Radiation & Radiation Protection – Comprehensive Study Notes

Radiology: Scope & Required Knowledge

• Radiology employs ionizing radiation for diagnosis & therapy.

• Competent use demands understanding of:
  • Basic nature & origins of radiation (electromagnetic vs particulate).
  • Radiation–matter interactions (ionization, excitation, scattering, absorption).
  • Radiation detection / dosimetry principles.
  • Biological effects (cellular → organism, deterministic vs stochastic).
  • Cost–benefit & safety limitations in medical applications.

Classification, Nature & Origin of Radiation

• Two overarching classes:

  1. Electromagnetic (EM) radiation – X-rays, $\gamma$-rays.

  2. Particle (corpuscular) radiation – $\alpha$, $\beta$, n, heavy ions, fission fragments.

Electromagnetic Radiation

• X- & $\gamma$-rays occupy $\lambda$ range $10^{-4}\,\text{nm}\,\rightarrow\,10^1\,\text{nm}$ (eV–MeV energies).

• Photon concept: EM behaves as packets with energy
  $E = h\nu = \frac{h c}{\lambda}$
  Planck constant h = 6.62\times10^{-34}\,\text{J·s} = 4.12\times10^{-21}\,\text{MeV·s}.

X-ray Production

1. Characteristic radiation – electronic de-excitation (e.g.
   $K<em>{\alpha}, K</em>{\beta}$ lines) with $E_{\gamma}=\Delta$electron binding.

2. Bremsstrahlung – deceleration of fast charged particles (usually e¯) in nuclear coulomb field ⇒ continuous spectrum.

$\gamma$-Rays

• Originate from de-excitation of nuclei.

• Nucleus: Z protons, N neutrons, A = Z + N.

• Binding Energy $\text{BE}=\big(m<em>pZ+m</em>nN-m_{\text{nucleus}}\big)c^2$; higher BE ⇒ greater stability.

• Isotopic terminology:
  • Isotopes (same Z) e.g. $^{16,17,18}!\text{O}$.
  • Isotones (same N) e.g. $^{17}\text{N},^{18}\text{O},^{19}\text{F}$.
  • Isobars (same A) e.g. $^{18}\text{N},^{18}\text{O},^{18}\text{F}$.

• Nuclear excitation modes: rotational, vibrational, single-particle; $\gamma$-emission carries transition energy.

Particle Radiation & Nuclear Decay

• General driver: move toward higher BE (lower mass).

• $\beta^-$ decay: $n \rightarrow p + e^- + \bar\nu_e$.

• $\beta^+$ decay: $p \rightarrow n + e^+ + \nu_e$.
  • Both give continuous electron/positron spectra (energy shared with neutrino).

• $\alpha$ decay: emission of $^{4}_{2}\text{He}^{2+}$; common for heavy nuclides; fixed kinetic energies from Q-value.

• Delayed-neutron emission & fission: key medical neutron sources.

Radioactive Decay Law

• Activity $A=\lambda N$ where $\lambda$ = decay constant.

• Differential: $\frac{dN}{dt}=-\lambda N\;\Rightarrow\;N(t)=N<em>0 e^{-\lambda t},\;A(t)=A</em>0 e^{-\lambda t}$.

• Half-life $t_{1/2}=\frac{\ln 2}{\lambda}$.

• Mean lifetime $\tau=\frac{1}{\lambda}\;(\approx1.44 t_{1/2})$ (population drops to 36.8 %).

• Units of activity:
  • Becquerel $1\,\text{Bq}=1\,\text{s}^{-1}$.
  • Curie $1\,\text{Ci}=3.7\times10^{10}\,\text{s}^{-1}=37\,\text{GBq}$.

• Worked example ( $^{24}\text{Na},\;t<em>{1/2}=15\,\text{h}$): • Initial $A</em>0=10\,\text{MBq}$.
  • After $t=2.5\,\text{d}=60\,\text{h}$ ⇒ $A=A_0 e^{-\lambda t}=1.88\,\text{MBq}$ (note consistent time units).

