Nuclei Class 12 Notes | CBSE Physics Chapter 13

Nuclei is Chapter 13 of CBSE Class 12 Physics. This chapter covers the composition and size of the nucleus, nuclear binding energy, radioactivity (alpha, beta, gamma decay), and nuclear fission and fusion — the processes that power nuclear reactors and stars.

This chapter carries 4–5 marks. Binding energy, radioactive decay law, and fission/fusion are commonly tested.

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Key Concepts

1. Composition of Nucleus

• Protons (Z): positive charge; Neutrons (N): no charge
• Mass number A = Z + N; nuclide notation: ᴬZX
• Isotopes: same Z, different A (e.g., ¹H, ²H, ³H)
• Isobars: same A, different Z (e.g., ⁴⁰₁₈Ar, ⁴⁰₂₀Ca)

Nuclear radius: R = R₀A^(1/3) where R₀ ≈ 1.2 fm

Nuclear density ≈ 2.3 × 10¹⁷ kg/m³ (same for all nuclei — incredibly dense!)

2. Mass Defect and Binding Energy

Mass defect (Δm): The mass of a nucleus is less than the sum of its constituent protons and neutrons.

Δm = [Zmp + Nmn] − M_nucleus

Binding energy: BE = Δm × c² = Δm × 931.5 MeV/u

Binding energy per nucleon (BE/A): Higher → more stable nucleus.

Peak stability: Iron-56 (BE/A ≈ 8.75 MeV). Light and heavy nuclei have lower BE/A.

3. Radioactivity

Type	Particle	Change	Penetration
Alpha (α)	⁴₂He	Z → Z−2, A → A−4	Low (stopped by paper)
Beta-minus (β⁻)	Electron	Z → Z+1, A unchanged	Medium (stopped by aluminium)
Gamma (γ)	Photon	No change in Z or A	High (needs lead/concrete)

Radioactive Decay Law

N = N₀e^(−λt)

Half-life: T₁/₂ = 0.693/λ (time for half the nuclei to decay)

After n half-lives: N = N₀/2ⁿ

4. Nuclear Fission and Fusion

Feature	Fission	Fusion
Process	Heavy nucleus splits into lighter nuclei	Light nuclei combine to form heavier nucleus
Example	²³⁵U + n → ¹⁴⁴Ba + ⁸⁹Kr + 3n + energy	4¹H → ⁴He + 2e⁺ + energy (in stars)
Energy per event	~200 MeV	~24 MeV (but per nucleon: higher)
Application	Nuclear reactors, atomic bomb	Hydrogen bomb, stars (sun)
Condition	Neutron bombardment	Extremely high temperature (~10⁷ K)

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Solved Examples

Example 1

The half-life of a radioactive element is 5 years. What fraction remains after 15 years?

Answer: n = 15/5 = 3 half-lives. Fraction = 1/2³ = 1/8

Example 2

Find the binding energy per nucleon of ⁵⁶Fe (mass = 55.9349 u, Z = 26, N = 30).

Answer: Δm = 26(1.00783) + 30(1.00867) − 55.9349 = 26.2036 + 30.2601 − 55.9349 = 0.5288 u

BE = 0.5288 × 931.5 = 492.6 MeV. BE/A = 492.6/56 = 8.79 MeV/nucleon

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Quick Revision Points

• R = R₀A^(1/3); nuclear density same for all nuclei (~2.3 × 10¹⁷ kg/m³)
• BE = Δm × 931.5 MeV; BE/A peaks at Fe-56 (most stable)
• α: Z−2, A−4; β⁻: Z+1, A same; γ: no change
• N = N₀e^(−λt); T₁/₂ = 0.693/λ
• Fission: heavy → light + energy (reactors); Fusion: light → heavy + energy (stars)

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Next: Ch 14 — Semiconductor Electronics