MYP Physics · topic MYP-19.04
Nuclear medicine and patient benefit
Connect the ideas, make your working visible, and test the result. Use the hints when you need a starting point; open the full solution after your attempt.
Extra challenging questions
Work through the linked stages and explain what each result means.
Choosing a tracer with physical and biological clearance
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. A diagnostic tracer has physical half-life 6 h and biological half-life 12 h in the relevant organ. Assume the two removal processes are independent exponentials and initial organ activity is 80 MBq. The supplied graph gives the expected organ activity for the combined removal. Use 1/Teffective = 1/Tphysical + 1/Tbiological. Supplied data (Time / h; Activity / MBq): (0, 80), (4, 40), (8, 20), (12, 10). (a) Find effective half-life and expected organ activity after 12 h. Explain why biological removal does not change a nucleus's physical decay law. [3 marks] (b) Evaluate replacing this tracer by one with the same biological behaviour but physical half-life 30 years. Name the evidence needed for a patient-benefit decision. [3 marks]
Expected organ activity
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Activity / MBq
Horizontal axis (x): Time / h
Read the exact data as a table
| Time / h | Activity / MBq |
|---|---|
| 0 | 80 |
| 4 | 40 |
| 8 | 20 |
| 12 | 10 |
These are the supplied values, not a worked answer. Lines join the supplied values; they are not a fitted model.
Show a hint
Begin with part (a): Find effective half-life and expected organ activity after 12 h. Explain why biological removal does not change a nucleus's physical decay law.
Reveal the worked solution
- 1/Teff = 1/6+1/12 = 1/4 h⁻¹, so Teff = 4 h.
- Twelve hours is three effective half-lives, giving 80/2³ = 10 MBq remaining in the organ.
- Biological clearance moves radionuclides out of the measured organ or body; it does not alter their intrinsic decay constant. Cleared material can still be radioactive elsewhere.
- A useful diagnostic tracer should remain measurable for preparation and imaging, then have limited unnecessary retention and exposure; 'shortest possible' is not automatically best if it decays before use.
- The emitted radiation must escape sufficiently for detection, while energy, branching ratio, chemistry and organ uptake determine image quality and dose.
- Compare expected diagnostic benefit, administered activity, absorbed and effective dose estimates, alternatives, logistics and patient-specific circumstances. Activity in MBq alone is not a complete measure of risk or image quality.
Answer (a) Effective half-life = 4 h; organ activity after 12 h = 10 MBq. (b) A very long physical half-life may leave unnecessary prolonged activity; suitability also depends on emissions, uptake and diagnostic performance.
Compare the assumptions, method and units with your attempt. Explain any correction before trying another question.