Class 12 Physics Nuclei Notes

13.1 Introduction

The nucleus is the central part of the atom containing protons and neutrons. Understanding nuclear properties explains radioactivity, nuclear forces, and energy released in nuclear reactions.

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13.2 Atomic Masses and Composition of Nucleus

• Nucleus contains protons (Z) and neutrons (N).
• Mass number:

$$A = Z + N$$A=Z+N

• Atomic mass unit (u) used to express masses of nuclei.
• Mass of nucleus < sum of masses of individual nucleons → mass defect.

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13.3 Size of the Nucleus

• Nuclei are extremely small:

$$R = R_0 A^{1/3}, \quad R_0 \approx 1.2 \times 10^{-15} \text{ m}$$R=R0​A1/3,R0​≈1.2×10−15 m

• Determined using scattering experiments (e.g., Rutherford alpha scattering).

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13.4 Mass-Energy and Nuclear Binding Energy

• Mass defect (Δm\Delta mΔm): Difference between mass of nucleus and sum of nucleons.
• Binding energy (B.E.): Energy required to disassemble a nucleus into protons and neutrons:

$$B.E. = \Delta m \, c^2$$B.E.=Δmc2

• High binding energy → stable nucleus.
• Binding energy per nucleon graph shows Fe-56 most stable.

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13.5 Nuclear Force

• Strong short-range force that binds nucleons in the nucleus.
• Characteristics:
  • Attractive at ~1–2 fm, repulsive at very short distances
  • Charge-independent
  • Saturation property: each nucleon interacts with a limited number of neighbors

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13.6 Radioactivity

• Spontaneous emission of particles/radiation from unstable nuclei.
• Types:
  • Alpha (α\alphaα) decay: Emission of He nucleus
  • Beta (β\betaβ) decay: Emission of electron/positron
  • Gamma (γ\gammaγ) decay: Emission of high-energy photon
• Half-life: Time for half the nuclei to decay.

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13.7 Nuclear Energy

• Energy released in nuclear fission and fusion.
• Fission: Splitting heavy nuclei (e.g., U-235) → chain reaction.
• Fusion: Combining light nuclei (e.g., H → He) → high energy output.
• Applications: Nuclear reactors, atomic bombs, stellar energy.