Modelling Radioactive Decay (OCR A Level Physics)

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Katie M


Katie M



Modelling Radioactive Decay

Iterative Modelling

  • We can use:
    • a spreadsheet to model the exponential decay of nuclei
    • the activity equation to calculate the remaining number of undecayed nuclei

Activity & The Decay Constant equation 1

  • Where:
    • A = activity of the sample (Bq)
    • ΔN = number of decayed nuclei
    • Δt = time interval (s)
    • λ = decay constant (s-1)
    • N = number of nuclei remaining in a sample


  1. Start with a given number of undecayed nuclei, N in the sample
    • N= 1000 is a logical number to start with

       2. Choose a very small interval of time, Δt 

    • This should be significantly shorter than the half-life of the isotope chosen

       3. Calculate the number of nuclei decaying, ΔN during the time period

    • fraction numerator increment N over denominator increment t end fraction space equals space minus lambda N 
    • So, ΔN = (λΔt) x N

     4. Calculate the number of undecayed nuclei, N now left at the end of the time period, Δt 

    • N- ΔN N

     5. Repeat this process by iterating your value for as your new N for many values of Δt 


Step 1: N= 1000

Step 2: Δt  = 0.10 s

Step 3: ΔN = (λΔt) x N

    • λ = decay constant = 0.693 s-1 
    • So, ΔN = (0.693 x 0.1) x N
    • ΔN = 0.0693N

Step 4: N- ΔN N

    • 1000 - 0.0693N
    • So, 1000 = N + 0.0693N
    • 1000 = 1.0693N
    • Therefore, fraction numerator 1000 over denominator 1.0693 end fraction = 935.2 

Step 5: N= 935.2

    • In the second iteration, N= previous N
    • Δt  = 0.10 s as before
    • So, fraction numerator N subscript 0 over denominator 1.0693 end fraction for all iterations

Table of Results

  • It is important to details your iteration as a table of results



Exam Tip

It is really important to keep your final answer in your calculator and use that as the next value of N0  for the iteration. If you clear your calculator and round your answer, this will significantly change your value of N . 

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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.

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