Introduction to Nuclei

The chapter Nuclei is a fundamental part of Class 12 Modern Physics that explains the structure, properties, and behavior of atomic nuclei. It deals with radioactive decay, nuclear reactions, binding energy, and nuclear processes.

For JEE Main, this chapter is important because it deals with alpha, beta, gamma decay, half-life, mass defect, binding energy, fission, and fusion, which frequently appear in conceptual, derivation-based, and numerical questions.

Direct Links to Download JEE Main - Chapter Wise Previous Year Papers Physics (PDF)

► Click “Download Here” next to your subject to access the free PDF.

Importance of Nuclei in JEE Main

Studying Nuclei helps students:

• Understand atomic nucleus composition (protons and neutrons)

• Solve problems on radioactive decay and half-life

• Analyze binding energy and mass defect

• Calculate energy released in fission and fusion reactions

JEE Main often tests conceptual understanding, derivations, and numerical problems, making this chapter high-yield for exam preparation.

Structure of the Nucleus

• Nucleus composed of protons (Z) and neutrons (N)

• Mass number: A = Z + N

• Nuclear density: ρ ≈ 2.3 × 10¹⁷ kg/m³

• Nuclear radius: R = R₀ A^(1/3), R₀ ≈ 1.2 × 10⁻¹⁵ m

• Applications in JEE Main:

  • Calculating nuclear radius

  • Understanding nuclear density and size of nucleus

Radioactive Decay

• Alpha (α) decay: Emission of helium nucleus

• Beta (β) decay: Conversion of neutron to proton (β⁻) or proton to neutron (β⁺)

• Gamma (γ) decay: Emission of high-energy photons without change in Z or N

• Radioactive decay law: N = N₀ e^(−λt)

• Half-life: T₁/₂ = 0.693 / λ

Applications in JEE Main:

• Calculating remaining nuclei after time t

• Determining decay constant and half-life

• Solving α, β, γ decay problems

Mass Defect and Binding Energy

• Mass defect (Δm): Difference between mass of nucleons and actual mass of nucleus

• Δm = Z m_p + N m_n − m_nucleus

• Binding energy: E_b = Δm c²

• Binding energy per nucleon = E_b / A

• Applications in JEE Main:

  • Calculating mass defect and binding energy

  • Determining stability of nuclei

Nuclear Fission

• Definition: Splitting of heavy nucleus into smaller nuclei with release of energy

• Example: ²³⁵U + n → ⁹⁵Kr + ¹³⁹Ba + 3n + energy

• Energy release: E = Δm c²

• Applications: Nuclear reactors, atomic bombs

• JEE Main problems: Energy released per fission, number of neutrons produced

Nuclear Fusion

• Definition: Combination of light nuclei to form heavier nucleus with release of energy

• Example: ²H + ³H → ⁴He + n + energy

• Occurs in stars and hydrogen bombs

• Applications: Stellar energy production, controlled fusion reactors

• JEE Main problems: Energy released per fusion, mass defect calculation

Decay Series and Nuclear Reactions

• Decay series: Sequence of radioactive decays leading to stable nucleus

• Nuclear reactions: Conservation of charge and mass number

• Applications:

  • Solving nuclear reaction equations

  • Understanding radioactive chains in natural decay series

Applications in Daily Life and Engineering

• Radioactive isotopes in medical diagnosis and treatment

• Nuclear reactors for energy production

• Radiocarbon dating in archaeology

• Nuclear fission and fusion for power and weapons

• Understanding nuclear stability and binding energy

Understanding real-life applications helps students visualize and solve JEE Main nuclear physics problems effectively.

Problems on Nuclei

• Calculating half-life and decay constant

• Mass defect and binding energy problems

• Energy released in fission and fusion

• Determining remaining nuclei in decay series

• Nuclear reaction equation calculations

JEE Main numericals often combine radioactive decay, mass defect, binding energy, and nuclear reactions.

Common Mistakes Students Make

• Confusing decay constant and half-life formulas

• Neglecting mass-energy equivalence in fission/fusion

• Forgetting number of neutrons emitted in α or β decay

• Miscalculating binding energy per nucleon

• Not conserving charge and mass number in nuclear reactions

Avoiding these mistakes ensures accuracy and confidence in solving JEE Main numericals.

Weightage of Nuclei in JEE Main

• 1–2 questions per exam

• Mix of conceptual, derivation-based, and numerical problems

• Moderate difficulty but high scoring for students who practice numericals

Preparation Tips for JEE Main Students

• Memorize radioactive decay formulas, mass defect, and binding energy relations

• Solve numericals on half-life, decay constant, and energy release

• Practice fission and fusion energy calculations

• Draw decay series and nuclear reaction diagrams

• Understand applications in nuclear energy, medicine, and astrophysics

Regular practice ensures speed, accuracy, and conceptual clarity.

Why Study Nuclei from Studentbro.in

Studentbro.in provides:

• Step-by-step explanations for radioactive decay, fission, and fusion

• Solved examples on half-life, mass defect, and binding energy

• Conceptual clarity for JEE Main-level numerical and derivation problems

• Chapter-wise preparation for effective exam learning

This ensures students can tackle both conceptual and numerical nuclear physics problems efficiently.

Conclusion

Nuclei is a fundamental Class 12 Physics chapter that explains structure, radioactivity, decay processes, half-life, mass defect, binding energy, fission, and fusion. Mastery of this chapter enables students to solve problems on nuclear reactions, energy released, decay constants, and nuclear stability with confidence. With structured guidance and practice from Studentbro.in, students can excel in JEE Main Physics and handle modern physics questions effectively.