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_y = 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

Bremsstrahlung X-ray Production

Answer 21

Process:

• High-speed electrons collide with a metal target (e.g., tungsten) and decelerate rapidly.
• Deceleration converts kinetic energy → X-ray photons (conservation of energy).

===

Key Features

1. Energy Conversion:
   
   • Only ~1% of electron kinetic energy becomes X-rays.
   • Remainder (99%) heats the anode (requires cooling).
2. X-ray Spectrum:
   
   • Produces continuous spectrum (“smooth hump” on intensity-wavelength graph).
   • The shortest wavelength X-ray produced is given by:λ_min = hc / eV
   • Photon energy range: 0 → maximum electron KE (depends on accelerating voltage).

Question 22

Characteristic X-ray Production

Answer 22

Process:

1. Inner-shell ionization:
   
   • Incoming high-energy electrons eject inner-shell electrons from tungsten atoms.
2. Electron transition:
   
   • Outer-shell electrons fill the vacancy, releasing X-ray photons with energy:
     E_photon = E_upper - E_lower = hc / λ
3. Discrete spectrum:
   
   • Produces sharp peaks (Kα, Kβ lines) at specific wavelengths.

===

• Target Material Dependence:
  • Each element has unique energy levels → unique X-ray fingerprint.
  • Tungsten shows two prominent peaks (Kα, Kβ).

Question 23

Simple Scattering and Compton Effect

Answer 23

1. Simple (Elastic) Scattering

Process:

• Low-energy X-ray photon deflects off an atomic electron.
• No energy loss: Wavelength/photon energy unchanged.

Effects:
- Causes image blurring/noise in detectors:
- Scattered X-rays reach detector from multiple angles.
- Reduces image contrast.
- Only occurs with low-energy X-rays (<~30 keV).

===

2. Compton Effect (Inelastic Scattering)

Process:

• X-ray photon transfers energy to outer-shell electron:
  
  1. Photon deflected with longer λ (lower energy).
  2. Electron ejected (recoil electron).
• Obeys conservation of momentum
  
  • electron and X-ray photon are deflected in different directions
• Dominates at intermediate X-ray energies (~0.5–5 MeV).

Question 24

Photoelectric Effect and Pair Production in X-ray Attenuation

Answer 24

Photoelectric Effect in X-ray Attenuation

Process:

• Inner-shell electron absorbs entire X-ray photon → ejected as photoelectron.
• Photon completely disappears (total absorption).

Photoelectric Equation:
hf = Φ + KE_max

Key Points:

• Dominates for low-energy X-rays (<100 keV) and high-Z materials (e.g., bone, contrast agents).
• Produces secondary radiation (characteristic X-rays when outer electrons fill the vacancy).

===

Pair Production

Process:

• High-energy X-ray photon (>1.02 MeV) interacts with nucleus → converts into electron-positron pair.
• Photon completely absorbed.

Threshold Energy:
E_min = 2m_e c² = 1.02 MeV
- m_e: Electron mass (equivalent to 0.51 MeV).

Key Points:

• Requires extremely high energies (only significant in radiotherapy/astrophysics).
• Positron fate: Annihilates with another electron → produces two 511 keV gamma photons.

Question 25

X-ray Attenuation

Answer 25

**X-ray Attenuation Definition** **Attenuation**: Reduction in X-ray beam **intensity/energy** when passing through matter due to interactions. === **Key Observations**: - **Bones** appear **white** on X-rays due to **high absorption** (high atomic number, density). - **Soft tissues** appear **gray** (lower absorption, more transmission). - Attenuation occurs via: - **Absorption** (Photoelectric effect) - **Scattering** (Compton, Rayleigh) === **Attenuation Equation** The intensity reduction follows an **exponential decay**: ``I = I₀ e^(-μx)`` - **I₀**: Incident intensity (W/m²) - **I**: Transmitted intensity (W/m²) - **μ**: Linear attenuation coefficient (m⁻¹) - Depends on: - **X-ray energy** (↑ energy → ↓μ) - **Material density/Z** (e.g., bone μ > muscle μ) - **x**: Thickness of material (m) === **Half-Value Thickness (HVT)** **Definition**: Thickness reducing intensity to **50%** of original value. **Calculation**: ``HVT = ln(2)/μ ≈ 0.693/μ``

