understand that the gamma-ray photons from an annihilation event travel outside the body and can be detected, and an image of the tracer concentration in the tissue can be created by processing the arrival times of the gamma-ray photons

Cambridge IGCSE/A‑Level Physics (9702) – Full Syllabus Notes

1. Quantities, Units, Vectors and Scalars (AO1, AO2)

• Base SI units: m (length), kg (mass), s (time), A (current), K (temperature), mol (amount), cd (luminous intensity).
• Derived units (selected): N = kg m s⁻², J = N m, W = J s⁻¹, Pa = N m⁻², V = W A⁻¹.
• Prefixes: k (10³), M (10⁶), m (10⁻³), µ (10⁻⁶), n (10⁻⁹).
• Vectors have magnitude and direction; scalars have magnitude only.
• Resultant of two vectors (parallelogram rule) – use components or trigonometry.

2. Kinematics (AO1, AO2)

Key equations (constant acceleration):

Worked example (car accelerates from 0 to 20 m s⁻¹ in 5 s):

\(a = (v-u)/t = 20/5 = 4\; \text{m s}^{-2}\);

\(s = ut + \tfrac12 at^2 = 0 + 0.5×4×25 = 50\; \text{m}\).

3. Dynamics, Forces and Momentum (AO1, AO2, AO3)

• Newton’s 1st, 2nd, 3rd laws.
• Resultant force: \(\mathbf{F}=m\mathbf{a}\).
• Weight: \(W=mg\); tension, normal, friction (static: \(fs\le\mus N\); kinetic: \(fk=\muk N\)).
• Momentum: \(\mathbf{p}=m\mathbf{v}\); impulse–momentum theorem \(\Delta\mathbf{p}= \mathbf{F}\Delta t\).
• Conservation of momentum in collisions – elastic vs inelastic.

4. Work, Energy and Power (AO1, AO2, AO3)

• Work: \(W = \mathbf{F}\cdot\mathbf{s}=Fs\cos\theta\) (J).
• Kinetic energy: \(Ek = \tfrac12 mv^2\); gravitational potential energy: \(Eg = mgh\).
• Conservation of mechanical energy (no non‑conservative forces): \(E{k1}+E{g1}=E{k2}+E{g2}\).
• Power: \(P = \dfrac{W}{t} = Fv\) (W).

5. Deformation, Stress and Strain (AO1, AO2)

• Stress: \(\sigma = \dfrac{F}{A}\) (Pa).
• Strain: \(\varepsilon = \dfrac{\Delta L}{L}\) (dimensionless).
• Young’s modulus: \(Y = \dfrac{\sigma}{\varepsilon}\) (Pa).
• Hooke’s law (elastic region): \(F = kx\) where \(k = Y A / L\).

6. Waves – Transverse and Longitudinal (AO1, AO2)

• Wave speed: \(v = f\lambda\).
• Transverse: displacement ⟂ direction of travel (e.g., light, water surface).
• Longitudinal: displacement ‖ direction (e.g., sound).
• Superposition principle – constructive & destructive interference.

7. Superposition and Standing Waves (AO1, AO2)

• Resultant displacement = algebraic sum of individual displacements.
• Standing wave condition in a string fixed at both ends: \(L = n\lambda/2\) (n = 1,2,3…).
• Fundamental frequency: \(f_1 = \dfrac{v}{2L}\).

8. Electricity – Current, Potential and Resistance (AO1, AO2, AO3)

• Current: \(I = \dfrac{Q}{t}\) (A).
• Potential difference: \(V = \dfrac{W}{Q}\) (V).
• Ohm’s law: \(V = IR\); resistance \(R = \rho\frac{L}{A}\).
• Power in circuits: \(P = VI = I^2R = \dfrac{V^2}{R}\).

9. DC Circuits (AO1, AO2, AO3)

• Series: \(R_{\text{eq}} = \sum R\); same current, total voltage = sum.
• Parallel: \(\dfrac{1}{R_{\text{eq}}}= \sum \dfrac{1}{R}\); same voltage, total current = sum.
• Kirchhoff’s rules – junction rule (ΣI = 0) and loop rule (ΣV = 0).
• Potential divider: \(V{\text{out}} = V{\text{in}}\dfrac{R2}{R1+R_2}\).

10. Particle Physics – Radioactivity and Decay (AO1, AO2, AO3)

• Radioactive decay law: \(N = N0 e^{-\lambda t}\); half‑life \(t{1/2}= \dfrac{\ln2}{\lambda}\).
• Types of decay: α (He‑nucleus), β⁻ (electron + antineutrino), β⁺ (positron + neutrino), γ (photon).
• Conservation laws: charge, nucleon number, energy, momentum.
• Activity: \(A = \lambda N\) (Bq).

11. Practical Skills (Paper 3 & 5) (AO3)

Typical investigations:

• Measuring acceleration due to gravity using a ticker‑timer.
• Determining the resistance of a wire (V‑I method, length‑area dependence).
• Investigating the attenuation of X‑rays through different materials.
• Testing coincidence timing in a PET detector prototype.

General checklist for any experiment:

1. State the aim and hypothesis.
2. Identify variables (controlled, independent, dependent).
3. Draw a clear schematic diagram with symbols.
4. Take multiple readings, record uncertainties.
5. Analyse data (graphs, linear fits, propagation of errors).
6. Evaluate – sources of error, improvements, relevance to theory.

Medical Physics – Production and Use of X‑rays

1. Production mechanisms (AO1, AO2)

• Bremsstrahlung (braking radiation) – high‑energy electrons are decelerated in the Coulomb field of target nuclei.

