Lecture 5c- Half Life

Radioactivity and Half-Life

• Definition of Half-Life: The time required for half of the atoms in a radioactive sample to decay.

• Variation in Half-Lives: Different isotopes have vastly different half-lives.

  • Example:

    • Polonium-216: Half-life of 0.002 seconds.

    • Uranium-238: Half-life of 4.5 billion years.

Isotopes

• Definition of Isotope: Variations of an element that have the same number of protons but different numbers of neutrons.

  • Example:

    • Carbon-14: 6 protons and 8 neutrons, radioactive.

    • Carbon-12: 6 protons and 6 neutrons, stable.

• Radioactive vs. Non-Radioactive: Some isotopes are radioactive, while others are not.

Stability of Isotopes

• Half-Life and Stability:

  • Short Half-Life: Indicates a less stable isotope.

    • Example: Bismuth-212 has a half-life of 60.5 seconds.

  • Long Half-Life: Indicates greater stability.

    • Example: Uranium-238, with a half-life of 4.5 billion years, remains abundant.

Consistency of Half-Lives

• Half-lives are constant and not affected by external conditions (e.g., temperature).

  • Unlike chemical reactions, nuclear decay rates do not change with environmental factors.

Determining Half-Lives

• Measurement Methodology:

  • Scientists utilize exponential decay equations to plot decay curves based on measured radiation emitted from samples.

  • Geiger Counter: Instrument used to measure the amount of radioactive decay in a sample.

Concept of Decay Over Time

• Decay Process:

  • After each half-life, half of the original sample remains undecayed.

  • Example with Cobalt-60: A half-life of 5.27 years means:

    • Starting with 10 grams after 5.27 years = 5 grams remaining.

    • After another 5.27 years (total 10.54 years) = 2.5 grams remaining.

    • This process continues, with each amount halving.

Example Calculations Using Half-Lives

1. Technetium-99 Example:

   • Initial amount: 200 grams; half-life: 6 hours.

   • After 12 hours (2 half-lives): 200 → 100 grams → 50 grams remaining.

2. Arsenic-81 Example:

   • Half-life: 2.7 seconds; total time: 13.5 seconds.

   • % remaining:

     • 100% → 50% → 25% → 12.5% → 6.25% → 3.125%. (5 half-lives total).

3. Finding Half-Life from Decay:

   • Starting with 500 grams, decaying to 62.5 grams in 24.3 hours.

   • Process:

     • 1st half-life: 500 → 250 grams.

     • 2nd: 250 → 125 grams.

     • 3rd: 125 → 62.5 grams.

   • Conclusion: 3 half-lives = 24.3 hours → 1 half-life = 8.1 hours.

Practical Application: Carbon Dating

• Carbon-14 Dating: Utilizes the constant cosmic radiation to measure ages of organisms.

  • Incorporation into living organisms through CO2 during photosynthesis.

  • Once an organism dies, the Carbon-14 decays without replenishment.

  • Useful for dating up to 50,000 years (10 half-lives of 5,730 years each).

Uranium Dating for Older Samples

• Uranium Isotopes: Used for dating objects far older than 50,000 years.

  • Uranium-238 to Lead-206 and Uranium-235 to Lead-207 through radioactive decay.

  • High ratios of lead isotopes indicate older samples, while lower ratios indicate younger samples.

• Comparison with Carbon Dating:

  • Suitable for young samples (e.g., 2,000 years: prefer Carbon dating).

  • Long half-lives enable uranium dating of ancient artifacts.