mass, c = speed of light

Explanation:

  • The packing fraction might be positive, negative, or 0 percent.
  • If the packing fraction is more than one, the nucleus is unstable and will undergo fusion or fission, depending on the packing fraction.
  • The nuclei are particularly stable if the packing fraction is negative and vice versa. In this scenario, mass defects reveal the presence of binding energy.
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