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 (LD50).

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}{38}\text{Sr} (t{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}{53}\text{I} (t{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}{7}\text{N}(n,p)\,^{14}{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}{92}\text{U}+\,^{1}{0}\text{n}\rightarrow^{91}{36}\text{Kr}+^{142}{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=N0e^{-\lambda t}=N0\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.