Nuclear

Question 1

Alpha Particle Scattering Experiment

Answer 1

(Rutherford, 1911)

• Setup:
  
  • α-particles (He nuclei, 2+ charge) fired at thin gold foil.
  • Detector measured deflection angles.

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Key Observations & Conclusions

1. Majority passed straight through (A):
   
   • Implication: Atoms are mostly empty space.
2. Some deflected at small angles (<10°) (B):
   
   • Implication: Small, positively charged nucleus (repels α-particles).
3. Very few rebounded (>90°) (C):
   
   • Implication: Nucleus is extremely dense (contains most mass).

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Revolutionary Conclusions

• Nuclear Model:
  
  • Dense, positive nucleus (∼10^-15 m).
  • Electrons orbit nucleus (atom size ∼10^-10 m).
• Overturned Plum Pudding Model:
  
  • Disproved Thomson’s “positive sphere with embedded electrons

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• Why Gold Foil?:
  
  • Thin (few atomic layers), malleable, high atomic mass (stronger repulsion).

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1. Key Principle:
   
   • At closest approach (r), alpha particle’s kinetic energy converts entirely to electric potential energy:
     E_k = E_p
2. Equations:
   • Kinetic energy:
     E_k = ½mv²
   • Electric potential energy:
     E_p = (Qq)/(4πε₀r)
     where Z = atomic number of nucleus.
3. Solving for r:
   r = (Qq)/(4πε₀E_k)

Question 2

Atomic Size and Density

Answer 2

Size

• Neutral Atoms: Equal numbers of protons (+) and electrons (-).
• Size Comparison:
  
  • Atom diameter: 1×10^-10 m
  • Nucleus diameter: 1×10^-15 m
  • Atom ≈ 100,000× larger than nucleus.

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Nuclear Radius (R)

• Typical size: ~10^-15 m (1 femtometre, fm).
• Mass number dependence:
  R = R₀A^(1/3)
  
  • R₀ = empirical constant (~1.2 fm).
  • A = nucleon number (protons + neutrons).

Key Observations

1. Non-linear growth:
   
   • Adding nucleons increases size, but not proportionally (volume ∝ A).
2. Graph behavior:
   
   • Steep initial slope → flattens as A increases.

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Nuclear Density (ρ)
1. Calculation:

• Volume:
  V = (4/3)πR³ = (4/3)π(R₀A^(1/3))³ ∝ A
• Mass:
  m = Au (u = atomic mass unit = 1.66×10^-27 kg)
• Density:
  ρ = m/V = Au / [(4/3)πR₀³A] = 3u/(4πR₀³) ≈ 3×10¹⁷ kg/m³

2. Key Conclusion:
   
   • Constant density (~10¹⁷ kg/m³) for all nuclei.
   • Implies nucleons are uniformly packed, regardless of size.

Question 3

Isotopes

Answer 3

Isotopes

• Definition: Atoms of the same element with:
  
  • Same proton number (Z)
  • Different neutron numbers → different mass numbers (A).

Key Properties

1. Chemical Behavior:
   • Identical for all isotopes (same electron configuration).
   • Only physical properties (e.g., density) vary due to mass differences.
2. Nuclear Stability:
   • Unstable if neutron:proton ratio is too high/low (→ radioactivity).

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AᵣX Notation

• Mass Number (A): Protons + neutrons (nucleons).
• Atomic Number (Z): Protons only.
• Example: ¹⁴₆C vs. ¹²₆C (carbon isotopes).

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OCR Exam Focus

• Calculations:
  
  • Find neutrons: N = A - Z.
  • Identify isotopes: Same Z, different A.
• Applications:
  
  • Radiocarbon dating (¹⁴C).
  • Medical tracers (e.g., ¹³¹I).

Question 4

Strong Nuclear Force

Answer 4

Strong Nuclear Force

• Purpose: Binds nucleons (protons/neutrons) together against electrostatic repulsion.
• Range: Extremely short (~3 femtometres, fm).

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Key Features

1. Distance Dependence:
   • Repulsive (<0.5 fm): Prevents collapse.
   • Max Attraction (~1 fm): Balances proton repulsion.
   • Zero (>3 fm): No effect beyond nuclear scale.
2. Compared to Other Forces:
   • Strength: 100× stronger than EM force.
   • Range: 10^-15 m (vs. infinite for gravity/EM).

