Lecture Notes: Phosphorus-32 and Half-Life

Key Concepts

• Phosphorus-32:

  • A radioactive isotope.
  • Undergoes beta decay to transform into sulfur.

• Half-Life:

  • Definition: Time it takes for half of the radioactive nuclei to decay.
  • Example with Phosphorus-32: Starting with 4 mg, after 14.3 days, 2 mg remains.
  • Symbol: Represents the half-life duration.

Half-Life Examples

• Phosphorus-32:

  • Half-life is 14.3 days.
  • Starting with 4 mg, after 14.3 days, only 2 mg remains.

• Uranium-238:

  • Much longer half-life than Phosphorus-32, approximately 4.47 x 10^9 years.

Graphing Decay

• Graph Elements:

  • Y-axis: Amount of phosphorus-32 in milligrams.
  • X-axis: Time in days.

• Graph Data Points:

  • Start with 4 mg at time zero.
  • After 14.3 days, 2 mg remains.
  • After 28.6 days (two half-lives), 1 mg remains.
  • After 42.9 days (three half-lives), 0.5 mg remains.
  • Demonstrates exponential decay.

Problem Solving Example

• Example Problem: How much phosphorus-32 is left after 57.2 days?
  • Calculate number of half-lives: 57.2 days / 14.3 days = 4 half-lives.
  • Starting with 4 mg:
    • After first half-life: 2 mg.
    • After second half-life: 1 mg.
    • After third half-life: 0.5 mg.
    • After fourth half-life: 0.25 mg.
• Mathematical Calculation:
  • Alternative method: Multiply by 1/2 for each half-life.
  • Formula: 4 mg x (1/2)^4 = 0.25 mg.

Conclusion

• Different methods (calculation or graphing) yield the same result.
• Reinforces understanding of exponential decay and half-life calculations.

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We'll further explore graphing techniques in the next video.