Question 26

X-ray Imaging

Answer 26

**X-ray Safety & Filtration** - **Ionising Hazard**: X-rays can damage DNA → cancer risk. - **Aluminum Filters**: - Remove **low-energy (long λ ) X-rays**: - These are more absorbed by tissue → no image benefit, only health hazard. === **Image Quality Factors** **1. Contrast** - **Definition**: Difference in blackening between tissues. - **Improved by**: - **X-ray energy selection**: - **Bone imaging**: 60-100 keV (hard X-rays). - **Soft tissue**: 20-40 keV (soft X-rays). - **Using a contrast media** (high-Z materials) **2. Sharpness** - **Definition**: How well defined the edges of structures are - **Improved by**: - **Collimators**: Reduce scattered X-rays. - **Smaller pixels**: Higher resolution detectors. - **Lead grids**: Absorb off-angle scattered photons. - Using a **narrower** X-ray beam

Question 27

CAT Scans

Answer 27

1. **X-ray Tube Rotates** around the patient, taking hundreds of 2D images from different angles. 2. **Computer Combines** these images to build a 3D slice-by-slice picture. === **Advantages of CT Scans** 1. **Superior image detail** - Software enhances images with *colour* and *sharpening* - Can edit out unwanted parts 2. **Better tissue differentiation** - Distinguishes tissues with **similar attenuation coefficients** - Higher **resolution** than standard X-rays 3. **3D imaging capability** - Combines multiple slices to create **rotatable 3D models** - No overlapping structures (e.g., bones don't hide organs) 4. **Complete examination** - Images **soft tissue and bone** simultaneously **Disadvantages of CT Scans** 1. **Radiation exposure** - Delivers **much higher dose** than conventional X-rays 2. **Contrast media risks** - Possible allergic reactions to iodine/barium agents

Question 28

Medical Tracers

Answer 28

**Definition**: - **Radioactive substances** absorbed by tissues to study **organ structure/function**. === **Suitable Isotopes**: 1. **Technetium-99m** - *Half-life*: **6 hours** - Emits **gamma (γ) radiation** - Binds to organic molecules (e.g., water) - Decays to **stable technetium-99** (⁹⁹Tc) 2. **Fluorine-18** - *Half-life*: **110 minutes** - Used in **PET scans** as *fluorodeoxyglucose* (FDG) (Glucose molecule with **fluorine-18** attached) - Decays via **β⁺ decay** (emits positrons) === **How Tracers Work**: 1. Administered via **injection/swallowing** 2. Absorbed by target tissues → appear as **bright areas** on scans 3. Gamma/positron emission detected by: - **Gamma cameras** (Technetium) - **PET scanners** (Fluorine-18) === **Clinical Applications**: - **Cancer diagnosis** (tumour metabolism) - **Heart function** (blood flow detection) - **Brain disorders** (Alzheimer’s, dementia) === **Key Physics Principles** - **Half-life choice**: Short enough to **minimize patient dose**, long enough to complete imaging. - **Radiation type**: - γ-rays penetrate tissue → detected externally. - β⁺ annihilation produces **511 keV photons** (PET).

Question 29

Gamma Camera

Answer 29

**1. Collimator** - **Purpose**: Filters gamma rays to improve image resolution - **How it works**: - Made of **lead tubes** angled parallel to desired detection path - Only **parallel γ-rays** pass through → scattered photons absorbed - **Narrower/longer tubes** = more gamma rays absorbed = sharper images (but reduced intensity) **2. Scintillator Crystal** - **Material**: Typically sodium iodide (NaI) with thallium doping - **Process**: 1. γ-ray hits crystal → excites electrons 2. Electrons return to ground state → emit **visible light photons** **3. Photomultiplier Tubes (PMTs)** - **Function**: **detect** faint light signals and **converts** them into voltage pulses then **amplifies** - **Key stages**: - **Photocathode**: Converts **light** → (releases) **electrons** - **Dynodes**: Accelerate electrons through a series of dynodes, each at a progressively higher potential. - **Energy gained** by each acceleration triggers the **release of more electrons** resulting in a **stronger electrical signal** - **Anode**: Outputs electrical pulse proportional to γ-ray energy **4. Image Formation** - **Computer processing**: - Maps **photon arrival times** and **intensities** - Bright spots = high tracer concentration (e.g., tumour sites) === **OCR Exam Focus** - **Why lead collimators?** - High Z absorbs scattered γ-rays → reduces image blur - **Scintillator requirements**: - High density (efficient γ-ray absorption) - Fast decay time (avoid signal overlap) - **SPECT Imaging**: Uses rotating gamma camera for 3D tracer mapping

