Radiation & Nuclear Chemistry – Comprehensive Exam Notes

Geiger Counter

• Definition & Function
  • A Geiger counter is a portable instrument that detects ionizing radiation.
  • Detects specifically:
  • Beta ($\beta$) radiation
  • Gamma ($\gamma$) radiation
  • Working Principle
  • Incoming radiation ionizes the gas inside the Geiger tube.
  • The ion pairs generated complete an electrical circuit, creating a measurable current (clicks/beeps proportional to intensity).

Units for Measuring Radiation

• Three independent but related categories are used.

Activity (Rate of Nuclear Disintegration)

• Curie (Ci)
  • Historical unit based on radium-$226$.
  • $1\ \text{Ci}=3.7\times10^{10}\ \text{disintegrations·s}^{-1}$ (i.e., the activity of $1$ g of $\,^{226}_{88}\text{Ra}$).
• Becquerel (Bq) – SI unit
  • $1\ \text{Bq}=1\ \text{disintegration·s}^{-1}$.
  • Relationship: $1\ \text{Ci}=3.7\times10^{10}\ \text{Bq}$.

Absorbed Dose (Energy Deposited per Mass)

• rad (radiation absorbed dose)
  • Measures energy absorbed by $1$ g of any material.
• gray (Gy) – SI unit
  • $1\ \text{Gy}=1\ \text{J·kg}^{-1}$ (energy / mass).
  • $1\ \text{Gy}=100\ \text{rad}$.

Biological Damage (Dose × Quality Factor)

• rem (radiation equivalent in man/humans)
  • Incorporates type of radiation via a Quality Factor (QF).
  • $1\ \text{rem}=1000\ \text{millirem (mrem)}$.
• sievert (Sv) – SI unit
  • $1\ \text{Sv}=100\ \text{rem}$.

Quality (Weighting) Factors

• $\beta$ or $\gamma$ QF $=1$.
• High-energy protons & neutrons QF $\approx10$.
• $\alpha$ particles QF $=20$.
• Equivalent Dose (in rem or Sv) $=\text{absorbed dose (rad or Gy)}\times\text{QF}$.

Measuring & Monitoring Radiation Exposure

• Dosimeters

  • Film badges, TLD, electronic badges worn in labs/hospitals.
  • Detect cumulative exposure to X-rays, $\gamma$-rays, $\beta$-particles.

• Typical Reporting Unit

  • $\text{mrem}$ (millirem) or $\text{mSv}$ (milli-sievert).

Typical Background & Man-Made Exposure (U.S.)

• Average annual dose ≈ $3.6\ \text{mSv}$.
• Natural Sources
  • Ground/soil $0.2\ \text{mSv}$.
  • Food & water $0.3\ \text{mSv}$ (e.g., $\,^{40}\text{K}$ in bananas).
  • Cosmic rays $0.4\ \text{mSv}$ (higher at altitude).
  • Building materials (wood, concrete, brick) $0.5\ \text{mSv}$.
  • Radon (inhaled) ≈ $2\ \text{mSv}$ (highly variable).
• Medical Imaging
  • Chest X-ray $0.2\ \text{mSv}$; dental X-ray $0.2\ \text{mSv}$.
  • Mammogram $0.4\ \text{mSv}$; hip X-ray $0.6\ \text{mSv}$;
    lumbar spine $0.7\ \text{mSv}$; upper GI series $2\ \text{mSv}$.
• Other
  • Nuclear power $0.001\ \text{mSv}$.
  • Television $0.2\ \text{mSv}$.
  • Air travel $0.1\ \text{mSv}$ per year (domestic flyer).

Acute Radiation Effects & Lethality

• Detection threshold: < $0.25\ \text{Sv}$ typically undetectable biologically.
• Whole-body $1\ \text{Sv}$ → transient leukopenia (↓white cells).
• >$1\ \text{Sv}$ → Radiation sickness (nausea, vomiting, fatigue).
• $5\ \text{Sv}$ whole-body dose ⇒ ~$50\%$ mortality (LD$50$).

LD50 Values (Single Acute Dose)

• Insect $1000\ \text{Sv}$.
• Bacteria $500\ \text{Sv}$.
• Rat $8\ \text{Sv}$.
• Human $5\ \text{Sv}$.
• Dog $3\ \text{Sv}$.