• Produces a continuous spectrum up to a maximum photon energy equal to the electron kinetic energy.
• Maximum photon energy: \(E_{\max}=eV\) where V is the accelerating voltage.
• The syllabus only requires a qualitative statement that intensity increases with the atomic number (Z) of the target and with the accelerating voltage. The empirical relation \(I_{\text{brem}}\propto Z\,V^{3}\) is useful for deeper study but is not exam‑required.

• Characteristic X‑rays – an inner‑shell electron is ejected; an outer‑shell electron fills the vacancy and emits a photon whose energy equals the difference between the two atomic levels:

  \(E = E{\text{inner}}-E{\text{outer}}\).

• Lines are discrete (e.g., Kα, Kβ) and element‑specific.

Typical characteristic lines for tungsten (Z = 74)

2. X‑ray tube (AO1, AO2)

• Cathode – heated filament emits electrons (thermionic emission).
• Anode (target) – usually tungsten (high Z, high melting point) to maximise bremsstrahlung.
• Vacuum chamber – prevents electron scattering by air.
• Cooling system – water‑ or oil‑cooled anode removes the ≈ 99 % of electron energy that becomes heat.
• High‑voltage supply – 30–150 kV for diagnostic work; voltage determines the maximum photon energy (see §3).

3. Relationship between accelerating voltage and minimum wavelength (AO1, AO2)

If the entire kinetic energy of an electron (\(eV\)) is converted into a single photon, then

\(eV = \dfrac{hc}{\lambda_{\min}}\)

which rearranges to the familiar expression

\(\displaystyle \lambda_{\min}= \frac{hc}{eV}\)

where h = 6.626 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.602 × 10⁻¹⁹ C.

Worked example (V = 100 kV):

• Electron energy: \(eV = 100 \text{kV}=1.00\times10^{5}\,\text{eV}\).
• \(\lambda_{\min}= \dfrac{1240\;\text{eV·nm}}{1.00\times10^{5}\;\text{eV}} = 0.0124\;\text{nm}=0.124\;\text{Å}\).

This lies well within the X‑ray region (≈ 0.01–10 nm).

4. X‑ray energy ranges and typical applications (AO2)

5. Safety and radiation protection – ALARA (AO3)

1. Shielding – lead, concrete or acrylic to attenuate X‑rays.
2. Collimation – restrict beam to the region of interest, reducing dose.
3. Exposure control – pulsed/gated emission, automatic exposure control.
4. Monitoring – personal dosimeters, area monitors; keep cumulative dose below regulatory limits.
5. Time, distance, shielding – minimise exposure time, maximise distance, use appropriate shielding.

Gamma‑ray Photons from Annihilation Events and PET Imaging

1. Positron emission and annihilation (AO1, AO2)

• A β⁺‑emitting radionuclide (e.g. ¹⁸F) decays: \(^{A}{Z}\!X \rightarrow\;^{A}{Z-1}\!Y + e^{+} + \nu_{e}\).
• The emitted positron travels a few millimetres, then annihilates with an electron:

  \(e^{+}+e^{-}\;\rightarrow\;\gamma{1}+\gamma{2}\)

  Each photon carries 511 keV (the rest‑mass energy of the electron/positron) and the two photons are emitted almost exactly 180° apart.

2. Detection of the 511 keV photons (AO1, AO2, AO3)

• Detectors are arranged in a ring (or multiple rings) surrounding the patient.
• Scintillation crystals (e.g. LSO, BGO) absorb a γ‑photon and emit a short burst of visible light.
• Light is collected by photomultiplier tubes (PMTs) or silicon photomultipliers (SiPMs) and converted into an electrical pulse.
• Coincidence detection – two detectors opposite each other must register pulses within a narrow time window (≈ 10 ns). The principle is that only photons originating from the same annihilation can satisfy this simultaneity, defining a *line of response* (LOR) on which the event occurred.

3. Time‑of‑Flight (TOF) PET and image reconstruction (AO2, AO3)

TOF PET measures the tiny difference in arrival times (Δt) of the two photons, allowing localisation of the annihilation point along the LOR:

\(x = \dfrac{c\,\Delta t}{2}\)

where c is the speed of light. Modern systems achieve timing resolutions of 200–400 ps, giving positional accuracies of 3–6 cm along the LOR.

Reconstruction workflow

1. Collect millions of coincidence events and record precise arrival times.
2. For each event, use the TOF equation to place a point (or short segment) on its LOR.
3. Bin all points into a 3‑D histogram (voxel grid) representing tracer activity.
4. Apply a reconstruction algorithm:

   • Filtered Back‑Projection (FBP) – fast, linear method.
   • Iterative methods (e.g. Maximum‑Likelihood Expectation‑Maximisation, MLEM) – improve noise characteristics and quantitative accuracy.

4. Applications and advantages of PET (AO2)

• Oncology – high glucose uptake visualised with ¹⁸F‑FDG highlights malignant tumours.
• Neurology – mapping cerebral metabolism, neurotransmitter receptors, amyloid deposition.
• Cardiology – assessing myocardial perfusion, viability, inflammation.
• Research & drug development – quantitative pharmacokinetic studies, receptor occupancy.

Key benefits:

• Very high sensitivity – detects picomolar tracer concentrations.
• Quantitative – activity concentration expressed in Bq ml⁻¹ or Standardised Uptake Value (SUV).
• When combined with CT or MRI, PET provides precise anatomical localisation.

Assessment Objective (AO) Mapping Summary

Use this mapping to focus revision on the specific objectives required for each exam paper.