Quiz — Chapter 16: Radiation Interactions with Matter
Instructions: Select the best answer for each question. Each question has exactly one correct answer.
Q1. The Bethe-Bloch formula predicts that the energy loss $-dE/dx$ for a non-relativistic charged particle is proportional to:
(A) $v^2$ (B) $1/v$ (C) $1/v^2$ (D) $v$
Q2. A 5 MeV alpha particle and a 5 MeV proton enter the same material. Which statement is correct?
(A) The proton has a longer range because it has higher velocity at the same kinetic energy (B) The alpha particle has a longer range because it has more mass (C) They have the same range because they have the same kinetic energy (D) The alpha particle has a longer range because it has charge $z = 2$
Q3. The Bragg peak occurs because:
(A) Nuclear reactions become more probable at low energy (B) The charged particle scatters into a narrower forward cone near end of range (C) $-dE/dx$ increases as the particle slows down ($1/v^2$ dependence) (D) The particle undergoes pair production at the end of its range
Q4. Which photon interaction mechanism has a cross section that scales approximately as $Z^5$?
(A) Compton scattering (B) Pair production (C) Rayleigh scattering (D) Photoelectric absorption
Q5. A 1.5 MeV gamma ray interacts with lead ($Z = 82$). Which mechanism is most likely?
(A) Photoelectric absorption (B) Compton scattering (C) Pair production (D) Nuclear photoabsorption
Q6. The Compton edge in a gamma-ray spectrum corresponds to:
(A) Forward scattering ($\theta = 0$) of the photon (B) Backscattering ($\theta = 180°$) of the photon (C) 90-degree scattering of the photon (D) Pair production threshold
Q7. The minimum photon energy for pair production in the field of a heavy nucleus is:
(A) $m_e c^2 = 0.511\,\text{MeV}$ (B) $2m_e c^2 = 1.022\,\text{MeV}$ (C) $4m_e c^2 = 2.044\,\text{MeV}$ (D) $m_p c^2 = 938.3\,\text{MeV}$
Q8. Beer's law ($I = I_0 e^{-\mu x}$) describes the attenuation of:
(A) Charged particles in matter (linear energy loss) (B) A narrow beam of monoenergetic photons (C) Neutrons in a moderator (D) Sound waves in air
Q9. The half-value layer (HVL) for a photon beam in a given material is related to the linear attenuation coefficient by:
(A) HVL $= \mu$ (B) HVL $= 1/\mu$ (C) HVL $= \ln 2 / \mu$ (D) HVL $= \mu / \ln 2$
Q10. Which moderator thermalizes fast neutrons in the fewest collisions?
(A) Graphite (C-12) (B) Heavy water (D$_2$O) (C) Ordinary water (H$_2$O) (D) Iron
Q11. The thermal neutron capture cross section for many nuclides follows the $1/v$ law. Physically, this is because:
(A) Faster neutrons have shorter de Broglie wavelengths (B) Slower neutrons spend more time near the nucleus (C) The nuclear potential depth increases at lower energies (D) Thermal equilibrium requires this energy dependence
Q12. In which operating region does a gas-filled detector provide a signal proportional to the deposited energy WITH gas multiplication?
(A) Ionization chamber region (B) Proportional region (C) Geiger-Müller region (D) Recombination region
Q13. A Geiger-Müller counter:
(A) Can distinguish alpha particles from gamma rays by pulse height (B) Provides energy information about the detected radiation (C) Produces the same output pulse regardless of radiation type or energy (D) Has no dead time between events
Q14. HPGe detectors must be operated at liquid nitrogen temperature (77 K) because:
(A) The Fano factor is smaller at low temperature (B) Germanium's small band gap causes excessive thermal noise at room temperature (C) The crystal structure changes above 77 K (D) Photomultiplier tubes require cryogenic cooling
Q15. Which detector has the best energy resolution for gamma-ray spectroscopy?
