6.9.7 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

• 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

Procedure

1. Start with a given number of undecayed nuclei, N₀  in the sample

• • N₀  = 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

• •  
  • So, ΔN = (λΔt) x N

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

• • N₀ - ΔN = N

     5. Repeat this process by iterating your value for N as your new N₀  for many values of Δt 

Example

Step 1: N₀ = 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: N₀ - ΔN = N

• • 1000 - 0.0693N = N
  • So, 1000 = N + 0.0693N
  • 1000 = 1.0693N
  • Therefore, N =  = 935.2 

Step 5: N₀ = 935.2

• • In the second iteration, N₀ = previous N
  • Δt  = 0.10 s as before
  • So, N =  for all iterations

Table of Results

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