GCSE · Physics · AQA · Spec 8463
Different half-lives of radioactive isotopes (physics only)
Same number of radioactive nuclei. One sample's half-life is minutes, the other's thousands of years. Which is more dangerous? The honest answer is 'it depends', and here's why.
Same nuclei, different half-life: watch the danger change shape
Every curve starts with exactly the same number of unstable nuclei. Only the half-life changes. The small dot sits one half-life along the time axis, so the activity there is always half the starting value. Drag it left to shorten the half-life: the same nuclei now decay in less time, so far more decay every second. At 1 day the curve is a tall spike that has almost died away within a week. Drag it right: the start drops lower, but the curve stays up for far longer. (An illustrative sample: the numbers show the pattern, not a real isotope.)
Time scale
Half-lives of different radioactive isotopes are spread right across this axis, from well under a second to billions of years. It's a logarithmic scale: each tick is 10 000 times longer than the one before. Tap a dot to see what a half-life that long would mean.
A second
1 s
With a half-life of one second, one minute is already 60 half-lives: the activity has halved 60 times, to less than a billion-billionth of where it started.
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Why a short half-life and a long half-life are dangerous in completely different ways.
What you need to know
- Half-lives of radioactive isotopes range from well under a second to billions of years.
- Short half-life (same number of nuclei): high activity at first, but it falls away quickly.
- Long half-life: lower activity, but it lasts a very long time.
- So the hazard depends on the half-life: intense and brief, or weaker and long-lasting.
The big picture
Radioactive isotopes have an enormous range of half-lives, from well under a second to billions of years. For the same number of unstable nuclei, a short half-life means the decays are crammed into a short time: a high activity that dies away quickly. A long half-life spreads the decays out: a lower activity that lasts a very long time. That's why the hazard from radioactive material depends on the half-life involved.
Key points
Worked example
Problem
Two sealed samples, A and B, start with the same number of unstable nuclei. A has a half-life of 6 hours. B has a half-life of 30 years. Which sample is the bigger hazard during the first day, and which is the bigger hazard over the next ten years?
⚠ Watch out
Saying 'the longer the half-life, the more dangerous' (or 'the shorter, the safer'). For the same number of nuclei, a longer half-life means a lower activity that lasts longer. A shorter one means a higher activity that dies away sooner. Always say both parts: how intense and how long.
Memory hook
Short half-life: sharp and short. Long half-life: low and long. Same box of matches, either struck all at once in one blinding flash, or one at a time all night.
Check yourself
Sample M has a 20-minute half-life; sample N, 500 years. Both start with the same number of unstable nuclei. Which starts with the higher activity, and which is still a hazard a year later? Why?
Flashcards
(6)How wide is the range of half-lives of radioactive isotopes?
Same number of nuclei: what happens to the starting activity if the half-life is doubled?
What is the hazard from a short half-life material like?
What is the hazard from a long half-life material like?
Is a longer half-life simply 'more dangerous'?
Why are half-lives shown on a logarithmic scale?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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