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Underlying Physics

• Acts between quarks (constituents of protons/neutrons).
• Mediated by gluons (force carriers).
• Calculations: Nuclear density ≈ 10¹⁷ kg/m³.

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Why It Matters

• Explains:
  
  • Why nuclei don’t fly apart (despite proton repulsion).
  • How fusion/fission release energy (changing binding energy).

Question 5

Antimatter

Answer 5

• Definition: Particles with same mass but opposite charge to their matter counterparts.
• Key Examples:
  
  • Positron (e⁺): Anti-electron (+1 charge).
  • Antiproton (p̄): -1 charge.
  • Antineutron (n̄): Neutral (but distinct from neutron).

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Key Properties

1. Mass & Energy:
   
   • Identical rest mass and rest mass-energy (E = mc²) to matter particles.
   • Example:
     
     • Electron/positron: m = 9.11×10^-31 kg → E = 0.511 MeV.
2. Neutral Particles:
   
   • Some (e.g., photons, Z⁰ bosons) are their own antiparticles.

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Matter-Antimatter Pairs

• Proton (p) ↔ Antiproton (p̄): +1 ↔ -1
• Neutron (n) ↔ Antineutron (n̄): Neutral but distinct
• Electron (e^-) ↔ Positron (e⁺): -1 ↔ +1

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OCR Exam Focus

• Data Sheet: Rest masses/energies for protons (938 MeV), electrons (0.511 MeV), etc.
• Annihilation:
  
  • Matter + antimatter → pure energy (2mc² per pair).

Question 6

Hadrons

Answer 6

• Definition: Composite particles made of quarks, affected by the strong nuclear force

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Two Classes of Hadrons

1. Baryons:
   
   • Structure: 3 quarks (e.g., uud = proton, udd = neutron).
   • Examples:
     
     • Proton: Stable, charge = +1.
     • Neutron: Decays via β⁻ decay (weak force).
2. Mesons:
   
   • Structure: Quark-antiquark pair (e.g., ūd = π⁺, s̄u = K⁻).
   • Examples:
     
     • Pions (π): Mediate nuclear force.
     • Kaons (K): Contain strange quarks.

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Two Classes of Anti-Hadrons

1. Anti-Baryons:
   
   • Structure: 3 antiquarks (e.g., ūūd̄ = antiproton, ūd̄d̄ = antineutron).
   • Charge: Integer values (e.g., antiproton = -1e).
   • Rule: All 3 must be antiquarks (no quark-antiquark pairs).
2. Anti-Mesons:
   
   • Structure: Antiquark-quark pair (e.g., d̄u = π⁻, sū = K⁺).
   • Key Point: Swaps quark/antiquark roles vs. original meson.

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Key Properties

• Forces:
  
  • Strong force: Binds quarks.
  • EM force: Acts if charged (e.g., π⁺ vs. π⁰).
• Decay: Via weak force (e.g., neutron → proton + e⁻ + ν̄ₑ).
• Charge: Always integer (unlike quarks’ fractional charges).
• Annihilation: Colliding with matter hadrons → pure energy (e.g., p + p̄ → 2γ).

Question 7

Leptons

Answer 7

• Definition: Fundamental particles with no internal structure (not made of quarks).
• Key Property: Not affected by strong nuclear force.

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Lepton Types (6 Total)

1. Charged Leptons (all have charge = -1e):
   
   • Electron (e⁻)
     
     • Mass: 0.0005u (9.11×10^-31 kg).
   • Muon (μ⁻)
     
     • Mass: 0.1u (~200× electron).
   • Tau (τ⁻)
     
     • Mass: 2u (~3,500× electron).
2. Neutrinos (charge = 0, near-zero mass):
   
   • Electron neutrino (νₑ).
   • Muon neutrino (ν_μ).
   • Tau neutrino (ν_τ).

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Key Interactions

• Forces:
  
  • Weak force (all leptons).
  • EM force (charged leptons only).
  • Gravity (all, but negligible).
• Pair Production:
  
  • e.g., β⁻ decay: n → p + e⁻ + ν̄ₑ.