Question 30

PET Scans

Answer 30

**Definition**: A nuclear imaging technique that maps **cellular metabolic activity** using positron-emitting tracers. === **Key Stages** 1. **Preparation**: - Patient injected with **fluorine-18** (β⁺ emitter) tracer (e.g., FDG). - Tracer accumulates in **high-activity tissues** (e.g., tumours). 2. **Scanning**: - Patient lies inside **ring of gamma detectors**. - β⁺ annihilation process: ``e⁺ + e⁻ → 2γ (511 keV each, 180° apart)`` - **Coincidence detection**: - Only photon pairs arriving **<1 ns apart** are counted. - Determines annihilation location via **time-of-flight**. 3. **Image Formation**: - Computer reconstructs 3D metabolic map from γ-ray data. - **Bright spots** = high tracer uptake (e.g., cancer cells). - **Line of Response (LOR)**: Connects detector pairs where γ-rays hit === **OCR Exam Focus** - **Isotope choice**: F-18 (110 min half-life) balances scan duration/safety. - **Annihilation photons**: - **Energy**: Always 511 keV (mass-energy equivalence). - **Direction**: Back-to-back (conserves momentum). - **Why two photons?** - Confirms real annihilation events (rejects scattered γ-rays). - **Advantage over CT**: - Shows **cellular function** (not just anatomy).

Question 31

Ultrasound

Answer 31

**Ultrasound Definition** - Sound waves with **frequency >20 kHz** (inaudible to humans). === **A-Scan (Amplitude Scan)** **How It Works**: 1. **Single transducer** emits/receives pulses. 2. Measures **time delay** (Δt) between pulse emission and echo return. 3. Calculates distance: ``distance = (speed of sound × Δt) / 2 `` **Uses**: - Measuring **depth** of structures (e.g., eye length for surgery planning). - Detecting **tumours** or abnormalities. **Limitations**: - **1D output** (distance only, no image). === **B-Scan (Brightness Scan)** **How It Works**: 1. **Multiple transducers** (or a moving transducer) emit/receive pulses. 2. Combines **multiple A-scans** to build 2D/3D images. 3. **Pixel brightness** = echo strength. **Optimising Image Quality**: - **Pulsed waves**: Prevent interference between sent/received waves. - **Shorter wavelengths**: Improve resolution (diffract around finer details). **Uses**: - Imaging **organs**, **muscles**, **bones**. - **Pregnancy scans** (foetal development). === **Key Physics** - **Speed of sound**: ~1540 m/s in soft tissue. - **Resolution**: ∝ **1/wavelength** (higher frequency = clearer images).

Question 32

Ultrasound Transducer

Answer 32

**Piezoelectric Effect** - **Definition**: Certain crystals generate a **potential difference (p.d.)** when mechanically deformed (compressed/stretched). - **Key Properties**: - **Reversible**: Applying high frequency p.d. causes deformation (expansion/contraction). - **Frequency matching**: Alternating p.d. → vibrations at same frequency (Resonate) - **Example Material**: - **Quartz (SiO₂)**: Lattice distortion creates charge separation → electric field →current - Applying alternating **pd** cause lattice to alternate shape, produces a sound wave === **Ultrasound Transducer Operation** **1. Generating Ultrasound** - Alternating p.d. applied → crystal vibrates → emits **sound waves**. - **Damping (epoxy resin)**: - Reduces prolonged vibrations → **short pulses** for better resolution. **2. Detecting Ultrasound** - Reflected sound waves deform crystal → generate **alternating p.d.** (received signal). **Components**: - **Piezoelectric crystal** (e.g., quartz, PZT). - **Electrodes**: Apply/measure p.d. === **OCR Exam Focus** - **Why damping?** - Short pulses = better **axial resolution** (distinguish close structures). === **Key Equations** - **Resonant frequency**: ``f = v / (2 × crystal <sub>thickness</sub> ) `` (where *v* = speed of sound in crystal).

