Lecture Notes: Understanding Half-Life in Radioactive Isotopes

Key Learning Objectives

• Describe what is meant by the half-life of a radioactive isotope.
• Determine the half-life of a radioactive isotope.
• Calculate the decrease in radioactive count rate after a given number of half-lives (higher-tier students).

Introduction to Radioactive Decay

• Radioactive isotopes release radiation from their atomic nuclei.
• Decay is a random process—scientists cannot predict when a nucleus will decay.

Half-Life Concept

• Definition:
  • The half-life of a radioactive isotope is the time required for half of the nuclei in a sample to decay.
  • Alternatively, the half-life is also the time it takes for the count rate (or activity) from a sample to fall to half its initial level.
• Observation:
  • Some isotopes have longer half-lives, indicating slower decay rates.
  • Others have shorter half-lives, indicating faster decay rates.

Measuring Half-Life

• Can be determined using a graph that shows the decay of nuclei over time.
• Example:
  • Start with 1,000 nuclei.
  • Determine when the nuclei count falls to 500 (half of 1,000).
  • If it takes 20 minutes, the half-life is 20 minutes.
  • After another 20 minutes, the count falls to 250.

Calculating Decrease in Count Rate

• Example Problem:
  • A radioactive isotope has a half-life of 15 days and an initial count rate of 200 counts per second.
  • Determine the count rate after 45 days.
• Solution Steps:
  • 45 days is equivalent to 3 half-lives (15 days per half-life).
  • After each half-life, the count rate halves:
    • After 15 days: 200 halves to 100 counts/s.
    • After another 15 days: 100 halves to 50 counts/s.
    • After another 15 days: 50 halves to 25 counts/s.

Additional Resources

• Practice questions available in the revision workbook.
• Link to workbook provided in the video.