Overview
This lecture explains the concept of half-life in radioactive isotopes, how to determine it from data or graphs, and how to calculate the decrease in count rate over several half-lives.
Radioactive Decay & Randomness
- Radioactive isotopes decay by emitting radiation from their nuclei.
- The decay of individual nuclei is random; scientists cannot predict exactly when a specific nucleus will decay.
Definition and Concept of Half-Life
- The half-life of a radioactive isotope is the time taken for half its nuclei in a sample to decay.
- Isotopes with a long half-life decay slowly; those with a short half-life decay quickly.
- Half-life can also be defined as the time for the count rate (decays per second) to drop to half its initial value.
Determining Half-Life from Data or Graphs
- On a graph, the half-life is the time taken for the number of undecayed nuclei to fall to half their original amount.
- Example: If a sample starts with 1,000 nuclei and reaches 500 after 20 minutes, the half-life is 20 minutes.
Calculating Decrease in Count Rate
- After each half-life, the count rate of a radioactive sample halves.
- To find the count rate after several half-lives, keep halving for each period.
- Example: Starting with 200 counts/sec, after 3 half-lives (45 days if half-life = 15 days), rate reduces to 25 counts/sec (200 → 100 → 50 → 25).
Key Terms & Definitions
- Radioactive Decay — The process by which an unstable nucleus emits radiation.
- Isotope — Atoms of the same element with different numbers of neutrons.
- Half-Life — Time for half of the radioactive nuclei in a sample to decay, or for count rate to halve.
- Count Rate — Number of decays per second, often measured with a Geiger counter.
Action Items / Next Steps
- Practice questions on half-life, especially using graphs and multi-step count rate calculations.
- Review workbook problems linked in the lecture for additional practice.