Energy and particles · GCSE Physics
Half-life
Teacher-written GCSE Physics revision on half-life: the time for net count rate or unstable nuclei to halve, background subtraction, decay graphs, and a full numerical example with units.
Half-life is the time for the number of unstable nuclei, or the net count rate, to fall to half. Subtract background first. After n half-lives, (½)ⁿ remains.
The important bits
What you need to know
- 1
Radioactive decay is random for a single nucleus. Half-life describes a large sample: it is constant for a given isotope and does not depend on the starting amount.
- 2
Half-life T½ is the time for the number of unstable nuclei to halve, or for the activity (becquerels, Bq) to halve, or for the net count rate to halve.
- 3
Measured count rate includes background radiation (rocks, radon, cosmic rays, medical sources). Net count rate = measured − background. Always subtract first.
- 4
After 1 half-life, 1/2 remains; after 2, 1/4; after 3, 1/8; after 4, 1/16. Remaining fraction = (1/2)^n where n is the number of half-lives.
- 5
On a graph of net count rate against time, read the time from a value down to half of that value. Repeat for a second pair and average if the data wobble.
- 6
A medical tracer needs a half-life long enough to take the measurement but short enough that the patient is not radioactive for weeks.
- 7
Carbon-14 dating uses T½ ≈ 5700 years — useless for a two-week tracer, ideal for archaeology. Nuclear waste with a long half-life must be stored for a long time.
- 8
Activity is decays per second in Bq. Count rate on a school detector is not the same as activity, but both fall with the same half-life once background is removed.
Quotations worth analysing
Short evidence. Real method.
“Half-life is the time taken for the number of nuclei of the isotope in a sample to halve.”
It is also the time for activity or net count rate to halve. Do not say “the time for the source to stop being radioactive”.
“Subtract the background count before you find the half-life.”
Background does not decay with the sample. Leaving it in makes the curve refuse to fall to half, and your T½ will be too long.
“Decay of an individual nucleus is random.”
You cannot predict which nucleus decays next. Half-life is a property of the huge sample, like a reliable average of a random process.
Go deeper
Half-life is a graph skill with a numerical engine
Subtract background count first if it is given. Plot net count rate against time, or use a table. Find the time from a value to half of that value; repeat for a second pair and average if the data wobble. After one half-life, half remains; after two, a quarter; after three, an eighth. A medical tracer needs a half-life long enough to take the measurement but short enough that the patient is not radioactive for weeks. Carbon-14 dating uses a half-life of about 5700 years. Never say a nucleus “uses up half its radiation”. The decay is random; half-life describes the sample. If a question gives activity in Bq, treat it like net count rate: the same halving rule applies.
Go deeper
Choosing an isotope is a half-life question in disguise
Smoke-alarm americium has a long half-life so the activity stays almost constant for years; you do not want the alarm to fade as the source decays. A hospital tracer needs hours, not millennia, so the activity falls after the scan. Dating needs a half-life comparable to the age you are measuring: carbon-14 for thousands of years, uranium isotopes for rocks. In six-mark comparisons, name the job, name a suitable half-life, and say why a much shorter or much longer value would fail. That evaluation is more than reciting the definition. Units: time on the axis must match the data — minutes, hours or years — and activity in Bq, not a vague “amount of radiation”.
See the idea in action
A sample has a measured count rate of 880 counts per minute, including a background of 80 counts per minute. Net count rate = 880 − 80 = 800 counts/min. After 3.0 hours the measured count is 480 counts/min, so net = 480 − 80 = 400 counts/min. After 6.0 hours the measured count is 280 counts/min, so net = 200 counts/min. The net count has halved from 800 to 400 in 3.0 h, and from 400 to 200 in another 3.0 h, so T½ = 3.0 hours. After 9.0 hours (three half-lives) the net count would be 100 counts/min, so the measured count including background would be 100 + 80 = 180 counts/min. After three half-lives, (1/2)³ = 1/8 of the original net activity remains.
Exam technique
Turn knowledge into marks
Always subtract background before finding half-life. Show the halving steps with times. Remaining fraction = (1/2)^n. Pick isotopes for jobs by matching half-life to the time scale of the use.
Common mistakes
Do not give these marks away
- 01
Forgetting to subtract background count, or treating half-life as half the time the source exists.
- 02
Halving the measured count including background, which refuses to fall towards zero correctly.
- 03
Saying a nucleus “uses up half its radiation”, or claiming half-life depends on the size of the sample.
A source has a net count rate of 640 Bq. The half-life is 2.0 hours. What is the net count rate after 6.0 hours?
A320 Bq
B160 Bq
C80 Bq
D107 Bq
Show the answer
80 Bq. 6.0 hours is three half-lives. 640 → 320 → 160 → 80 Bq. Remaining fraction = (1/2)³ = 1/8, and 640 / 8 = 80 Bq.
Quick questions
If this is the bit you searched
What is half-life?
The time taken for the number of unstable nuclei in a sample, or the net count rate or activity, to fall by half. It is constant for a given isotope.
Why subtract background radiation?
Detectors always pick up radiation from the surroundings. That extra count does not come from the sample and would distort the half-life if you left it in.
How much of a sample is left after four half-lives?
One sixteenth: (1/2)⁴ = 1/16. Activity and net count rate fall by the same fraction.
Does half-life change if I take a smaller sample?
No. A smaller sample has a smaller activity, but it still halves in the same time. Half-life is a property of the isotope, not of the lump size.