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
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Step 1: Write down the given values. - T P = 6 hours - T B = 12 hours
- S2
Step 2: Use the equation for effective half-life. 1/T E = 1/T P + 1/T B
- S3
Step 3: Substitute the given values into the equation. 1/T E = 1/6 + 1/12
- S4
Step 4: Find a common denominator and add the fractions. 1/T E = (2 + 1) / 12 = 3/12 = 1/4
- S5
Step 5: Take the reciprocal to find T E . T E = 4 hours
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Step 1: Write down the given values. - T P = 6 hours - T B = 12 hours
- S2
Step 2: Use the equation for effective half-life. 1/T E = 1/T P + 1/T B
- S3
Step 3: Substitute the given values into the equation. 1/T E = 1/6 + 1/12
- S4
Step 4: Find a common denominator and add the fractions. 1/T E = (2 + 1) / 12 = 3/12 = 1/4
- S5
Step 5: Take the reciprocal to find T E . T E = 4 hours
Final answer: 4 hours
Common mistakes
- Confusing physical half-life with biological half-life. — 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. — 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 . — 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. — 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 . — 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. — Always find a common denominator before adding or subtracting fractions. This ensures that the calculations are accurate and consistent.
Where the marks go
- Full worked solution (all marking points)5 marks