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Nuclei cheat sheet

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JEE · Physics

Cheat sheet

Class 12 · Chapter 13Nuclei

Mass defect × c² = binding energy.

1. Nucleus

R=R0A1/3R = R_0A^{1/3}
Δm=[Zmp+(A−Z)mn]−M\Delta m = [Zm_p + (A - Z)m_n] - M

R0≈1.2R_0 \approx 1.2 fm; nuclear density is nearly constant.

2. Binding Energy

Eb=Δm c2E_b = \Delta m\,c^21 u=931.5 MeV/c21\ \text{u} = 931.5\ \text{MeV}/c^2
  • BE per nucleon max for Fe-56 (~8.8 MeV).
  • Nuclear force: short-range, strongest, charge-independent.

3. Fission & Fusion

Fission

heavy nucleus splits (U-235 + n); chain reaction; nuclear reactors.

Fusion

light nuclei join (H → He); powers the Sun; needs very high temperature.

4. Key Points

  • Isotopes, isobars, isotones.
  • Moderators slow neutrons.
  • Control rods absorb neutrons (cadmium).
  • Energy released when BE/nucleon increases.

Remember: R ∝ A^(1/3) | mass defect | BE curve | fission vs fusion

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