Science
What is radioactivity, and what is half-life?
Quick answer
Radioactivity is when unstable atomic nuclei break down and give out radiation: alpha, beta or gamma. Half-life is the time it takes for half of the radioactive nuclei in a sample to decay.
In one sentence
Radioactivity is what happens when the nucleus of an unstable atom breaks down by itself and gives out radiation, turning into a more stable nucleus.
Explained
Every atom has a tiny nucleus made of protons and neutrons. Most nuclei are stable and stay the same forever. Some have the wrong mix of protons and neutrons, or too much energy, and are unstable. Sooner or later an unstable nucleus decays: it throws out a particle or a burst of energy and becomes a different, more stable nucleus. That emission is nuclear radiation, and the substance is radioactive.
banana
rock
hospital
Radioactive decay is random. Nobody can say when one particular nucleus will decay, just as you cannot say which coin will land heads. With billions of nuclei, though, the pattern is very predictable, and that is what half-life describes.
There are three main types of radiation:
- Alpha (α): 2 protons and 2 neutrons, the same as a helium nucleus. It is the most ionising (it knocks electrons off atoms easily) but the least penetrating: a few centimetres of air, a sheet of paper or the outer layer of skin stops it.
- Beta (β): a fast electron that comes from the nucleus when a neutron turns into a proton. It is less ionising and goes further; a few millimetres of aluminium stops it.
- Gamma (γ): not a particle but an electromagnetic wave with very high energy (see the electromagnetic spectrum). It is the least ionising and the most penetrating; thick lead or concrete reduces it.
Half-life is the time for half of the unstable nuclei in a sample to decay, or for the activity (the count rate) to fall to half. It is different for each isotope: about 6 hours for technetium-99m, about 8 days for iodine-131, about 5,730 years for carbon-14 and about 4.5 billion years for uranium-238. After one half-life ½ is left, after two ¼, after three ⅛. The amount never quite reaches zero; it keeps halving.
Activity is measured in becquerels (Bq): 1 Bq is one decay per second. A Geiger–Müller tube connected to a counter detects radiation and gives a count rate. The sievert (Sv) measures the effect of radiation on the body. You cannot see, hear, smell or feel radiation, which is why detectors matter.
We are all exposed to a little background radiation all the time: radon gas from rocks such as granite, cosmic rays from space, the rocks and building materials around us, and food. Bananas contain potassium, and a tiny fraction of natural potassium is radioactive potassium-40. The amount is very small, and bananas are perfectly safe to eat.
Examples
| Type | What it is | Stopped by | Ionising | Change to the nucleus |
|---|---|---|---|---|
| Alpha (α) | 2 protons + 2 neutrons | paper, skin, a few cm of air | strongly | mass number −4, atomic number −2 |
| Beta (β) | fast electron | a few mm of aluminium | moderately | mass number same, atomic number +1 |
| Gamma (γ) | electromagnetic wave | thick lead or concrete (reduces it) | weakly | no change in the numbers |
Worked examples of nuclear equations (top number = mass number, bottom = atomic number):
- Alpha decay: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Check: 238 = 234 + 4 and 92 = 90 + 2.
- Beta decay: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e. Check: 14 = 14 + 0 and 6 = 7 + (−1).
Uses: gamma rays sterilise medical equipment and are used in radiotherapy to kill cancer cells; short half-life tracers such as technetium-99m help doctors see organs; smoke alarms contain a tiny alpha source (americium-241); beta sources check the thickness of paper in factories; carbon-14 dates old wood and bone.
Common mistakes
- "After two half-lives it has all gone." After one half-life ½ is left, after two only ¼, not zero.
- Forgetting background radiation. Subtract the background count before halving, then add it back if the question asks for the reading on the counter.
- Mixing up ionising and penetrating. Alpha is the most ionising but the least penetrating; gamma is the opposite.
- Mixing up irradiation and contamination. Being irradiated (exposed to radiation from outside) does not make you radioactive. Contamination means radioactive material has got onto or into something.
Step by step
Step by step
- Find the half-lifeRead it from the question, or from a graph: find the time for the count rate to fall from any value to half of it.
- Count the half-livesNumber of half-lives = time passed ÷ half-life.
- Remove the backgroundIf you are given count rates, subtract the background count first.
- Halve that many timesAmount left = starting amount × (½)ⁿ, where n is the number of half-lives.
- Check and give unitsAdd the background back if needed and keep the units (Bq, counts per minute, grams).
Working backwards works the same way: if 1/8 of the carbon-14 is left, that is 3 half-lives (½ × ½ × ½), so the sample is 3 × 5,730 = 17,190 years old.
Practice questions
Radioactivity and half-life
Try each one, then check your answer.