Question 33

Acoustic Impedance

Answer 33

**Acoustic Impedance (Z)** - **Definition**: `` Z = ρ × c `` (resistance to ultrasound beam) - **ρ** = density of medium (kg m^-3) - **c** = speed of sound in medium (m s^-1) - **Units**: kg m^-2 s^-1 - **Key Relationships**: - Sound travels **faster in denser materials** (solids > liquids > gases). - Higher Z → **greater resistance** to ultrasound transmission. === **Boundary Behavior** 1. **Reflection & Transmission**: - At boundaries between **different Z values**: - Some wave energy **reflects**, some **transmits**. - **Larger ΔZ** → more reflection (e.g., air/tissue boundary). 2. **Impedance Matching**: - Gel reduces reflection by **matching Z** of transducer - Two media have a similar acoustic impedance = no reflection === **Intensity Reflection Coefficient (α)** - **Equation**: `` α = (Z<sub>2</sub> - Z<sub>1</sub>)<sup>2</sup> / (Z<sub>2</sub> + Z<sub>1</sub>)<sup>2</sup> `` - **Interpretation**: - **α ≈ 0**: Perfect matching (no reflection). - **α ≈ 1**: Total reflection (e.g., air/tissue: α = 0.999).

Question 34

Doppler Effect (Ultrasound)

Answer 34

**Definition**: - Frequency change of waves due to **relative motion** between source and observer. - **Key Observations**: - Moving **towards** transducer → **↑ frequency** (shorter λ). - Moving **away** → **↓ frequency** (longer λ). **Medical Application** 1. **Process**: - Transducer emits **ultrasound pulses** (2-10 MHz). - Moving blood cells reflect waves → **frequency shift**. - Iron in hemoglobin enhances reflection. - **No radiation** - safer than X-rays for some applications 2. **Detection**: - **Positive Δf**: Blood flowing **towards** probe. - **Negative Δf**: Blood flowing **away**. === **Ultrasound Reflection Principles** 1. **Transducer Operation**: - Emits **high-frequency sound waves** (2-18 MHz) into body. - Detects echoes from **tissue boundaries** (e.g., muscle/bone). 2. **Image Formation**: - **Time delay** of echo → calculates distance: ``distance = (speed of sound × time delay)/2`` - Multiple echoes → constructs **2D greyscale image**. === **What Echoes Tell Us** - **Depth information**: Time delay shows how far away boundary is - **Tissue nature**: Echo strength indicates boundary type - Strong echo = big impedance change (e.g., tissue/bone) - Weak echo = similar tissues (e.g., muscle/fat) === **Frequency vs Resolution** - **Higher frequency** (e.g., 10 MHz): - **↑ Resolution**: Distinguishes <1 mm structures. - **↓ Penetration**: Limited to superficial tissues. - **Lower frequency** (e.g., 3 MHz): - **↓ Resolution** but **↑ Penetration** (deep organs).

Question 35

Contrast Media

Answer 35

**Definition** - A **substance**, such as barium or iodine, which is a **good absorber of X-rays**. - Administered to patients to **improve image contrast** between tissue === - **Mechanism**: - High-Z elements → **large μ (attenuation coefficient)** → more X-ray absorption. - Follows **exponential attenuation law**: ``I = I₀ e^(-μx)`` === **Why Barium/Iodine?** - K-shell binding energies match diagnostic X-ray energies → **strong photoelectric absorption**. === **Clinical Need** - Used when: - Target organ has **similar μ (attenuation coefficient)** to surrounding tissues - Natural contrast is insufficient for diagnosis (e.g., blood vessels, digestive tract)