What is half-life?

The time for a radioactive sample to decay completely The time it takes for half of the radioactive nuclei in a sample to decay Half the time it takes for a radioactive substance to become safe The time for the radiation from a sample to halve in energy

A radioactive sample starts with 800 atoms. After 3 half-lives, how many undecayed atoms remain?

400 atoms 200 atoms 100 atoms 50 atoms

An isotope has a half-life of 10 years. A sample currently has an activity of 2,000 decays per second. What will the activity be in 30 years?

1,000 decays per second 500 decays per second 250 decays per second 0 decays per second — it has completely decayed

Does the half-life of a radioactive isotope change if you heat it, cool it, or chemically combine it with other elements?

Yes — heating makes nuclei decay faster because they have more energy Yes — chemical bonding changes the electron shells, which affects nuclear stability No — half-life is a property of the nucleus and is completely unaffected by external physical or chemical conditions Only extreme temperatures (near absolute zero) can change the half-life

How does radiocarbon (carbon-14) dating work?

Scientists compare the weight of the sample to a modern sample — heavier samples are older Living organisms maintain a constant C-14/C-12 ratio by absorbing atmospheric carbon; at death, C-14 decays (t₁/₂ = 5,730 yr) — the ratio's change gives the age Carbon-14 emits light of a specific colour that fades with age — matching to a colour chart gives the date Scientists count the number of C-14 atoms and compare to the atomic number of carbon

Why can carbon-14 dating only date organic material up to about 50,000 years old?

Carbon-14 only forms in living things up to 50,000 years old — older organisms didn't have it After ~8–9 half-lives (about 50,000 years), so little C-14 remains that the signal becomes too small to measure accurately above background noise At 50,000 years, C-14 transforms into a different isotope that cannot be detected The law of conservation of energy prevents dating beyond 50,000 years

Why do nuclear medicine imaging agents need short half-lives?

Short half-lives mean the tracer emits more energy, making images clearer Short half-lives mean the radioactive dose to the patient decays quickly — the tracer delivers enough radiation for imaging but clears the body before causing significant harm Short half-lives are cheaper to produce in particle accelerators Isotopes with short half-lives are always more chemically stable

Nuclear power stations produce radioactive waste with very long half-lives. Why is this a challenge?

Long half-lives make the waste more chemically reactive and explosive Long half-lives mean the waste stays dangerously radioactive for thousands to millions of years, requiring secure storage far beyond any human institution's lifetime Long half-lives mean the waste emits less radiation, so it is actually safer The waste can simply be diluted in the ocean — the long half-life means it spreads harmlessly

Uranium-238 has a half-life of 4.5 billion years. Earth is about 4.5 billion years old. What fraction of Earth's original uranium-238 remains today?

None — it has all decayed after 4.5 billion years All of it — uranium-238 does not decay appreciably on Earth's timescale Approximately half — one half-life has elapsed since Earth formed One quarter — two half-lives have elapsed

The activity of a radioactive sample (decays per second) is measured in becquerels (Bq). Why does activity decrease over time even though half-life is constant?

The constant half-life means the activity should stay the same over time Activity decreases because the remaining atoms become 'tired' and decay more slowly Activity depends on the number of undecayed atoms present — as atoms decay, fewer remain to decay, so the rate (activity) falls proportionally The energy of each decay decreases over time, reducing the measured activity