- Which type of radiation is a helium nucleus?
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Alpha - Which type of radiation is an electromagnetic wave?
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Gamma - What fraction of a sample is left after 4 half-lives?
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½ × ½ × ½ × ½ = 1/16 - What fraction of a sample has decayed after 3 half-lives?
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1/8 is left, so 7/8 has decayed. - A source has an activity of 800 Bq and a half-life of 6 hours. What is its activity after 18 hours?
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18 ÷ 6 = 3 half-lives: 800 → 400 → 200 → 100 Bq - 64 g of an isotope has a half-life of 5 years. How much is left after 20 years?
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20 ÷ 5 = 4 half-lives: 64 → 32 → 16 → 8 → 4 g - A count rate falls from 2,000 to 250 counts per minute in 24 days. What is the half-life?
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2,000 → 1,000 → 500 → 250 is 3 half-lives, so 24 ÷ 3 = 8 days - Iodine-131 has a half-life of 8 days. How long until 40 MBq falls to 5 MBq?
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40 → 20 → 10 → 5 is 3 half-lives: 3 × 8 = 24 days - A source gives 3,000 decays in one minute. What is its activity in becquerels?
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3,000 ÷ 60 = 50 Bq - Complete the alpha decay: radium-226 (atomic number 88) → ? + ⁴₂He
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226 − 4 = 222 and 88 − 2 = 86: radon-222 (²²²₈₆Rn) - In beta decay, what happens to the mass number and the atomic number?
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Mass number stays the same; atomic number goes up by 1. - A counter reads 75 counts/min; the background is 15 counts/min. What will it read after 2 half-lives?
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Source alone: 75 − 15 = 60 → 30 → 15. Add the background: 15 + 15 = 30 counts/min - A bone has ¼ of the carbon-14 of living bone. Carbon-14's half-life is 5,730 years. How old is it?
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¼ = 2 half-lives: 2 × 5,730 = 11,460 years - Does being irradiated by an X-ray or gamma source make you radioactive?
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No. Only contamination with radioactive material does; irradiation stops when the source is removed.
Word problems
Radioactivity in real life
Try each one, then check your answer.
- A hospital injects a tracer of 400 MBq of technetium-99m (half-life 6 hours) at 9:00. What is its activity at 21:00?
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12 hours = 2 half-lives: 400 → 200 → 100 MBq - Why do doctors choose a gamma emitter with a short half-life as a tracer inside the body?
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Gamma passes out of the body to the detector and is weakly ionising; a short half-life means the activity falls quickly after the scan. - A paper factory uses a beta source to check thickness. Why not alpha or gamma?
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Alpha would be stopped completely by the paper; gamma would pass through whatever the thickness. Beta is partly absorbed, so the count changes with thickness. - A wooden tool has ⅛ of the carbon-14 of living wood. How old is it?
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⅛ = 3 half-lives: 3 × 5,730 = 17,190 years (about 17,000 years) - Radon-222 has a half-life of 3.8 days. What fraction of the radon in a sealed jar of air is left after 11.4 days?
Show answer
11.4 ÷ 3.8 = 3 half-lives: ⅛
Questions people ask
What is radioactivity in simple words?
Some atoms have an unstable centre (nucleus). Radioactivity is that nucleus breaking down by itself and shooting out a particle or a burst of energy, called radiation.
Who discovered radioactivity?
Henri Becquerel discovered it in 1896 with uranium salts. Marie and Pierre Curie went on to discover polonium and radium, and Marie Curie gave the effect its name. The three shared the 1903 Nobel Prize in Physics.
What is radioactivity measured in?
Activity is measured in becquerels (Bq), one decay per second; this is the SI unit. The effect of radiation on the body is measured in sieverts (Sv), usually millisieverts (mSv).
Are bananas radioactive?
Very slightly, like many foods, because they contain potassium and a tiny fraction of natural potassium is radioactive potassium-40. The amount is very small, and bananas are safe to eat.
Is radioactivity dangerous?
It can be. Ionising radiation can damage cells and DNA, and the risk depends on the type of radiation, the dose and the time of exposure. Background radiation is low, and people who work with radiation follow safety rules: limit the time, keep your distance and use shielding.
What is the difference between natural and artificial radioactivity?
Natural radioactivity comes from substances in nature, such as uranium in rocks, radon gas and potassium-40. Artificial radioactivity comes from isotopes made by people in reactors or particle accelerators, first produced by Irène and Frédéric Joliot-Curie in 1934.
How do you detect radioactivity?
With a detector such as a Geiger–Müller tube and counter, which clicks or shows a count rate. Photographic film also darkens when radiation hits it, which is how Becquerel noticed it.
Quick quiz
Radioactivity
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