Study Notes: Half-Life, Radioactivity Applications, and Chain Reactions

1. Exam Logistics & Strategy

  • Format: 3535 paper questions, hand-graded, 75 min75\,\text{min}.

  • Materials: One double-sided 8.5×11 inch8.5 \times 11\,\text{inch} reference sheet allowed.

  • Scoring:

    • True/False (2 pts2\,\text{pts}): Correct = 2 pts2\,\text{pts}; Circle "WTF" = 1 pt1\,\text{pt} guaranteed.

    • Multiple Choice (4 pts4\,\text{pts}): 11 answer = 4 pts4\,\text{pts}; 22 answers (one correct) = 2 pts2\,\text{pts}; 33 answers (one correct) = 1 pt1\,\text{pt}.

  • Scope: Conceptual principles only; no calculators or numerical calculations.

2. Half-Life & Decay Chains

  • Exponential Decay: Rate depends on remaining mass (mass is conserved).

  • Key Half-Lives: Iodine-131 (8 days8\,\text{days}), Carbon-14 (6,000 years6,000\,\text{years}), Potassium-40 (1.3 billion years1.3\,\text{billion years}), Uranium-238 (4.5 billion years4.5\,\text{billion years}).

  • Decay Chains:

    • Multi-step (High Hazard): Uranium-238 emits alpha particle →\rightarrow Thorium-234 →⋯→\rightarrow \dots \rightarrow stable Lead-206.

    • Single-step (Low Hazard): Carbon-14 undergoes single beta decay to Nitrogen.

3. Practical Applications

  • RTGs: Convert decay heat to electricity via temperature gradients (7 %7\,\% efficiency; powers Voyager 1 and Mars rovers).

  • Smoke Detectors: Americium-241 ionizes air; smoke or steam interrupts current to trigger alarm.

  • Radiometric Dating:

    • Carbon-14: Useful up to 1010 half-lives (∼60,000 years\sim 60,000\,\text{years}); cannot date dinosaurs.

    • Long-term: Potassium-40 (1.3 billion year1.3\,\text{billion year} half-life) dates ancient rocks and fossils.

  • Geiger Counters: Ionize internal gas to count particles audibly.

4. Chain Reactions & Exponential Growth

  • Fission & Doubling: Neutrons split nuclei (1→2→4→8…1 \rightarrow 2 \rightarrow 4 \rightarrow 8 \dots).

  • Biological Doubling: Zygote cell division (101110^{11} cells in 37 days37\,\text{days}); apoptosis clears defective cells.

  • Population: Reached ∼8 billion\sim 8\,\text{billion} around 2025; constrained by environmental and economic factors.

  • Other Examples: Computer/biological viruses, lightning cascades, dominoes, self-sustaining fires, misinformation.

5. Frequently Asked Clarifications

  • Infinite Halving Paradox: Physically limited by discrete atoms; stops when the final atom decays.

  • Memorization: Focus on conceptual scale (e.g., low vs. high Earth orbit), not specific numbers.