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OCR Exam Focus

• Mass Hierarchy: e⁻ < μ⁻ < τ⁻.
• Neutrino Facts:
  
  • Most abundant particles in universe.
  • Rarely interact (detection challenges).

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• Leptons:
  
  • No quarks → no strong force.
  • Include neutrinos (neutral).
• Quarks:
  
  • Bind via strong force → form hadrons.
  • Always confined (never isolated).

Question 8

Quark Model

Answer 8

• Fundamental Principle: Quarks are elementary particles that combine to form hadrons.
• Key Rule: Quarks are never observed in isolation (always confined in groups).

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Proton & Neutron Composition

1. Proton (p⁺):
   
   • Quarks: uud
   • Charge Calculation: (+⅔e) + (+⅔e) + (-⅓e) = +1e
2. Neutron (n⁰):
   
   • Quarks: udd
   • Charge Calculation: (+⅔e) + (-⅓e) + (-⅓e) = 0e

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• Up (u): Charge = +⅔e → Antiquark (ū) = -⅔e.
• Down (d): Charge = -⅓e → Antiquark (d̄) = +⅓e.
• Strange (s): Charge = -⅓e → Antiquark (s̄) = +⅓e.

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Key Properties

• Hadron Types:
  
  • Baryons: 3 quarks (e.g., protons, neutrons).
  • Mesons: Quark-antiquark pairs (e.g., π⁺ = ūd).
• Antiquarks: Identical mass but opposite charge to quarks.

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OCR Exam Focus

• Memorise:
  
  • u = +⅔e, d/s = -⅓e.
  • Proton (uud), neutron (udd).
• Typical Question:
  “Show that the Σ⁺ particle (uus) has charge +1e.”

Question 9

Beta Decay

Answer 9

Beta Decay (Weak Interaction)

• Mechanism: Involves quark flavour change via W^± boson exchange.

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1. Beta-Minus (β⁻) Decay

• Process:
  n → p + e⁻ + ν̄ₑ
  • Quark Level: d → u + e⁻ + ν̄ₑ (down quark → up quark).
• Nuclear Changes:
  
  • Proton number (Z): +1
  • Nucleon number (A): Unchanged.
• Example:
  ¹⁴₆C → ¹⁴₇N + e⁻ + ν̄ₑ

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2. Beta-Plus (β⁺) Decay

• Process:
  p → n + e⁺ + νₑ
  • Quark Level: u → d + e⁺ + νₑ (up quark → down quark).
• Nuclear Changes:
  
  • Proton number (Z): -1
  • Nucleon number (A): Unchanged.
• Example:
  ²²₁₁Na → ²²₁₀Ne + e⁺ + νₑ

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Key Physics

• Force Carrier: W^± boson (weak force).
• Neutrinos:
  
  • β⁻: Emits anti-electron neutrino (ν̄ₑ).
  • β⁺: Emits electron neutrino (νₑ).
• Energy: Shared between e⁺/e⁻ and neutrino.

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• Quark Changes:
  
  • β⁻: d → u.
  • β⁺: u → d.

Question 10

Radioactive Decay

Answer 10

• Definition: Random, spontaneous emission of radiation from unstable nuclei to achieve stability.
• Key Properties:
  • Random: Cannot predict which nucleus decays or when.
  • Spontaneous: Unaffected by external conditions (temperature/pressure).

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Why Nuclei Are Unstable

1. Neutron-Proton Imbalance:
   
   • Too many/few neutrons (e.g., ¹⁴C vs. stable ¹²C).
2. Large Size:
   
   • Heavy nuclei (e.g., uranium) destabilized by long-range repulsion.

