Class 12 Physics Chapter 13: Nuclei

CBSE 2026–27 | NCERT-aligned free study resource

1. Composition and Size of the Nucleus

The nucleus contains protons and neutrons, collectively called nucleons. Nuclear radius is approximately R = R₀A^1/3, showing that nuclear volume is approximately proportional to mass number A.

2. Nuclear Force

The nuclear force is strong and short-ranged. It binds nucleons together and is approximately charge independent over relevant nuclear scales.

3. Radioactivity

Unstable nuclei can spontaneously transform by emitting radiation. Alpha particles are helium nuclei, beta radiation involves electrons or positrons depending on the decay process, and gamma radiation is electromagnetic radiation of high energy.

4. Radioactive Decay Law

The number of undecayed nuclei follows N = N₀e^−λt. Activity A = λN. Half-life T_1/2 = 0.693/λ.

5. Mass Defect and Binding Energy

The mass of a bound nucleus is less than the sum of the masses of its separated constituent nucleons. The difference is the mass defect. Binding energy is E = Δmc². Binding energy per nucleon helps compare nuclear stability.

6. Binding-Energy Curve

Binding energy per nucleon generally rises for light nuclei, reaches a broad maximum around medium-mass nuclei, and decreases for very heavy nuclei. This helps explain why both fusion of light nuclei and fission of heavy nuclei can release energy.

7. Nuclear Fission

A heavy nucleus can split into lighter nuclei with release of energy and additional neutrons. A chain reaction can occur when emitted neutrons cause further fissions.

8. Nuclear Fusion

Light nuclei can combine under suitable conditions to form a heavier nucleus, releasing energy because the products can have greater binding energy per nucleon.

Worked Example

If a radioactive sample has half-life 10 days, after 30 days the remaining fraction is (1/2)³ = 1/8.

Common Exam Traps

• Half-life is independent of the initial number of nuclei for a given radioactive isotope.
• Do not confuse decay constant with half-life.
• Binding energy is associated with mass defect through E = Δmc².

Practice Questions

1. Derive the relation between half-life and decay constant.
2. Explain alpha, beta and gamma radiation.
3. Define mass defect and binding energy.
4. Explain the shape of the binding-energy-per-nucleon curve.
5. Differentiate nuclear fission and fusion.

Nuclear Physics: Binding Energy & Reactions

Mass Defect

The mass of a bound nucleus is less than the combined mass of its separated nucleons. The difference is the mass defect, and binding energy is E=Δmc².

Binding-Energy Curve

The binding-energy curve helps explain why fusion of light nuclei and fission of very heavy nuclei can release energy.

Radioactive Decay

Radioactive decay follows N=N₀e^−λt. Half-life is related to decay constant by t_1/2=0.693/λ.

Worked Numerical

If a sample has decay constant λ=0.231 day⁻¹, its half-life is approximately 0.693/0.231=3 days.

Fission and Fusion

Fission splits a heavy nucleus into lighter nuclei; fusion combines light nuclei. Both are governed by changes in binding energy per nucleon and conservation laws.

Common Mistakes

• Confusing mass number with atomic mass.
• Using half-life and decay constant formulas incorrectly.
• Assuming all nuclear reactions release energy.

Practice

1. Calculate binding energy from mass defect.
2. Find remaining nuclei after a specified number of half-lives.
3. Calculate decay constant from half-life.
4. Interpret the binding-energy curve.
5. Compare fission and fusion.