Dosimetry & Radiological Units

Exposure, E

• Interaction of X/$\gamma$ with air – ion charge produced.
  Definition: $1\,\text{R} = 2.58\times10^{-4}\,\text{C kg}^{-1}$ (at 22 °C, 760 Torr).

• Exposure rate: $ER=\frac{\Gamma A}{d^2}$ where $\Gamma$ = exposure constant (\text{R·cm}^2)/(\text{h·mCi}).

Absorbed Dose, D

• Energy per unit mass: $D=\frac{E_{\text{abs}}}{m}$.

• Units: Gray (SI) & rad (1 Gy = 100 rad = 1 J kg⁻¹).

• For air: $W_{\text{air}}\approx34\,\text{eV ion}^{-1}\Rightarrow 1\,\text{R}\rightarrow0.88\,\text{rad}$.

• Roentgen-to-rad factor C depends on photon energy & absorber (≈1 for soft tissue, >1 for bone at low keV).

Dose Equivalent, H

• Accounts for radiation quality (LET): $H = D \times Q$.
  • $Q(\gamma,X,\beta)\approx1$.
  • $Q(\alpha)\approx20$; neutrons vary (≈2–20, 11 for 2 MeV n).

• Units: Sievert (Sv) & rem (1 Sv = 100 rem).

• Example: 100 μCi $^{22}\text{Na}$ at 50 cm gives $H_R\approx0.456\,\text{mrem h}^{-1}$; 2 months undetected ≈0.67 rem.

Effective Dose, $H_e$

• Organ sensitivity weighting: $H<em>e = \sum</em>T w<em>T H</em>T$; $\sum w_T=1$.

• Provided examples:
  • Uniform exposure: $H<em>e = H</em>T$.
  • Mixed radiation/organ example (lung $\alpha$, thyroid $\beta$, external $\gamma$) ⇒ $H_e≈42\,\text{mSv}$.

Summary Conversion Table (key points)

• $1\,\text{R} = 2.58\times10^{-4}\,\text{C kg}^{-1}$.

• $1\,\text{rad}=10\,\text{mGy}$; $100\,\text{rad}=1\,\text{Gy}$.

• $K_{\text{air}}(\text{mGy}) = 0.0873\times E(R)$.

• $1\,\text{Sv} = Q\times1\,\text{Gy};\;1\,\text{rem}=Q\times1\,\text{rad}$.

Penetrating Power

• $\alpha$ stopped by paper / skin.

• $\beta$ stopped by mm–cm plastic/aluminium.

• $\gamma$ highly penetrating; needs cm-lead or >1 m concrete.

Biological Interaction & Effects

LET & RBE

• LET ↑ ⇒ ionization density ↑.

• RBE ~ LET for low LET region; peaks then drops (“over-kill”).

Direct vs Indirect Action

• Direct: ionization of critical biomolecules (e.g.
  DNA double-strand breaks).

• Indirect (dominant for low-LET):

  1. Radiation ionizes $\text{H}_2\text{O}$.

  2. Radiolysis species: $\text{H}^+,\;e^-_{\text{aq}},\;\text{OH}^·,\;\text{H}^·$.

  3. $\text{OH}^·$ radicals attack DNA ⇒ mutations, cell death.

• Time scales:
  • Physical (≤$10^{-15}\,\text{s}$) → chemical micro-seconds → biological (minutes → years).

Dose–Response & Ranges

• Statistical (probabilistic) damage; dose–response curves differ for high- vs low-LET.

• Immediate effects at high doses:
  • Skin erythema, epilation etc.

• Acute Radiation Syndrome (ARS): prodromal → latent → manifest illness.
  • LD₅₀₋₆₀ ~ $3–4\,\text{Gy}$ whole-body without care.
  • Hematopoietic (0.5–5 Gy), GI (10–50 Gy), CNS (>50 Gy) syndromes; detailed staging table provided.

