# Modelling Radioactive Decay(OCR A Level Physics)

## Revision Note

Author

Katie M

Expertise

Physics

#### 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, N in the sample

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

• N- ΔN N

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

#### Example

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, = 935.2

Step 5: N= 935.2

• In the second iteration, N= previous N
• Δt  = 0.10 s as before
• So,  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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