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1. Alpha (α) Particles

• Composition: 2 protons + 2 neutrons (helium nucleus).
• Source: Very heavy nuclei (e.g., uranium, plutonium).
• Properties:
  
  • Charge: +2e
  • Penetration: Low (stopped by paper/skin).
  • Range: ~5 cm in air.
  • Ionisation: High (damages cells severely).
• New element
  
  • The mass number decreases by 4
  • The atomic number decreases by 2

2. Beta (β⁻) Particles

• Composition: High-speed electrons (from neutron → proton decay).
• Source: Neutron-rich nuclei (e.g., carbon-14).
• Properties:
  
  • Charge: -1e
  • Penetration: Moderate (stopped by 3mm aluminium).
  • Range: 0.2–3 m in air.
  • Ionisation: Moderate (less than α, more than γ).
• New element
  
  • The atomic number increases by 1

3. Gamma (γ) Rays

• Composition: Electromagnetic waves (high-energy photons).
• Source: Energy release after α/β decay (e.g., cobalt-60).
• Properties:
  
  • Charge: 0
  • Penetration: Very high (requires lead/concrete).
  • Range: Infinite (intensity decreases with distance).
  • Ionisation: Low (but dangerous due to penetration).

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Randomness Evidence

• Simulations:
  
  • Dice Rolling: Six = decayed nucleus.
  • Coin Flips: Tails = decayed nucleus.
  • Popcorn: Each “pop” = decay event.

Question 11

Activity & Decay Constant

Answer 11

Key Definitions

• Activity (A):
  
  • Decays per second (measured in Becquerels, Bq).
  • Equation:
    A = λN
    • λ = decay constant (probability of decay per second).
    • N = number of undecayed nuclei.

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• Decay Constant (λ):
  • Probability a nucleus decays in 1 second.
  • Higher λ → faster decay.

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Half-Life (t₁/₂)

• Definition: Time for half the nuclei to decay.
• Equation:
  t₁/₂ = ln(2)/λ ≈ 0.693/λ
• Key Points:
  
  • Inversely proportional to λ.
  • Shorter half-life → more radioactive.

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Exponential Decay Equations

1. Undecayed Nuclei:
   N = N₀e^(-λt)
2. Activity:
   A = A₀e^(-λt)
3. Count Rate:
   C = C₀e^(-λt)

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Graph Features

• Shape: Exponential curve starting at N₀.
• Slope: Steeper = larger λ = shorter t₁/₂.

Question 12

Radioactive Dating

Answer 12

Carbon-14 Dating

• Principle: Measure remaining ¹⁴C in organic matter to determine age.
• Half-life: 5730 years.

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How ¹⁴C Forms
n + ¹⁴N → ¹⁴C + p
- Cosmic rays convert atmospheric nitrogen into radioactive carbon.

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Key Process

1. Living Organisms:
   
   • Maintain constant ¹⁴C/¹²C ratio via photosynthesis/food.
2. After Death:
   
   • ¹⁴C decays exponentially → ratio decreases.

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Dating Equation

t = [ln(N₀/N)] / λ
- N₀ = initial ¹⁴C (assumed = modern ratio).
- N = measured ¹⁴C in sample.
- λ = decay constant (≈1.21 × 10⁻⁴ yr⁻¹).

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• Too Young (<1k yrs):
  
  • High activity → imprecise ΔA measurements.
• Too Old (>40k yrs):
  
  • Count rate ≈ background → noise dominates.

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Limitations

• Assumption: Historic ¹⁴C/¹²C ratio matches today’s (varies slightly).
• Calibration: Tree rings (dendrochronology) used to correct dates.

Question 13

Pair Production and Annihilation

Answer 13

Annihilation

• Definition: Particle + antiparticle → pure energy (γ photons).
• Example:
  e⁻ + e⁺ → 2γ

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• Key Rules:
  1. Energy Conservation:
     
     • Each photon energy = rest mass + KE
       rest energy of particle:
       E_γ = mₑc² = 0.511 MeV (electron)
  2. Momentum Conservation:
     
     • Photons emitted in opposite directions.

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Pair Production

• Definition: High-energy photon → particle + antiparticle.
• Requirements:
  1. Photon Energy:
     E_γ ≥ 2mₑc² = 1.022 MeV
  2. Nucleus Presence: Needed to conserve momentum.
• Example:
  γ → e⁻ + e⁺

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Key Equations

1. Mass-Energy Equivalence:
   E = mc²
2. Photon Energy:
   E_γ = hf = hc/λ

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OCR Exam Focus

• Calculations:
  
  • Find minimum photon wavelength for pair production:
    λ_min = hc/(2mₑc²) = 1.21 pm

Question 14

Mass Defect & Binding Energy

Answer 14

Mass Defect (Δm)

• Definition:
  Difference between the sum of nucleon masses and the actual nuclear mass.
• Equation:
  Δm = [Z·mₚ + (A-Z)·mₙ] - m_nucleus
  • Z = proton number, A = nucleon number.
  • mₚ = proton mass = 1.673 × 10⁻²⁷ kg.
  • mₙ = neutron mass = 1.675 × 10⁻²⁷ kg.

