"Nuclear Fission and Fusion"

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The nucleus holds enormous energy — released either by splitting heavy nuclei (fission) or combining light ones (fusion). This chapter explains both processes, how nuclear reactors work, how stars shine, and how to calculate the energy released in nuclear reactions.

Key Concepts

27.1 Nuclear Reactions

Governed by conservation of:

• Mass number (A)
• Atomic number (Z)
• Energy and momentum

Examples:

• ¹⁹F₉ + ¹H₁ → ¹⁶O₈ + ⁴He₂
• ²⁷Al₁₃ + ¹n₀ → ²⁴Na₁₁ + ⁴He₂
• ²³⁴Th₉₀ → ²³⁴Pa₉₁ + ⁰e₋₁ (β⁻ decay)
• ⁶³Cu₂₉ + ²D₁ → ⁶⁴Zn₃₀ + ¹n₀

Q-value (energy released): $Q=\Delta m\times 931.5\text{ MeV/u}$

Where $\Delta m=m_{\text{reactants}}-m_{\text{products}}$.

27.2 Nuclear Fission

The splitting of a heavy nucleus (e.g., ²³⁵U) into two lighter nuclei when bombarded with a neutron, releasing huge energy.

${}^{235}\text{U}+n\to \text{fission fragments}+2-3n+\sim 200\text{ MeV}$

Chain reaction: The released neutrons trigger further fissions — controlled (reactor) or uncontrolled (bomb).

Nuclear reactor components:

• Fuel: ²³⁵U
• Moderator: Slows neutrons (heavy water, graphite)
• Control rods: Absorb neutrons (cadmium, boron)
• Coolant: Transfers heat

27.3 Nuclear Fusion

Combining light nuclei (e.g., hydrogen isotopes) to form heavier ones, releasing energy.

${}^2\text{H}{+}^3\text{H}{\to }^4\text{He}+n+17.6\text{ MeV}$

• Requires extremely high temperature (~10⁷ K) — thermonuclear reaction
• Powers the Sun and stars (hydrogen → helium)
• Advantage: abundant fuel, less radioactive waste
• Challenge: confinement of plasma

INTEXT QUESTIONS 27.1

Q1. Complete the nuclear reactions:

(a) ¹⁹F₉ + ¹H₁ → ¹⁶O₈ + ? Ans: A: 19 + 1 − 16 = 4. Z: 9 + 1 − 8 = 2. → ⁴He₂ (α-particle).

(b) ²⁷Al₁₃ + ¹n₀ → ? + ⁴He₂ Ans: A: 27 + 1 − 4 = 24. Z: 13 + 0 − 2 = 11. → ²⁴Na₁₁.

(c) ²³⁴Th₉₀ → ²³⁴Pa₉₁ + ? Ans: A: 0, Z: −1. → ⁰e₋₁ (β-particle).

(d) ⁶³Cu₂₉ + ²D₁ → ⁶⁴Zn₃₀ + ? Ans: A: 63 + 2 − 64 = 1. Z: 29 + 1 − 30 = 0. → ¹n₀ (neutron).

Q2. Calculate energy released in ¹⁰B₅ + ²D₁ → ?

Ans: $m_{\text{reactants}}=10.01294+2.014103=12.027043$ u $m_{\text{products}}=11.011434+1.008665=12.020099$ u $\Delta m=0.006944$ u $Q=0.006944\times 931.5=6.47$ MeV

Terminal Exercise

1. Distinguish between nuclear fission and nuclear fusion. Give two examples of each.

2. What is a chain reaction? Explain the difference between controlled and uncontrolled chain reactions.

3. Describe the principle and working of a nuclear reactor with a labelled diagram.

4. Explain the proton-proton cycle in stars.

5. Calculate the energy released in the fission of 1 g of ²³⁵U. (Energy per fission ≈ 200 MeV, $N_A=6.02\times 10^{23}$)

6. Complete the reactions: (a) ²³⁵U₉₂ + ¹n₀ → ¹⁴¹Ba₅₆ + ⁹²Kr₃₆ + ? (b) ²H + ²H → ³He + ?

7. State the advantages and challenges of fusion energy.

8. Calculate the Q-value of: ²H + ³H → ⁴He + n. (Given: m(²H) = 2.014102 u, m(³H) = 3.016049 u, m(⁴He) = 4.002603 u, m(n) = 1.008665 u)

9. Why are neutrons more effective than protons in inducing nuclear reactions?

10. What is critical mass? Why is it important for a chain reaction?

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