MCAT® ExamChemical and Physical Foundations of Biological SystemsMedium
A patient is undergoing a medical scan that utilizes a radioactive isotope with a half-life of 6 hours. If the initial activity of the isotope is 800 MBq, what will be the approximate activity after 18 hours?
- A100 MBq
- B400 MBq
- C200 MBq
- D50 MBq
Show answer & explanationAnswer & explanation
Correct answer: A. 100 MBq
The half-life is 6 hours. The total time elapsed is 18 hours. Number of half-lives = Total time / Half-life = 18 hours / 6 hours = 3 half-lives. After 1 half-life: 800 MBq / 2 = 400 MBq. After 2 half-lives: 400 MBq / 2 = 200 MBq. After 3 half-lives: 200 MBq / 2 = 100 MBq.
Why the other options are wrong
- B. This would be the activity after 1 half-life.
- C. This would be the activity after 2 half-lives.
- D. This would be the activity after 4 half-lives.
Radioactive Half-Life
The time it takes for half of the radioactive nuclei in a sample to decay, or for the activity of a radioactive sample to decrease by half.
- Half-life is a constant for a given isotope and is independent of initial concentration, temperature, or pressure.
- After 'n' half-lives, the remaining amount (or activity) is (1/2)ⁿ of the initial amount.
- Radioactive decay follows first-order kinetics.
- It's used in medicine for diagnostics (e.g., PET scans) and therapy.
Memory trick: Divide by two, count the halves, and you're through!