CBSE Class 12 · Physics · NCERT Physics Part-II
Nuclei: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Nuclear composition
- Nuclear size
- Mass defect and binding energy
- Binding energy per nucleon
- Radioactive decay
- Decay law
- Nuclear reactions
- Formulas and facts
- E = m × c²
- R = R₀ × A^(1/3)
- Mass defect
- Binding energy
- N(t) = N₀ × e^(−λt)
- T₁/₂ = 0.693/λ = ln 2/λ
- τ = 1/λ
- Watch out for
- Confusing atomic mass number A with…
- Using total binding energy instead…
- Forgetting that mass defect must be…
- Assuming half-life means all nuclei…
- Writing wrong daughter nucleus in…
What this chapter is about
This chapter explores the structure of the atomic nucleus, the tiny core at the centre of every atom. After studying atomic models and electron behaviour in earlier chapters, you now turn inward to understand what the nucleus itself is made of, how it holds together, and why some nuclei are stable while others spontaneously break apart.
Key ideas
- Nuclear composition: A nucleus contains Z protons and N neutrons, where A = Z + N is the mass number. Nuclei with the same Z but different N are called isotopes.
- Nuclear size: The radius of a nucleus follows R = R₀ × A^(1/3), where R₀ ≈ 1.2 × 10⁻¹⁵ m. This means nuclear density is nearly constant for all nuclei, about 2.3 × 10¹⁷ kg/m³.
- Mass defect and binding energy: The mass of a nucleus is always less than the sum of masses of its free nucleons. This difference, Δm, when multiplied by c², gives the binding energy that holds the nucleus together.
- Binding energy per nucleon: This quantity peaks around A ≈ 56 (iron region). Nuclei with higher binding energy per nucleon are more stable. This curve explains why fusion of light nuclei and fission of heavy nuclei both release energy.
- Radioactive decay: Unstable nuclei emit alpha particles (helium nuclei), beta particles (electrons or positrons), or gamma rays (high-energy photons) to reach more stable configurations.
- Decay law: The number of undecayed nuclei decreases exponentially: N(t) = N₀ × e^(−λt), where λ is the decay constant. Half-life T₁/₂ = 0.693/λ is the time for half the nuclei to decay.
- Nuclear reactions: In fission, a heavy nucleus splits into lighter fragments; in fusion, light nuclei combine. Both processes convert mass to energy according to E = Δm × c².
Formulas and facts to remember
- Mass-energy relation: E = m × c², where c = 3 × 10⁸ m/s. One atomic mass unit (1 u) = 931.5 MeV/c².
- Nuclear radius: R = R₀ × A^(1/3), with R₀ ≈ 1.2 fm (1 fm = 10⁻¹⁵ m).
- Mass defect: Δm = [Z × mₚ + N × mₙ] − M_nucleus, where mₚ and mₙ are proton and neutron masses.
- Binding energy: B.E. = Δm × c², often expressed in MeV.
- Radioactive decay law: N(t) = N₀ × e^(−λt); Activity A = λN, measured in becquerel (1 Bq = 1 decay/s).
- Half-life relation: T₁/₂ = 0.693/λ = ln 2/λ.
- Mean life: τ = 1/λ.
- Alpha decay: Parent nucleus emits ⁴He; atomic number decreases by 2, mass number by 4.
- Beta-minus decay: A neutron converts to a proton, emitting an electron and an antineutrino; Z increases by 1.
Common mistakes
- Confusing atomic mass number A with atomic number Z → A is total nucleons, Z is only protons.
- Using total binding energy instead of binding energy per nucleon to compare stability → Always compare binding energy per nucleon; higher value means more stable.
- Forgetting that mass defect must be converted to energy units using 931.5 MeV per u → Without this conversion, the answer has wrong units.
- Assuming half-life means all nuclei decay in 2 × T₁/₂ → Decay is exponential; some nuclei always remain.
- Writing wrong daughter nucleus in decay equations by not conserving both Z and A → Check that both mass number and atomic number balance on each side.
Quick revision
- Nucleus = Z protons + N neutrons; A = Z + N.
- Nuclear radius ∝ A^(1/3); nuclear density is roughly constant for all nuclei.
- Binding energy = mass defect × c²; higher B.E. per nucleon means greater stability.
- Radioactive decay is random but follows N = N₀ × e^(−λt); half-life T₁/₂ = 0.693/λ.
- Fission splits heavy nuclei; fusion joins light nuclei — both release energy because products have higher B.E. per nucleon.
- Always conserve mass number and charge in nuclear reactions.