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Binding Energy (ΔE)

• Definition:
  Energy needed to split a nucleus into its constituent nucleons.
• Equation:
  ΔE = Δm·c²
  • c = speed of light = 3 × 10⁸ m/s.

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Key Steps for Calculation

1. Calculate Δm:
   Sum proton/neutron masses → subtract measured nuclear mass.
2. Convert to Energy:
   Multiply Δm by c² → gives binding energy in joules.
3. Per Nucleon:
   Divide ΔE by A to compare stability across nuclei.

Question 15

Binding Energy per Nucleon Graph

Answer 15

Y-axis: Binding energy per nucleon (MeV/nucleon)
X-axis: Nucleon number (A)

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Key Features

1. General Trend:
   
   • Rises sharply for light nuclei (A < 20).
   • Peaks at iron-56 (8.8 MeV/nucleon, most stable).
   • Gradual decline for heavy nuclei (A > 56).
2. Anomalies:
   
   • Helium-4 (α-particle, exceptionally stable).
   • Carbon-12/Oxygen-16: Local maxima (3-4 α-particles bound).

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• Fusion Favored: Light nuclei (H → He). Increases BE/A → releases energy (e.g., Sun).
• Fission Favored: Heavy nuclei (U → Ba + Kr). Increases BE/A → releases energy (e.g., nuclear reactors).

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Nuclear Stability Explained

• Low A (e.g., ¹H):
  
  • BE/A ≈ 0 MeV (single proton → no binding needed).
  • Easy to remove nucleons (weak strong-force binding).
• Peak (⁵⁶Fe):
  
  • Optimal volume-to-surface ratio → strong-force dominates.
  • Moderate proton count → minimal electrostatic repulsion.
• High A (e.g., ²³⁸U):
  
  • Large proton count → electrostatic repulsion reduces BE/A.
  • Hard to remove nucleons (but easier than mid-range nuclei).

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OCR Exam Checklist

• Graph Must Include:
  1. Curve: Smooth best-fit with peak at A=56.
  2. Helium-4: Mark with “×” at (A=4, ~7 MeV/nucleon).
  3. Axes Labels:
     
     • X: “Nucleon number (A)” (no A=0!).
     • Y: “Binding energy per nucleon (MeV/nucleon)”.
  4. Key Points:
     
     • Doesn’t start at A = 0
     • Iron-56 peak (~8.8 MeV).
     • Uranium-238 (A=238, ~7.5 MeV).

Question 16

Nuclear Fission

Answer 16

Nuclear Fission

• Definition: Splitting of a heavy nucleus (e.g., uranium, plutonium) into smaller daughter nuclei, releasing energy. (Binding energy)

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Key Process

1. Induced Fission (Most Common):
   
   • Neutron absorbed → unstable nucleus → splits.
   • Example:
     n + ²³⁵U → ²³⁶U* → ¹⁴¹Ba + ⁹²Kr + 3n + energy
2. Spontaneous Fission:
   
   • Rare; occurs without neutron absorption (e.g., ²³⁸U).

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Energy Release

• Source: Conversion of nuclear binding energy → kinetic energy of products.
• Output per fission: ~200 MeV (mostly as kinetic energy).

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Chain Reaction

• Mechanism:
  
  1. Single neutron triggers fission.
  2. Released neutrons induce further fissions.
• Criticality:
  
  • Controlled: Nuclear reactors (1 neutron/fission sustained).
  • Uncontrolled: Atomic bombs (exponential growth).

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OCR Exam Focus

• Fuel Examples:
  
  • ²³⁵U (0.7% natural uranium), ²³⁹Pu (bred from ²³⁸U).
• Waste Products:
  
  • Fission fragments (radioactive, e.g., ¹³⁷Cs, ⁹⁰Sr).

