A half-life calculation answers one question: how does the activity of this isotope fall with time in an idealised model? It does not tell anyone whether a person is at risk. Keeping those two things apart is good exam technique, and it is also honest science.
This lesson closes half-life and background. Its ideas build on successive halving and on the randomness explained in why one atom has no predictable decay time.
What does the model include, and what does it leave out?
The model takes a stated isotope, a stated half-life and a starting activity. It gives the activity after a chosen time. It assumes the half-life is correct and the sample is not being added to or removed.
It leaves out the things that decide risk for a person: the type and energy of the radiation, the distance, the shielding, the time spent nearby, and whether material is inside the body. It also leaves out how the body removes some substances.
How do I answer in a balanced way, step by step?
- Do the calculation and state the result with units.
- Say what it shows: the activity at that time, in the model.
- Say what it does not show: dose, health effects, or whether anyone is safe.
- Name what else is needed (radiation type, dose, time, distance, shielding) and who can judge it.
Worked example
(Invented data, for learning only.) A hospital uses a tracer with half-life 6 hours and starting activity 480 MBq (megabecquerels, millions of decays per second). What is the activity after 24 hours?
Number of half-lives: 24 ÷ 6 = 4.
Halve four times: 480 → 240 → 120 → 60 → 30. The activity after 24 h is 30 MBq, which is 1/16 of the start (480 ÷ 16 = 30).
What the model says: activity falls to one-sixteenth in a day.
What it does not say: whether a particular patient, nurse or visitor receives a harmful dose. That depends on the radiation, the dose absorbed and other factors. A trained radiation protection professional makes that judgement, not a half-life calculation.
The mistake to watch for
Mistaken answer: “After 24 hours it is only 30 MBq, so it is completely safe.”
The student turned a number into a safety statement.
There are two errors. The calculation gives an activity, not a dose, and 30 MBq is not zero.
The correction is a careful sentence: “The activity falls to 30 MBq, one-sixteenth of the start. Whether this is acceptable depends on the dose, which needs more information.”
Another slip is to say the source is gone after a number of half-lives. In the model the amount keeps falling, but it does not reach exactly zero.
Check yourself
1. Using the same tracer (480 MBq, half-life 6 h), what is the activity after 12 hours?
Show answer
12 ÷ 6 = 2 half-lives. 480 → 240 → 120. The activity is 120 MBq.
2. Decide whether each statement is a model calculation or personal risk advice: (a) “The activity is 120 MBq after 12 h.” (b) “You can stand next to the patient for an hour without harm.”
Show answer
(a) is a model calculation. (b) is personal risk advice. It needs dose, distance and shielding information, and a qualified person should judge it.
3. Why is a half-life alone not enough to judge harm?
Show answer
Harm depends on the type of radiation, the dose absorbed, the time and distance involved, shielding and whether the source is inside the body. Half-life describes only how activity decreases with time.
Where this leads next
Try the whole set together in the half-life and background practice set. From here the course moves into space physics, where again you must separate what a model shows from what it cannot.
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