Medical Radioisotopes: Technetium-99m's Short Half-Life
1 · Predict
Technetium-99m (used in medical imaging) has a half-life of only about 6 hours — far shorter than carbon-14's 5,730 years. Does its radioactive ACTIVITY (decays per second) also decrease over time, or does activity stay constant while only the total count of atoms drops?
- Activity decreases too, following the same exponential decay as the atom count, since activity is proportional to how many radioactive atoms remain.
- Activity stays constant even as the atom count drops.
- Activity actually increases as fewer atoms remain, since each remaining atom is more likely to decay.
2 · Set Up
- Open the tc99m-medical preset and press Reset. The half-life is fixed at 6 hours; the sample starts with 10¹⁰ atoms.
- Enable the activity readout.
- Set the elapsed time for each trial and record the sample's activity.
3 · Collect Data
| Elapsed time t (h) | Activity A (MBq) |
|---|---|
| 3 | |
| 6 | |
| 12 |
Plot activity A (y-axis) against elapsed time t (x-axis) for your three trials. Does it follow the same exponential shape as N(t)?
4 · Analyze
- For one trial, compute N(t) = N₀·(1/2)^(t/T½) using T½ = 6 hours, N₀ = 10¹⁰, then A = λN using λ = ln(2)/T½. Compare to the table.
- Explain why activity A = λN follows the exact same exponential decay curve as N(t) itself — activity is just the atom count scaled by the fixed decay constant λ.
5 · Extend
- Tc-99m's short half-life is exactly why it's used in medical imaging: it delivers a strong, useful radioactive signal quickly, then decays away to a safe level within about a day, minimizing a patient's long-term radiation exposure. Explain why carbon-14 (with its 5,730-year half-life) would be a terrible choice for this application.
- Because Tc-99m decays so quickly, hospitals can't stockpile it — it's typically 'milked' on-site from a longer-lived parent isotope (molybdenum-99) shortly before use. Explain, using the decay law, why shipping pre-made Tc-99m from a distant factory would waste most of the dose in transit.
The Physics Behind This Experiment
Radioactive Activity
A sample's activity — its rate of decay events per second — is A = λN, where λ = ln(2)/T½ is the decay constant and N is the number of undecayed nuclei remaining. Activity falls exponentially in lockstep with N.