GCSE · Physics · Edexcel · Spec 1PH0

Half-life definition

Nobody can say when one unstable nucleus will decay. Yet for a big sample, you can say how long it takes for half of them to go. That's the half-life.

Put your finger anywhere on the curve

time (minutes): 20. activity (Bq): 400

Drag the point to any time and note the activity. Now slide right until the activity is half that number. How many minutes did it take? Try again from a different start.

One nucleus vs a whole crowd of them

One unstable nucleusvsA large sample of the same isotope

Think of coins. Toss one and nobody can say whether it lands heads. Toss ten thousand and you can bet on roughly half being heads. Radioactive nuclei are like that: random one at a time, predictable in a crowd.

Focus

When will it decay?

One unstable nucleus

Nobody can say. It might decay in the next second, or not for a very long time. Its decay is random.

A large sample of the same isotope

You still can't say which nucleus goes next, but you can say how long it takes for half of them to decay.

The insight

Random for one, predictable for many. That's how a random process can still have a definite half-life.

Chance of decaying

One unstable nucleus

It has a certain chance of decaying in any given time.

A large sample of the same isotope

In a pure sample, every nucleus has that same chance.

When it decays

One unstable nucleus

It gives out ionising radiation and becomes a new, more stable daughter nucleus.

A large sample of the same isotope

Each decay leaves one fewer unstable nucleus, so the unstable nuclei gradually get used up.

Activity (decays per second)

One unstable nucleus

Doesn't really apply: it decays once, and that's it.

A large sample of the same isotope

Proportional to the number of undecayed nuclei. Halve the undecayed nuclei and you halve the activity.

Does 'half-life' mean anything?

One unstable nucleus

No. You can't have half of one decay.

A large sample of the same isotope

Yes: the time for half of the unstable nuclei to decay.

How much is left after three half-lives?

A source starts at 100% of its activity. What percentage of that original activity is left after three half-lives?

Your estimate

50%

A source starts at 100% of its activity. What percentage of that original activity is left after three half-lives? Estimate between 0% and 100%.

0%100%

So what does half-life actually mean?

Your friend says: "This isotope has a half-life of 3 hours, so after 6 hours it'll all have decayed."

Which idea is closest to what you think half-life means?

Half of the time it takes for all the nuclei to decay.The time it takes for each nucleus to decay.The time for half the unstable nuclei in a sample to decay.A time that gets shorter as the sample runs out of nuclei.

How sure are you?

I'm sureI think soI'm guessing

Half of the time it takes for all the nuclei to decay.

This is a common misconception

Easy to see why it's tempting: 'half' seems to go with 'the whole time'. But after one half-life only half the nuclei have gone, and after two half-lives a quarter of them are still there. There's no predictable time for every last nucleus to decay, so there's no 'total time' to take half of. Your friend's 6 hours leaves a quarter, not nothing.

The time it takes for each nucleus to decay.

This is a common misconception

No single nucleus has a decay time you can predict. Each one decays at random: one might go in the next second, its neighbour much later. Half-life only describes a large sample, never one nucleus.

The time for half the unstable nuclei in a sample to decay.

This matches the evidence

Yes. And because activity is proportional to the number of undecayed nuclei, that's also the time for the activity to fall to half. Same time, two ways of saying it.

A time that gets shorter as the sample runs out of nuclei.

This is a common misconception

Fewer nuclei does mean fewer decays per second, so the activity drops. But the time for whatever is left to halve stays the same. That's what you saw on the graph: from every starting point, the halving took 10 minutes.

Half-life is about halving what's left, not about finishing. There is no half-life at which the sample is 'all gone'.

Predict, then check

Two sources start with the same activity. Only their half-lives differ.

Isotope A has a half-life of 2 minutes. Isotope B has a half-life of 2 days. Which one will have given out most of its radiation within the first hour?

Now say it in your own words

Define half-life in two different ways. Then explain why a radioactive source becomes less radioactive over time. [4 marks]

Your answer

0 words · your answer stays on this page and is not sent anywhere.

