Half-Life (OCR A Level Physics)

Revision Note

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Katie M


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  • 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

Half-Life Graph, downloadable AS & A Level Physics revision notes

When a time equal to the half-life passes, the activity falls by half, when two half-lives pass, the activity falls by another half (which is a quarter of the initial value)

Determining the Half-Life of an Isotope

  • 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

Strontium-90 is a radioactive isotope with a half-life of 28.0 years. A sample of Strontium-90 has an activity of 6.4 × 109 Bq.Calculate the decay constant λ, in s–1, of Strontium-90.

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

Exam Tip

Make sure you are confident with the meanings of all the definitions and symbols in this unit. It is easy to get confused when completing an examination question. 

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Katie M

Author: Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.