Half-life is the time taken for half the nuclei of an isotope in any sample to decay.
Here is what that means and how 0625 tests it.
Start here
Half-life in one sentence
Short answer
Half-life is the time taken for half the nuclei of a particular isotope in any sample to decay.
That is the definition for IGCSE Physics 0625, in the nuclear physics section of the
syllabus. Both Core and Extended candidates need it.
Keep the word nuclei in your answer. Half-life is about unstable
nuclei changing, not about a sample shrinking or its radiation running out.
The idea
What half-life really means
Radioactive decay is spontaneous and random. You cannot predict when one particular
nucleus will decay.
A real sample holds an enormous number of nuclei, so the randomness averages out. In
any fixed stretch of time, the same fraction of the remaining nuclei decays. The
stretch of time in which half of them decay is the half-life.
Each isotope has its own half-life. It does not depend on how big the sample is,
which is why the definition says any sample. Half-lives range from tiny
fractions of a second to billions of years or more.
Halving, and halving again
After one half-life, half the nuclei remain. After two, a quarter remain. After
three, an eighth. Halving never reaches zero, so a sample never runs out after a set
number of half-lives.
You cannot count nuclei in the lab. Instead, a detector connected to a counter
measures the count rate, in counts/s or counts/minute. Fewer
undecayed nuclei means fewer decays each second, so the count rate halves over each
half-life too.
Plot count rate against time and you get a decay curve. It falls
steeply at first, then levels out. Pick any point on it, find half that value, and
the time between them is one half-life. With measured data, subtract background
first (Extended).
See it in action
Half-life with numbers
Take a sample of 4 000 undecayed nuclei of an isotope with a half-life of 8 days.
Each row below is one more half-life.
Half-lives
Time
Fraction left
Nuclei left
0
0 days
1
4 000
1
8 days
1/2
2 000
2
16 days
1/4
1 000
3
24 days
1/8
500
4
32 days
1/16
250
Illustrative numbers. In practice, decay is random, so a real sample only follows
this pattern on average.
Worked example · nuclei decayed[3 marks]
A sample contains 4 000 undecayed nuclei of an isotope. The half-life of the
isotope is 8 days. Calculate how many of the nuclei have decayed after 24 days.
N at start = 4 000half-life = 8 dayst = 24 daysFind: number decayed
Mark 1
Number of half-lives = 24 ÷ 8 = 3
Half-lives counted
Mark 2
Nuclei left: 4 000 → 2 000 → 1 000 → 500
Repeated halving
Mark 3
Decayed = 4 000 − 500 = 3 500
Answer to the question asked
3 500 nuclei have decayed
The mark split is our own illustration of how a mark scheme typically rewards
each stage, not taken from a real paper.
The last line is where marks go. The question asks how many have
decayed, not how many are left. Stopping at 500 answers a
different question.
Common confusions
What half-life is not
Four common mix-ups cost marks on half-life questions.
Means
Half the nuclei decay
In one half-life, half of the nuclei present at the start of that half-life decay.
Not the same as
Half the lifetime of the sample
Doubling the half-life does not give the time for the whole sample to decay. After two half-lives a quarter of the nuclei are still there.
Means
An average over many nuclei
Half-life describes what happens on average across many nuclei.
Not the same as
When one nucleus will decay
A single nucleus could decay in the next second or in a thousand years. Decay is random.
Means
The nuclei change
After alpha or beta decay, each nucleus becomes the nucleus of a different element.
Not the same as
Half the mass vanishing
The atoms do not disappear. The sample still has almost the same mass, but less of it is the original isotope.
Means
Fixed for an isotope
Every sample of the same isotope has the same half-life, large or small.
Not the same as
Shorter for a smaller sample
A smaller sample gives a lower count rate. It halves in the same time.
Exam technique
How half-life is examined
Expect three kinds of question. You may be asked to state the definition, or to find
a half-life from a table or decay curve. You may also need to use a half-life to
predict a count rate or a number of nuclei.
In Core questions you do not need to correct for background. On the Extended papers
(Papers 2 and 4), the readings may include background. Subtract it from every
reading first, then look for the halving.
Model answer · Extended[4 marks]
A detector placed near a radioactive source records these count rates. The
background count rate is 100 counts/minute. Determine the half-life of the source.
Answer with a unit; 200 → 100 and 100 → 50 also take 3 h each, which confirms it
Half-life = 3 hours
The mark split is our own illustration of how a mark scheme typically rewards
each stage, not taken from a real paper.
Skip the subtraction and the method breaks. Half of 500 is 250, and the measured
rate only reaches 250 somewhere between 3 h and 6 h. That gives a half-life over 4
hours, which is wrong.
Try it yourselfExtended · 3 marks
The measured count rate from a source is 340 counts/minute. Twelve minutes later it
is 100 counts/minute. The background count rate is 20 counts/minute. Calculate the
half-life of the source.