The mark scheme

Half-life is the time taken for half of the unstable nuclei in a sample to decay. (1 mark)
It is also the time taken for the activity of the sample to fall to half of its starting value. (1 mark)
Unstable nuclei decay into more stable daughter nuclei, so the number of unstable nuclei left goes down. (1 mark)
So there are fewer decays per second: the activity (in Bq) falls. (1 mark)

Model answer

Half-life is the time it takes for half of the unstable nuclei in a sample to decay. It is also the time it takes for the activity of the sample to fall to half its starting value. A source gets less radioactive because each decay turns an unstable nucleus into a more stable daughter nucleus. As the unstable nuclei are used up, fewer of them decay each second, so the activity falls.

Both definitions, every time: 'half the unstable nuclei decay' and 'the activity falls to half'. They describe the same moment.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

What you need to know

Unstable nuclei decay over time, giving out ionising radiation and forming new, more stable daughter nuclei.
Activity is the number of nuclei that decay each second, measured in becquerels (1 Bq = 1 decay per second).
Half-life is the time for half the unstable nuclei in a sample to decay, or for its activity to fall to half. Both give the same time.
To read half-life from a graph: pick any starting value, find where it has halved, and measure the time between.

The big picture

Radioactive isotopes have unstable nuclei that decay at random, giving out ionising radiation and forming more stable daughter nuclei. As the unstable nuclei are used up, the activity (decays per second, in Bq) falls. The half-life is the time for half the unstable nuclei to decay, which is also the time for the activity to fall to half. It's the same from any starting point, so each half-life halves what's left: ½, then ¼, then ⅛.

Key points

1Fewer unstable nuclei left means fewer decays per second, so a source becomes less radioactive over time.

2Every nucleus in a pure sample has the same chance of decaying, so activity is proportional to the number of undecayed nuclei.

3One nucleus is random and unpredictable; a large sample follows a predictable pattern with a definite half-life.

4Half-life is constant for an isotope: start the clock anywhere and the value has halved one half-life later.

5After 2 half-lives ¼ is left, after 3 half-lives ⅛. Half-life is not half the time for everything to decay.

6An isotope with a short half-life decays quickly, giving out most of its radiation over a short time.

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Worked example

Problem

A sample's activity–time graph passes through three points: 600 Bq at 4 hours, 300 Bq at 10 hours and 150 Bq at 16 hours. What is the half-life? What activity would you expect at 22 hours?

⚠ Watch out

Saying half-life is half the time it takes for the whole sample to decay. After two half-lives a quarter is still left, so 'two half-lives = all gone' is wrong: each half-life halves what's left.

🧠

Memory hook

Half-life halves what's LEFT: ½ → ¼ → ⅛ → … a staircase of halves. Keep halving and you never land on zero.

✓

Check yourself

A source's activity falls from 800 Bq to 400 Bq in 2 days. How long until it reaches 200 Bq? What fraction of 800 Bq is left after 6 days, and why isn't it zero?

Flashcards

(13)

What happens when an unstable nucleus decays?

It gives out ionising radiation and becomes a new, more stable daughter nucleus.

What is the activity of a radioactive sample?

The number of nuclei that decay each second.

What unit is activity measured in?

The becquerel (Bq). 1 Bq = one decay per second.

Why does a source become less radioactive over time?

Its unstable nuclei get used up, so fewer decay each second and the activity falls.

Give the two equivalent definitions of half-life.

The time for half the unstable nuclei in a sample to decay. The time for the activity of the sample to fall to half its starting value.

Why do the two definitions of half-life give the same time?

Activity is proportional to the number of undecayed nuclei, so halving the nuclei halves the activity.

Does the half-life depend on when you start timing?

No. It's constant for an isotope: from any starting point, the value has halved one half-life later.

What fraction is left after two half-lives? After three?

¼ after two (½ × ½); ⅛ after three (½ × ½ × ½).

Can you predict when one particular nucleus will decay?

No. The decay of a single nucleus is random.

If decay is random, why does a sample have a definite half-life?

Every nucleus has the same chance of decaying, so a large number of them follows a predictable pattern.

Is half-life half the time it takes for everything to decay?

No. After two half-lives a quarter is still left, and the time for every nucleus to decay can't be predicted.

How do you read a half-life from an activity–time graph?

Pick a starting value, find where it has fallen to half, and measure the time between the two points.

What does a short half-life tell you about an isotope?

It decays quickly, giving out most of its radiation over a short time.

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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Put your finger anywhere on the curve

How much is left after three half-lives?

So what does half-life actually mean?

Now say it in your own words

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