(455) Exponential decay [IB Physics SL/HL]

Exponential Decay

• Exponential decay is a process in which particles, mass, or activity decreases at a rate proportional to its current value.

• This process can be visualized as a curve, indicating how quantities reduce over time.

• Activity is defined as the number of decays per second, measured in Bequerels (Bq).

Understanding Half-Life

• Half-life (T1/2) is the time required for a quantity to reduce to half its initial amount.

• After each half-life, the remaining amount can be calculated by halving the previous amount:

  • 1st half-life: 100% to 50%

  • 2nd half-life: 50% to 25%

  • 3rd half-life: 25% to 12.5%

Example of Exponential Decay in a Lab

• Using 100 dice as a model for decay:

  • Roll the dice and remove any that show a certain outcome (e.g., sixes).

  • Record the number of remaining dice after each roll, creating a graph that illustrates exponential decay.

Parent and Daughter Nuclei

• In radioactive decay:

  • Parent nuclei are the original particles that decay.

  • Daughter nuclei are the new particles created from the decay.

  • As parent nuclei decrease, daughter nuclei increase until they reach asymptotic behavior.

Application Example with Isotopes

• Given an isotope with a half-life of 20 minutes and an initial amount of 1,024 grams:

  • 1st half-life: 1,024 g → 512 g

  • 2nd half-life: 512 g → 256 g

  • 3rd half-life: 256 g → 128 g

  • Total time for three half-lives: 3 * 20 minutes = 60 minutes.

Differences in Physics Curriculum

• Physics Standard Level (SL) focuses on whole number multiples of half-lives.

• Physics Higher Level (HL) involves more complex calculations, using decay constant (lambda) for non-integer half-lives.