Food Irradiation & Public Health

• FDA approved dose $0.3$ – $1\ \text{kGy}$ (kilogray) using $\,^{60}\text{Co}$ or $\,^{137}\text{Cs}$.
• Mechanism: penetrating $\gamma$-rays kill pathogens (Salmonella, Listeria, E. coli).
• Retail symbol (radura) mandatory.
• Produce currently treated: tomatoes, blueberries, strawberries, mushrooms, etc.
  • Example: irradiated strawberries remain mold-free after $2$ weeks while controls spoil.

Concept Review Exercise – Units

• Activity → $\text{Bq}$ (or $\text{Ci}$).
• Absorbed dose → $\text{rad}$/$\text{Gy}$ (milli-rad given: $\text{mrad}$).
• Biological damage → $\text{rem}$ or $\text{Sv}$.

Half-Life ($t_{1/2}$) & Radioactive Decay

• Definition: time for activity to drop to $\tfrac{1}{2}$ original.
• Decay follows exponential law $N=N_0\left(\tfrac12\right)^{n}$ where $n$ = elapsed half-lives.

Example 1 – $\,^{90}<em>{38}\text{Sr}$ ($t</em>{1/2}=38.1\ \text{yr}$)

• Initial $36\ \text{mg}$.
• $114.3\ \text{yr}=3$ half-lives.
• Remaining $=36\times(\tfrac12)^3=36\times\tfrac18=4.5\ \text{mg}$.

Example 2 – $\,^{123}<em>{53}\text{I}$ ($t</em>{1/2}=13.2\ \text{h}$)

• Initial $64\ \text{mg}$.
• $26.4\ \text{h}=2$ half-lives.
• Remaining $=64\times(\tfrac12)^2=16\ \text{mg}$.

Decay Curve

• I-$131$ ($t_{1/2}=8\ \text{d}$): every $8$ days activity halves (illustrated graphically).

Representative Half-Lives

• Natural: $\,^{14}\text{C}$ $5730\ \text{yr}$; $\,^{238}\text{U}$ $4.5\times10^{9}\ \text{yr}$.
• Medical: $\,^{99m}\text{Tc}$ $6\ \text{h}$; $\,^{18}\text{F}$ $110\ \text{min}$; $\,^{131}\text{I}$ $8\ \text{d}$.

Carbon-14 Dating

• Formation: $\,^{14}<em>{7}\text{N}(n,p)\,^{14}</em>{6}\text{C}$ in upper atmosphere.
• Plants fix $\text{CO}_2$ with same $\,^{14}\text{C}/\,^{12}\text{C}$ ratio as atmosphere until death.
• After death, radioactive decay decreases $\,^{14}\text{C}$; age derived via $t_{1/2}=5730\ \text{yr}$.

Radioisotopes in Medicine

• Selection Criteria
  • Short $t_{1/2}$ (hours→days) to minimize patient dose.
  • Emission type matched to diagnostic or therapeutic need (γ for imaging, β for therapy, positron for PET).

Table Summary of Common Medical Isotopes

• $\,^{99m}\text{Tc}$: $6\ \text{h}$, $\gamma$, versatile organ imaging (skeleton, heart, brain, etc.).
• $\,^{18}\text{F}$: $110\ \text{min}$, positron, PET (metabolic imaging).
• $\,^{131}\text{I}$: $8\ \text{d}$, $\beta$, thyroid ablation (Graves’, goiter).
• $\,^{198}\text{Au}$: $2.7\ \text{d}$, $\beta$, liver tumors.
• $\,^{90}\text{Y}$: $2.7\ \text{d}$, $\beta$, liver cancer therapy.

Learning Check Answer

• Likely medical: K-$42$ (QF short $t_{1/2}$ $=12\ \text{h}$) & I-$131$ ($8\ \text{d}$).

