CIE A Level Physics (9702) exams from 2022

Revision Notes

23.2.3 Half-Life

Half-Life Definition

  • Half life is defined as:

The time taken for the initial number of nuclei to reduce by half

  • This means when a time equal to the half-life has passed, the activity of the sample will also half
  • This is because activity is proportional to the number of undecayed nuclei, A ∝ N

Calculating Half-Life

  • To find an expression for half-life, start with the equation for exponential decay:

N = N0e–λt

  • Where:
    • N = number of nuclei remaining in a sample
    • N0 = the initial number of undecayed nuclei (when t = 0)
    • λ = decay constant (s-1)
    • t = time interval (s)
  • When time t is equal to the half-life t½, the activity N of the sample will be half of its original value, so N = ½ N0

Calculating Half-Life equation 1

  • The formula can then be derived as follows:

Calculating Half-Life equation 2

Calculating Half-Life equation 3

Calculating Half-Life equation 3a

  • Therefore, half-life t½ can be calculated using the equation:

Calculating Half-Life equation 4

  • This equation shows that half-life t½ and the radioactive decay rate constant λ are inversely proportional
  • Therefore, the shorter the half-life, the larger the decay constant and the faster the decay

Worked example: Calculating half-life

Calculating_Half-Life_Worked_Example_-_Calculating_Half-Life_Question, downloadable AS & A Level Physics revision notes

Step 1:            Convert the half-life into seconds

28 years = 28 × 365 × 24 × 60 × 60 = 8.83 × 108 s

Step 2:            Write the equation for half-life

Step 3:            Rearrange for λ and calculate

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