• Long-term stochastic risks: cancers, genetic; low statistics ⇒ rely on linear/no-threshold (LNT) or linear-quadratic models.

Tissue Sensitivities

• Very radiosensitive: bone marrow, GI epithelium, germ cells.

• Radiation-induced cancer frequencies (high → low): Female breast, thyroid (especially children), lung, leukemia, alimentary tract etc.

• No demonstrated human heritable effects to date; risk ≈ few disorders per million per rem parental exposure.

Risk & Protection Standards

• Nominal fatal cancer risk coefficients (low dose-rate):
  • General public $5\times10^{-2}\,\text{Sv}^{-1}$.
  • Workers $4\times10^{-2}\,\text{Sv}^{-1}$.

• Nonfatal cancer $1\times10^{-2}\,\text{Sv}^{-1}$.

• Fundamental goals: prevent deterministic effects; keep stochastic risks “as low as reasonably achievable” (ALARA).

Dose Limits (NCRP 116 / ICRP 60)

• Occupational:
  • 50 mSv y⁻¹ (ICRP : 50 mSv, 100 mSv across 5 y).
  • Lifetime cumulative: $10\,\text{mSv} \times \text{age}$.
  • Organ annual: lens 150 mSv; skin, hands & feet 500 mSv.

• Public:
  • 1 mSv y⁻¹ (may average 5 y); occasionally 5 mSv for infrequent exposure.

Natural Background & Enhanced Sources

Cosmic Radiation

• Shielded by atmosphere; dose rate ground ≈$3.2\,\mu\text{rem h}^{-1}$.

• Dose doubles each 1500 m altitude; 10 km flight ≈100× sea-level.

• Example: 10 h trans-Atlantic ⇒ $H≈3.2\,\text{mrem}\;(\text{one-way})$; frequent flyer (5 round trips) ≈31.5 mrem y⁻¹.

Terrestrial Radioactivity

• Four natural decay chains: U-238 (Uranium), U-235 (Actinium), Th-232 (Thorium), Pu-241 (Neptunium).

• Radon-222 (U-chain) – inert gas, $t<em>{1/2}=3.82\,\text{d}$, migrates into buildings. • Daughters $^{218}\text{Po},^{214}\text{Po}$ (strong $\alpha$) deposit in bronchi. • Typical indoor concentration ≈120 Bq m⁻³; yields ≈2 R y⁻¹ → absorbed $\approx1.9\,\text{rad y}^{-1}$; with $Q≈10$ ⇒ lung equivalent ≈19 rem y⁻¹; Effective dose $=0.12H</em>{lung}≈0.22\,\text{rem}=200\,\text{mrem}$.

Potassium-40

• Natural abundance 0.0118 %; $t_{1/2}=1.28\times10^9\,\text{y}$.

• Whole-body:
  • 80 kg person ⇒ $N\approx4.44\times10^{19}$ atoms ⇒ $A≈764\,\text{Bq}$.
  • Internal dose ≈38 mrad y⁻¹; external ≈28 mrad y⁻¹.

Man-Made & Technologically Enhanced

• Tobacco $^{210}\text{Po}$ (5.3 MeV $\alpha$, $t_{1/2}=138\,\text{d}$): smokers receive ≈16 rem y⁻¹ lung equivalent; population-averaged ~280 mrem effective.

• Fallout (bomb tests 1945-80): present dose ≤1 mrem y⁻¹; main long-term nuclide $^{14}\text{C}$.

• Consumer products, building materials, domestic water etc. contribute small amounts (few mrem y⁻¹).

• NCRP summary: total natural background ≈300 mrem y⁻¹; enhanced + medical raises average to ~360-620 mrem y⁻¹ depending on smoking & imaging usage.

Occupational Averages (U.S.)

• Uranium miners 2.3 rem y⁻¹ (high $\alpha$ fraction).