Diagnostic Imaging Modalities

• Gamma Camera Scans
  • Patient swallows/injects radio-tracer; gamma detector builds 2-D organ map (e.g., thyroid with $\,^{131}\text{I}$).
• PET
  • Uses positron emitters ($\,^{11}\text{C},\,^{13}\text{N},\,^{15}\text{O},\,^{18}\text{F}$).
  • Positron + electron → $2$ $\gamma$ $511\ \text{keV}$ photons detected in coincidence → 3-D metabolic image (brain function, cancer staging).
• CT
  • $\approx30{,}000$ narrow X-ray beams; computer reconstructs slices; shows density differences (e.g., brain tumor).
• MRI
  • No ionizing radiation; aligns $^1\text{H}$ nuclei in strong B-field; RF pulse perturbs; relaxation mapped to image (heart, soft tissue).

Nuclear Fission

• Process: Heavy nucleus $+$ slow neutron → unstable compound nucleus → splits into medium-mass nuclei $+$ $\sim3$ fast neutrons $+$ energy.
  • Example: $^{235}<em>{92}\text{U}+\,^{1}</em>{0}\text{n}\rightarrow^{91}<em>{36}\text{Kr}+^{142}</em>{56}\text{Ba}+3\,^{1}_{0}\text{n}+\text{energy}$.
• Energy Source: Missing mass converted via $E=mc^{2}$.
• Chain Reaction
  • Each fission yields $\sim3$ neutrons; if at least one induces another fission → self-sustaining.
  • Critical Mass required; controlled in reactors with neutron-absorbing control rods (Cd, B, Ag).

Nuclear Fusion

• Combines light nuclei (e.g., $^2\text{H}+^3\text{H}\rightarrow ^4\text{He}+n+\text{energy}$).
• Requires $\sim10^{8}\ ^\circ\text{C}$; powers Sun & stars.
• Advantages: higher energy per mass, minimal long-lived waste.

Nuclear Power Plants

• Employ controlled fission of $\,^{235}\text{U}$ or $\,^{239}\text{Pu}$.
• Components
  • Reactor core with fuel rods (< critical mass).
  • Control rods absorb excess neutrons.
  • Coolant (water or molten sodium) removes heat → steam → turbine → electricity.
• Provide ≈ $20\%$ of U.S. electricity.

Fission vs Fusion – Comparison Exercise

• A nucleus splits → fission.
• Large energy released → both.
• Small nuclei combine → fusion.
• Hydrogen nuclei involved → fusion.
• Neutron multiplication → fission.

Sample Fission Equation Completion

• Given: $^{137}\text{In}+^{235}\text{U}\rightarrow^{152}\text{Te}+^{97}\text{Zr}+2n+\text{energy}$.
  • Balances both mass ($137+235=372$ vs $152+97+2*1=252$??) [complete as per solution slide: $^{27}_{40}\text{Zr}$ etc.].

Concept Map Highlights (Narrative)

• Nuclear chemistry encompasses radioisotope decay (α, β, γ, positron), measurement (Ci/Bq, rad/Gy, rem/Sv), applications (medicine, power), and processes (fission, fusion).
• Half-life links to environmental dating & medical dosing.
• Radiation’s biological impact quantified via quality factors (QF) → protection guidelines.

Ethical, Environmental, & Practical Considerations

• Occupational monitoring (dosimeters) safeguards workers.
• Food irradiation improves safety yet requires public transparency (radura labeling).
• Nuclear power offers carbon-free electricity but demands safe waste disposal & critical mass control.
• Medical imaging balances diagnostic benefit vs radiation dose (ALARA – As Low As Reasonably Achievable principle).

Key Equations & Constants (Quick Reference)

• Activity: $A=\lambda N$ (where $\lambda=\frac{0.693}{t_{1/2}}$).
• Decay law: $N=N<em>0e^{-\lambda t}=N</em>0\left(\tfrac12\right)^{t/t_{1/2}}$.
• Equivalent Dose: $H=D\times QF$ (Gy→Sv or rad→rem).
• Energy–Mass: $E=mc^{2}$ $\left(c\approx3.00\times10^{8}\ \text{m·s}^{-1}\right)$.

Study Tips

• Memorize conversion factors (rem↔Sv, rad↔Gy, Ci↔Bq).
• Practice half-life problems: always compute number of half-lives first.
• Associate common medical isotopes with applications & half-lives.
• Differentiate fission vs fusion via reactant size & neutron role.