A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Radioactive Decay and Half-Life — mark scheme explained
The short answer
Radioactive decay is a fundamental process in nuclear physics, characterized by the random nature of the decay of atomic nuclei. This section delves into the mathematical models used to describe radioactive decay, including the decay equation, activity, and half-life.
The question
A sample of a radioactive isotope has an initial activity of 100 Bq. If the half-life of the isotope is 5 years, what will be the activity after 15 years?
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For calculation questions, marks are typically awarded for correct use of formulas, substitution of values, and final answers. For explanation questions, clarity and completeness of the answer are key. Graphical questions may award marks for accurate plotting and labeling.
What the command words demand
- Calculate
- Perform a numerical calculation to find a specific value.
- Determine
- Find the value of a quantity using given data and equations.
- Explain
- Provide a clear and detailed description or reasoning for a concept or process.
- Plot
- Draw a graph based on given data points or equations.
- Derive
- Show the steps to obtain a formula or equation from known principles.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 5-7 minutes per question to ensure you have enough time to carefully read the question, perform calculations, and check your work.
- Identify the given values: A 0 = 100 Bq, T 1/2 = 5 years, and t = 15 years.0 marks
- Calculate the decay constant using the half-life equation: λ = ln(2) / T 1/2 = ln(2) / 5 ≈ 0.1386 year -1 .2 marks
- Use the activity equation to find the activity after 15 years: A(t) = A 0 e -λt = 100 × e -0.1386 × 15 ≈ 12.5 Bq.2 marks
Final answer: 12.5 Bq
Work through every step correctly and you earn all 4 marks.
Another worked example
A sample of a radioactive isotope initially contains 10 6 nuclei. If the decay constant is 0.01 s -1 , how many nuclei will remain undecayed after 100 seconds?
- Identify the given values: N 0 = 10 6 nuclei, λ = 0.01 s -1 , and t = 100 seconds.0 marks
- Use the decay equation to find the number of undecayed nuclei: N(t) = N 0 e -λt = 10 6 × e -0.01 × 100 ≈ 367879 nuclei.3 marks
Final answer: 367879 nuclei
Work through every step correctly and you earn all 3 marks.
Common mistakes
Confusing the decay constant (λ) with the half-life (T 1/2 ).
Why it happens: Students often mix up these two concepts, leading to incorrect calculations.
Fix: Remember that the decay constant is a measure of the probability of decay per unit time, while the half-life is the time it takes for half of the initial nuclei to decay. Use the relationship T 1/2 = ln(2) / λ to convert between them.
Using the wrong base in logarithmic calculations.
Why it happens: Students sometimes use log base 10 instead of natural logarithm (ln).
Fix: Always use the natural logarithm (ln) when dealing with exponential decay equations. The relationship T 1/2 = ln(2) / λ uses the natural logarithm.
Forgetting to convert units in time calculations.
Why it happens: Students often forget to ensure that all time units are consistent, leading to incorrect results.
Fix: Always check that the time units (e.g., seconds, years) are consistent with the decay constant. Convert units if necessary before performing calculations.
Misinterpreting the activity equation as a linear relationship.
Why it happens: Students may incorrectly assume that activity decreases linearly over time, rather than exponentially.
Fix: Remember that activity decreases exponentially with time, following the equation A(t) = A 0 e -λt . This means that the rate of decay slows down over time.
Using the wrong initial value in decay equations.
Why it happens: Students sometimes use the final number of nuclei instead of the initial number when setting up decay equations.
Fix: Always use the initial number of undecayed nuclei ( N 0 ) or the initial activity ( A 0 ) in your calculations. The decay equation N(t) = N 0 e -λt and the activity equation A(t) = A 0 e -λt both require the initial value.
Incorrectly plotting logarithmic graphs.
Why it happens: Students may plot N(t) instead of ln(N(t)) , leading to a non-linear graph.
Fix: When using logarithmic graphs to linearize data, always plot ln(N(t)) against t . This will give you a straight line with a slope of -λ .
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Radioactive Decay Calculation | Calculate the remaining activity of an isotope after a given time using its half-life. | 4 |
| Radioactive Decay Calculation | Use the exponential decay law to find the number of undecayed nuclei after a given time. | 3 |
| Radioactive Decay Calculation | Use the half-life to find how many undecayed nuclei remain after a given time. | 4 |
| Radioactive Decay Calculation | Use the exponential decay law to find activity after a given time. | 3 |
| Radioactive Decay Calculation | Find the number of undecayed nuclei remaining after a given number of half-lives. | 4 |
| Calculate Radioactive Activity | Find the number of atoms from the mass, then multiply by the decay constant to get activity. | 4 |
| Total across these question types | 22 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.