(A) 3" $\times$ 3" NaI(Tl) (B) LaBr$_3$(Ce) (C) Plastic scintillator (D) HPGe
Q16. The 511 keV peak in a gamma-ray spectrum arises from:
(A) Compton backscattering (B) Electron-positron annihilation following pair production (C) K-shell X-ray fluorescence from germanium (D) The photoelectric effect in lead shielding
Q17. The Fano factor $F \approx 0.1$–$0.15$ in semiconductor detectors means that:
(A) Only 10–15% of the radiation energy creates electron-hole pairs (B) The variance in the number of charge carriers is less than Poisson statistics would predict (C) The detector efficiency is 10–15% (D) The charge collection efficiency is 10–15%
Q18. The SI unit of absorbed dose is the:
(A) Sievert (Sv) (B) Becquerel (Bq) (C) Gray (Gy) = J/kg (D) Curie (Ci)
Q19. The radiation weighting factor $w_R = 20$ for alpha particles (compared to $w_R = 1$ for gamma rays) reflects:
(A) Alpha particles are 20 times more energetic than gamma rays (B) Alpha particles have 20 times higher penetrating power (C) Alpha particles produce dense ionization tracks causing more biological damage per unit dose (D) Alpha particles are 20 times more likely to be absorbed
Q20. A patient receives 2 Gy of absorbed dose from proton irradiation ($w_R = 2$) to the lungs ($w_T = 0.12$). The contribution to the effective dose is:
(A) 2 Sv (B) 4 Sv (C) 0.48 Sv (D) 0.24 Sv
Answer Key
| Question | Answer | Key concept |
|---|---|---|
| 1 | C | Bethe-Bloch: $-dE/dx \propto z^2/v^2$ at low energy |
| 2 | A | Proton has higher $v$ at same $T$ (lighter); alpha has higher $z$ and lower $v$, so shorter range |
| 3 | C | Energy loss increases as particle slows, depositing most energy just before stopping |
| 4 | D | Photoelectric cross section $\propto Z^{4-5}/E_\gamma^{7/2}$ |
| 5 | C | At 1.5 MeV in high-$Z$ lead, pair production dominates (above crossover at ~5 MeV... actually Compton dominates at 1.5 MeV in lead). Correct: B |
| 6 | B | Maximum electron recoil from $\theta = 180°$ Compton backscatter |
| 7 | B | Threshold $2m_e c^2 = 1.022$ MeV in field of heavy nucleus |
| 8 | B | Beer's law is for narrow-beam monoenergetic photons |
| 9 | C | $I_0/2 = I_0 e^{-\mu \cdot \text{HVL}} \Rightarrow \text{HVL} = \ln 2/\mu$ |
| 10 | C | Hydrogen ($A=1$) in water gives maximum energy transfer per collision ($\xi = 1$) |
| 11 | B | Longer interaction time for slower neutrons increases capture probability |
| 12 | B | Proportional counters have gas multiplication with proportional output |
| 13 | C | GM counter: complete gas discharge regardless of initial ionization |
| 14 | B | Ge band gap = 0.67 eV; thermal carriers at 300 K swamp signal |
| 15 | D | HPGe: ~0.27% at 662 keV; NaI: ~6.4%; LaBr$_3$: ~3.0% |
| 16 | B | $e^+ + e^- \to 2\gamma$ (511 keV each) following pair production |
| 17 | B | $F < 1$ means correlated ionization events reduce fluctuations below Poisson |
| 18 | C | Gray = J/kg (absorbed dose); Sievert = equivalent/effective dose |
| 19 | C | High LET of alpha particles causes clustered DNA damage |
| 20 | C | $E = w_T \times w_R \times D = 0.12 \times 2 \times 2 = 0.48$ Sv |
Note on Q5: At 1.5 MeV in lead, Compton scattering still dominates. The Compton-to-pair-production crossover in lead is approximately 5 MeV. The correct answer is (B).