• Nuclear power 0.55 rem; radiotherapy 0.26 rem; airline crew 0.17 rem; diagnostic radiology 0.10 rem etc.

Radiation Monitoring & Instrumentation

Survey Instruments (Area/Source)

• Geiger-Müller (GM) counters:
  • Ionize fill gas; avalanche at high V (Geiger plateau).
  • Pulse height independent of incident energy ⇒ good for count rate, poor for dosimetry.
  • Sensitive to $\alpha,\beta,\gamma$ if window thin & particle energy adequate.
  • Calibration with known $\gamma$ sources converts cps → mR h⁻¹ (caution: window absorption under-reads).

• Potential–pulse regions (ion-chamber → proportional → GM) illustrated (pulse height vs voltage curve).

• Civil Defense meters:
  • CD V-715: 0–500 R h⁻¹ ion-chamber (high range).
  • CD V-700: GM tube, low range (mR h⁻¹).

Personal Monitoring

1. Film badge
   • Two photographic films + energy-discriminating filters (Al, Cu, Pb, plastic).
   • Sensitivity: $\gamma$ 10–1800 mrem; $\beta$ 50–1000 mrem; insensitive to $\alpha$.
   • Neutron film variants exist.

2. Pocket/pen ion-chamber dosimeter
   • Quartz fiber electroscope; user reads displacement vs scale; immediate reading; must be re-charged.

3. Digital electronic dosimeters – solid-state detectors with LCD, alarm.

Whole-Body Counting

• NaI(Tl) scintillator systems – good efficiency, modest resolution.

• HPGe systems – superior resolution; robust calibration/analysis, deconvolution & long-term stability.

Spacecraft Radiation Monitors

• Silicon-based Total Dose (5 krad–1 Mrad) & Dose-Depth monitors; Single Event Upset (SEU) proton monitors (cross-section $5\times10^{-7}\,\text{cm}^2$); low mass (350–500 g), power 300–900 mW; interfaces RS-232/422; operate −40 → +55 °C.

Epidemiological Foundations of Risk Models

• Major cohorts:
  • A-bomb survivors (≈120 k); 483 excess cancers (mean dose 0.23 Sv).
  • Ankylosing spondylitis radiotherapy (14 k; 1–25 Gy to marrow).
  • Post-partum mastitis breast irradiation; radium dial painters; Thorotrast recipients.

• Findings underpin risk coefficients; limitations: dose reconstruction, confounders, high vs low dose extrapolation.

Key Equations Cheat-Sheet

• Photon energy: $E=h\nu=\frac{hc}{\lambda}$.

• Binding energy: $\text{BE}=\big(Z m<em>p + N m</em>n - m_{\text{nuc}}\big)c^2$.

• Decay: $N=N<em>0e^{-\lambda t};\;A=A</em>0e^{-\lambda t};\;t_{1/2}=\frac{\ln2}{\lambda}$.

• Exposure–activity: $ER=\frac{\Gamma A}{d^2}$.

• Absorbed dose: $D=\frac{E_{\text{abs}}}{m}$.

• Dose rate (source internal): $\dot D = \frac{A E_{\text{mean}}}{m}$.

• Dose equivalent: $H=D Q$.

• Effective dose: $H<em>e=\sum w</em>T H_T$.

Practical Implications & Ethical Considerations

• ALARA principle balances diagnostic/therapeutic benefit vs stochastic risk.

• Protection programmes: monitoring, shielding design, administrative controls.

• Ethical duty: informed consent, justification of exposures, tracking cumulative dose.

• Societal risk acceptance aligns radiation worker limits with “safe industry” fatal-accident statistics (~10⁻³ y⁻¹).

These notes consolidate and expand the transcript’s content, preserving every quantitative reference, example calculation, conceptual definition and contextual linkage to real-world radiological practice and protection standards. They can serve as a complete study guide independent of the original slides.