Nucleus and Radioactivity — NEET Physics Notes
This topic covers nuclear structure, radioactivity, nuclear reactions, and the physics of nuclear energy — an essential chapter in NEET Physics with consistent question weightage.
Quick Revision
- Nuclear Composition: Protons (Z) + Neutrons (N) = Mass number (A)
- Isotopes: Same Z, different N (e.g., ¹₂H, ²₂H, ³₂H)
- Radioactive Decay Laws: N = N₀ e^(−λt)
- Half-Life: T½ = ln2/λ = 0.693/λ
- Mean Life: τ = 1/λ
- Activity: A = λN, measured in Becquerel (Bq) or Curie (Ci)
- Mass Defect: Δm = [Zmp + Nmn] − M_nucleus
- Binding Energy: E = Δmc², often expressed in MeV (1 u = 931.5 MeV)
- Radioactive Series: U-238, Th-232, U-235 series — decay until stable Pb
Standard Study
Nuclear Structure
- Size: Radius R = R₀A^(1/3), R₀ ≈ 1.2 fm
- Nuclear Density: ~10¹⁷ kg/m³ — extremely high, almost independent of A
- Nuclear Force: Short-range (~1 fm), attractive, strongest force in nature
- Neutron-Proton Ratio: N/Z ratio increases with atomic number for stable nuclei
Binding Energy and Stability
- Binding energy per nucleon peaks at Iron-56 (~8.8 MeV/nucleon)
- Light nuclei: fusion releases energy (combining lighter nuclei)
- Heavy nuclei: fission releases energy (splitting heavier nuclei)
- Binding energy curve explains why nuclear reactions release energy
Radioactivity Types
| Type | Symbol | Nature | Penetration | Ionisation |
|---|---|---|---|---|
| Alpha (α) | ⁴₂He | He nucleus, charge +2 | Low | High |
| Beta minus (β⁻) | ⁰₋₁e | Electron | Medium | Medium |
| Beta plus (β⁺) | ⁰₊₁e | Positron | Medium | Medium |
| Gamma (γ) | γ | High-energy photon | Very High | Low |
Alpha Decay: A → (A-4) + ⁴₂He; He nucleus emitted Beta Decay: n → p + e⁻ + ν̄ₑ (neutron converts to proton) Gamma Decay: Nucleus releases excess energy as photon
Decay Laws
- Activity: A = −dN/dt = λN
- Decay constant λ: Probability per unit time that a nucleus will decay
- Half-life T½: Time for half the nuclei to decay
- Mean life τ: Average lifetime of a nucleus = T½/ln2 ≈ T½/0.693
- Number of nuclei remaining: N = N₀(1/2)^(t/T½) = N₀e^(−λt)
Soddy’s Displacement Law
- Alpha decay: mass number decreases by 4, atomic number decreases by 2
- Beta minus decay: mass number unchanged, atomic number increases by 1
- Gamma decay: no change in mass or atomic number
Nuclear Reactions
- Q-value (Energy of reaction): Q = (M_initial − M_final)c²
- Q > 0: Exothermic (releases energy)
- Q < 0: Endothermic (absorbs energy)
- Threshold energy for endothermic reactions: E_th = −(Q × (M_target/M_total))
Fission and Fusion
Nuclear Fission:
- Heavy nucleus (U-235) splits into lighter nuclei
- Produces 2-3 neutrons, releases ~200 MeV per fission
- Chain reaction occurs when neutrons cause further fissions
- Critical mass required for sustained chain reaction
Nuclear Fusion:
- Light nuclei combine to form heavier nucleus
- Releases more energy per unit mass than fission
- Occurs in stars (including the Sun) at very high temperatures
- Requires extreme temperature and pressure to overcome Coulomb barrier
Applications
- Radioisotopes in medicine: Cobalt-60 for cancer therapy, Iodine-131 for thyroid
- Carbon dating: ¹⁴C used to determine age of archaeological samples
- Nuclear power: Controlled fission for electricity generation
Deep Study
Nuclear Models
Liquid Drop Model:
- Nucleus treated as a drop of incompressible nuclear fluid
- Explains nuclear fission, mass formula with volume, surface, Coulomb, asymmetry terms
- Semi-empirical mass formula: B = aV − aS − aC − aA − δ(A)
Shell Model:
- Nucleons arranged in shells (magic numbers: 2, 8, 20, 28, 50, 82, 126)
- Explains nuclear stability, magic numbers, spin-orbit coupling
Conservation Laws in Nuclear Reactions
- Mass number (A) conserved
- Atomic number (Z) conserved
- Linear momentum conserved
- Energy (including rest mass energy) conserved
- Angular momentum conserved
- Parity conserved (in strong and electromagnetic interactions)
Rutherford Scattering Formula
- Scattering angle θ relates to impact parameter b
- For small angles, scattering reveals nuclear size
Radioactive Dating
- Carbon-14 dating: half-life 5730 years
- Uranium-Lead dating: for geological timescales (~4.5 billion years)
Exam Tips
- Alpha decay reduces atomic number by 2 and mass number by 4
- Beta minus decay increases atomic number by 1 (neutron → proton + electron)
- Gamma decay doesn’t change A or Z — just releases energy
- Half-life and decay constant relationship: T½ = 0.693/λ
- For fission/fusion energy calculations: use E = Δm × c²
- Binding energy per nucleon curve — Iron-56 is most stable
- Activity decreases exponentially: A = A₀e^(−λt)
- 1 u (atomic mass unit) = 931.5 MeV/c²
Common Pitfalls
- Confusing atomic number and mass number in decay equations
- Forgetting that gamma rays have no mass or charge
- Not balancing nuclear equations properly for mass number and atomic number
- Mixing up half-life with mean lifetime (τ = T½/ln2)
- Confusing fission (splitting) vs fusion (combining)
Suggested Study Order
- Nuclear structure — composition, size, density
- Binding energy and mass defect
- Radioactivity — types of decay, laws
- Decay equations and Soddy’s laws
- Half-life, mean life, activity calculations
- Nuclear reactions and Q-value
- Fission and fusion
- Applications — dating, medicine, power