A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Physical, Biological, and Effective Half-Lives — mark scheme explained
The short answer
In the field of medical physics, particularly in nuclear medicine, understanding the half-lives of radioactive substances is crucial. The three types of half-lives—physical (T P ), biological (T B ), and effective (T E )—are essential for predicting the behavior of radiopharmaceuticals in the body.
The question
A radiopharmaceutical has a physical half-life of 6 hours and a biological half-life of 12 hours. Calculate its effective half-life.
[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 substitution of values into the equation, showing working, and providing the final answer with units. For definition and explanation questions, marks are given for accuracy, completeness, and relevance to medical applications.
What the command words demand
- Define
- Provide a clear and concise definition of the term.
- Calculate
- Perform the necessary mathematical operations to find the required value.
- Explain
- Provide a detailed explanation, including practical implications and examples where appropriate.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 5-7 minutes for each question on this topic, depending on the complexity of the calculations and explanations required.
- Write down the given values. - T P = 6 hours - T B = 12 hours0 marks
- Use the equation for effective half-life. 1/T E = 1/T P + 1/T B1 mark
- Substitute the given values into the equation. 1/T E = 1/6 + 1/121 mark
- Find a common denominator and add the fractions. 1/T E = (2 + 1) / 12 = 3/12 = 1/41 mark
- Take the reciprocal to find T E . T E = 4 hours2 marks
Final answer: 4 hours
Work through every step correctly and you earn all 5 marks.
Another worked example
A radioactive isotope has a physical half-life of 8 hours. If the effective half-life in the body is 5 hours, calculate the biological half-life.
- Write down the given values. - T P = 8 hours - T E = 5 hours0 marks
- Use the equation for effective half-life and rearrange to solve for T B . 1/T E = 1/T P + 1/T B 1/T B = 1/T E - 1/T P2 marks
- Substitute the given values into the equation. 1/T B = 1/5 - 1/81 mark
- Find a common denominator and subtract the fractions. 1/T B = (8 - 5) / 40 = 3/401 mark
- Take the reciprocal to find T B . T B ≈ 13.3 hours2 marks
Final answer: ≈ 13.3 hours
Work through every step correctly and you earn all 6 marks.
Common mistakes
Confusing physical half-life with biological half-life.
Why it happens: Students may mix up the definitions of these two types of half-lives, leading to incorrect calculations and interpretations.
Fix: Memorize the precise definitions: Physical half-life is due to nuclear disintegration, while biological half-life is due to excretion or metabolism.
Using inconsistent units in calculations.
Why it happens: Students may use different time units (e.g., hours and minutes) without converting them, leading to incorrect results.
Fix: Always ensure that all time units are consistent before performing any calculations. Convert all units to the same base unit (e.g., hours or minutes).
Forgetting to take the reciprocal when solving for T E .
Why it happens: Students may correctly set up the equation but forget to take the reciprocal at the final step, leading to an incorrect value for T E .
Fix: After finding 1/T E , always remember to take the reciprocal to get T E . Double-check your work to ensure this step is not missed.
Misinterpreting the significance of effective half-life in medical applications.
Why it happens: Students may understand the calculation but fail to explain its practical implications, leading to incomplete answers.
Fix: Practice explaining the significance of effective half-life in terms of treatment optimization, patient safety, and diagnostic accuracy. Use specific examples to illustrate your points.
Incorrectly rearranging the equation to solve for T B or T P .
Why it happens: Students may make algebraic errors when rearranging the equation, leading to incorrect values for T B or T P .
Fix: Practice rearranging the equation step-by-step. Double-check your work to ensure that each step is correct and logical.
Failing to check for common denominators when adding or subtracting fractions.
Why it happens: Students may add or subtract fractions without finding a common denominator, leading to incorrect results.
Fix: Always find a common denominator before adding or subtracting fractions. This ensures that the calculations are accurate and consistent.
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 |
|---|---|---|
| Calculate Effective Half-Life | Combine physical and biological half-lives to find the effective half-life with units. | 5 |
| Calculate Biological Half-Life | Rearrange the effective half-life equation and solve for the biological half-life with units. | 6 |
| Calculate Half-Life | Rearrange the effective half-life equation to find the physical half-life from biological and effective values. | 6 |
| Effective Half-Life Calculation | Combine physical and biological half-lives to find effective half-life and explain its medical significance. | 8 |
| Total across these question types | 25 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.