Activity and Half-life

May 23, 2024

Activity and Half-life

Key Concepts

  • Unstable Isotopes: Some materials contain unstable isotopes which decay to become more stable by emitting radiation (alpha particles, beta particles, or gamma rays).
  • Radioactive Materials: Materials containing these unstable isotopes are called radioactive.

Activity

  • Definition: The overall rate of decay of all isotopes in a sample.
  • Measurement: Activity is measured in becquerels (Bq), where one becquerel equals one decay per second.
  • Example: If a sample has an activity of 600 Bq, then 600 isotopes are decaying each second.

Half-life

  • Definition: Time taken for the number of radioactive nuclei in a sample, or the activity, to halve.
  • Two Perspectives:
    1. Time for the number of radioactive nuclei to halve (e.g., from 1 million to 500,000).
    2. Time for the activity to halve (e.g., from 600 decays per second to 300 decays per second).

Decay Process

  • Random Nature: The decay process is completely random, unpredictable for individual isotopes.
  • Decrease in Rate: As more isotopes decay, the number of unstable particles left decreases, leading to a decrease in overall rate of decay (activity).
  • Correlation: The decrease in the number of radioactive nuclei is directly correlated to the decrease in activity.

Graphing Decay

  • Decay Curve: A graph plotting activity (in becquerels) against time shows a declining activity over time. The decline rate also decreases, resulting in a curved line.
  • Determining Half-life: Identify the time it takes for the activity to halve. For instance, if activity drops from 600 to 300 in 2 hours, the half-life is 2 hours. Confirm by checking another halving (e.g., from 300 to 150 in another 2 hours).
  • Different Samples: Different samples can have different half-lives, illustrated by varying steepness in the decay curves.

Measuring Activity

  • Geiger-Muller Tube: A device used to measure activity by recording all decays (alpha, beta, gamma) reaching it per second, producing a count rate which estimates the activity.

Example Problem

  • Problem: Half-life of a radioactive source is 40 hours. Initially, there are 3 million radioactive nuclei in the sample. How many nuclei remain after five days?

    1. Calculate total time: 5 days × 24 hours = 120 hours.
    2. Determine number of half-lives: 120 hours ÷ 40 hours/half-life = 3 half-lives.
    3. Apply halving process:
      • Initial: 3 million nuclei
      • After 1st half-life: 1.5 million nuclei
      • After 2nd half-life: 750,000 nuclei
      • After 3rd half-life: 375,000 nuclei
    4. Final Answer: 375,000 nuclei remain.