Question 17

Radiation Detection Methods

Answer 17

Geiger-Müller (GM) Tube

How It Works

1. Ionisation:
   
   • α/β particles or γ-rays enter through a thin mica window.
   • They ionise the inert gas (e.g., argon), creating electron-ion pairs.
2. Avalanche Effect:
   
   • A high voltage (~400–600 V) accelerates electrons toward the central anode wire.
   • Collisions create a cascade of ionisations (“Townsend avalanche”).
3. Signal Generation:
   
   • Each avalanche produces a current pulse (heard as a “click”).
   • Pulses are counted to measure activity in becquerels (Bq).
4. Quenching:
   
   • Halogen gas (e.g., bromine) prevents continuous discharge.

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Key Features
- Detects α, β, γ (γ requires high energy).
- Cannot distinguish radiation types.
- Random counts prove decay is spontaneous.

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Cloud Chamber

How It Works

1. Supersaturated Vapour:
   
   • A sealed chamber contains cooled alcohol vapour.
2. Particle Trails:
   
   • Charged particles (α/β) ionise the vapour along their paths.
   • Ions act as condensation nuclei, forming visible droplet trails.
3. Visualisation:
   
   • α particles: Short, thick trails (high ionisation).
   • β particles: Long, faint trails (low ionisation).
   • Magnetic fields curve paths to show charge.

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Key Features

• Reveals particle charge, mass, and energy.
• Cannot detect γ-rays.

Why It Matters

• GM Tubes: Used in radiation monitoring (hospitals, labs).
• Cloud Chambers: Key for particle physics discoveries (e.g., positrons).

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Exam Tips

• GM tube dead time (~100 µs) limits high-activity measurements.
• Cloud chamber tracks:
  
  • Thickness ∝ particle charge.
  • Length ∝ particle energy.

Question 18

Nuclear Fission Reactor & Waste

Answer 18

1. Fuel Assembly

• Fuel Rods: Contain pellets of ²³⁵U (fissile) and ²³⁸U (fertile → ²³⁹Pu).
• Criticality:
  
  • Supercritical: Chain reaction sustains power (controlled).
  • Subcritical: Reaction decays (safe shutdown).

2. Moderator (e.g., Water/Graphite)

• Purpose: Slow fast neutrons → thermal energies (~1 eV).
• Colliding with the molecules, loses momentum (reach thermal equilibrium)
• Why Thermal Neutrons?
  
  • Higher probability of ²³⁵U capture → efficient fission.

3. Control Rods (Boron/Cadmium)

• Function: Absorb neutrons to regulate reaction rate.
  
  • Insert fully: Emergency shutdown (absorbs all neutrons).
  • Partial retraction: Maintain steady power (1 neutron/fission survives).

4. Coolant (Pressurised Water/Helium)

• Purpose: Transfer energy released by the fission reactions
  → steam → turbines → electricity.
• Safety: Prevents overheating and contamination (primary/secondary loops).

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Energy Conversion Process

1. Fission: ²³⁵U + n → fission fragments + 2-3 neutrons + 200 MeV/fission.
2. Heat Removal: Coolant circulates through heat exchanger.
3. Electricity Generation: Steam drives turbines → generators.

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Waste Types:

• Low-Level:
  
  • Slightly contaminated materials.
  • Stored briefly → shallow disposal.
• High-Level:
  
  • Extremely radioactive/hot.
  • Requires deep geological storage.

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High-Level Waste Treatment

1. Cooling Ponds: Store spent rods underwater for ~10 years.
2. Reprocessing: Extract reusable ²³⁵U/²³⁹Pu.
3. Vitrification: Mix waste with molten glass → solid blocks.
4. Storage: Steel/lead/concrete containers 500m+ underground.

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Environmental & Safety Measures

• Reactor Design:
  
  • Pressure vessel + concrete shield → contains radiation.
  • Backup cooling systems → prevents meltdowns.
• Waste Sites: Geologically stable, earthquake-resistant, secure from terrorism.

Question 19

Nuclear Fusion

Answer 19

Definition

• Light nuclei (e.g., hydrogen isotopes) combine to form heavier nuclei (e.g., helium), releasing energy.

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Key Requirements

1. High Temperatures (~10⁷ K):
   
   • Overcomes electrostatic repulsion between protons.
2. High Pressure:
   
   • Ensures frequent collisions (e.g., in stellar cores).
3. Confinement:
   
   • Magnetic fields (tokamaks) or inertial confinement (lasers).

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Fusion in Stars

1. Proton-Proton Chain:
   ¹H + ¹H → ²H (deuterium) + e⁺ + νₑ
   ²H + ¹H → ³He + γ
   ³He + ³He → ⁴He + 2¹H
2. Energy Release:
   • Mass defect (Δm) → energy via E = Δmc².
   • Net output: 26.7 MeV per ⁴He produced.

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Challenges on Earth

1. Plasma Confinement:
   
   • Tokamaks (e.g., JET, ITER) use magnetic fields to contain 100M°C plasma.
2. Energy Capture:
   
   • 80% of energy carried by neutrons → difficult to harness.
3. Net Energy Gain:
   
   • Current reactors (e.g., ITER) aim for Q > 1 (more output than input).

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Advantages Over Fission

• Fuel: Abundant (deuterium from seawater, lithium for tritium).
• Waste: No long-lived radioactive byproducts.
• Safety: No risk of meltdown; stops if containment fails.

Question 20

X-Ray Components

Answer 20

1. Heated Cathode
   
   • Function: Releases electrons via thermionic emission when heated.
   • Material: Tungsten filament (high melting point).
2. Anode (Positive Terminal)
   
   • Function: Accelerates electrons using high voltage.
   • Key Feature: Rotates at 3000 rpm to prevent overheating.
3. Metal Target
   
   • Function: Converts electron kinetic energy → X-rays.
   • Material: Tungsten (high atomic number for efficient X-ray production).
4. High Voltage Power Supply
   
   • Function: Provides 50–200 kV to accelerate electrons.

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Supporting Components

• Vacuum Chamber: Ensures electrons travel unimpeded.
• Lead Shielding: Blocks stray X-rays for safety.
• Adjustable Window: Controls X-ray beam direction.

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Why Tungsten?

• High melting point (3422°C) → withstands electron bombardment.
• High atomic number (Z=74) → efficient X-ray emission.

Question 21

X-Ray Production

Answer 21

1. Bremsstrahlung (Braking Radiation)

• Process:
  
  • High-speed electrons decelerate rapidly in tungsten target.
  • Kinetic energy → X-ray photons (1% efficiency).
• Energy Range:
  
  • Continuous spectrum up to maximum energy (eV).

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• Key Equation:
  eV = hc/(λₘᵢₙ)
  eV = hf_max
  
  • V = accelerating voltage, e = electron charge.

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2. Characteristic Radiation

• Process:
  
  1. Incoming electron ejects inner-shell tungsten electron (e.g., K-shell).
  2. Outer-shell electron fills vacancy → emits X-ray photon.
• Energy:
  
  • Discrete values (e.g., tungsten Kα = 59.3 keV).
• Spectrum:
  
  • Sharp spikes at specific wavelengths

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• Medical Imaging:
  
  • Bremsstrahlung → broad-range diagnostics.
  • Characteristic → high-contrast bone scans.

Question 22

Simple Scattering

Answer 22

Process

• A low-energy X-ray photon interacts with an orbital electron.
• The photon is deflected (scattered) without losing energy (wavelength remains unchanged).

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Key Characteristics

• Energy Range: Typically < 30 keV (too low to eject electrons).
• No Ionisation: Electron remains bound to atom.
• Direction Change: Photon path alters, but energy conserved.

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Impact on Imaging

• Image Blurring: Scattered photons reach detector from multiple angles → reduces contrast (“noise”).
• Example:
  
  • In chest X-rays, ~10% of detected photons are scattered, degrading image quality.

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Mathematical Description
- Cross-section (probability) depends on:
- Atomic number (Z⁴).
- X-ray energy (E⁻²).

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Why It Matters

• Radiography: Anti-scatter grids are used to filter out scattered photons.
• Safety: Contributes to occupational radiation exposure.

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Exam Tip:

• Simple scattering dominates for low-energy X-rays and high-Z materials (e.g., bone).
• Distinct from Compton scattering (energy loss) and photoelectric effect (absorption).