Reading a half-life off a decay curve
Take the value at time 0 and halve it. Go across from that value to the curve and straight down to the time axis: that is one half-life. Halve again and the next step down takes the same time, which is a good check. For a count rate, take the background away first, halve the rest, and add the background back before you go across. Answers read from a graph are marked right within half a small square and close within one; worked answers are right to two or more significant figures.
Pick your course first. GCSE sets use count rates and background, chemistry sets use mass and logs, earth science uses the New York reference table half-lives and parent and daughter atoms, APES sets use fallout, radon and waste with units at every step, the CBSE Class 12 set follows NCERT Chemistry's first-order kinetics (t½ = 0.693 ÷ k and k = (2.303 ÷ t) log([R]₀ ÷ [R])), and the A-level and AP Physics set adds the decay constant, N = N₀e−λt and A = λN. For the order of rock layers before you date them, try Relative Dating Practice, listed in the footer.
Example: a zircon crystal
In set ZR2U22 (earth science), question 1 draws 16 atoms: 4 uranium-235 and 12 lead-207. The fraction of parent left is 4 ÷ 16 = 1/4, which is two halvings (1 → 1/2 → 1/4). Two half-lives of 713 million years make the crystal 1.43 billion years old (2 × 713 million = 1,426 million). Open set ZR2U22
Half-lives used for dating
| Parent | Decay product | NY reference table | Evaluated data (IAEA) |
|---|---|---|---|
| Carbon-14 | Nitrogen-14 | 5730 years | 5700 years |
| Potassium-40 | Argon-40 | 1.3 billion years | 1.248 billion years |
| Uranium-235 | Lead-207 | 713 million years | 704 million years |
| Uranium-238 | Lead-206 | 4.5 billion years | 4.468 billion years |
| Rubidium-87 | Strontium-87 | 48.8 billion years | 49.7 billion years |
Only about 11% of potassium-40 decays to argon-40; the rest becomes calcium-40. Like the reference table, these questions count every decayed atom as argon-40. Rubidium-87 decays so slowly that a rock as old as the Earth keeps over 93% of it, so it is never asked in whole half-lives.
Questions
How do you find the half-life from a graph?
Read the value at time 0 and halve it. Go across from that value to the curve, then straight down to the time axis: that time is one half-life. Check it by halving again; the next halving takes the same time. Any starting point works, not only time 0.
Why do you take away the background count?
A Geiger counter also picks up background radiation from rocks, air and space, and that part does not decay. Take the background away from every reading first, halve what is left, then add the background back if you read the half-life off a graph of the measured count rate.
What fraction is left after 3 half-lives?
One eighth. Each half-life halves what is left: 1/2, then 1/4, then 1/8, which is 12.5%. After n half-lives the fraction left is (1/2) to the power n, and the fraction that has decayed is 1 minus that, 7/8 here.
How do you find the age of a rock from its parent and daughter atoms?
Assume there was no daughter when the rock formed. The fraction of parent left is parent divided by parent plus daughter. Count the halvings to reach it, then multiply by the half-life. With 1 parent atom to 3 daughter atoms, 1/4 is left: two half-lives.
Is the half-life of carbon-14 5730 or 5700 years?
Both are in use. The New York Earth and Space Sciences reference tables and many chemistry textbooks, such as OpenStax Chemistry 2e, give 5730 years. The current evaluated nuclear data give 5700 years, plus or minus 30. The questions here use 5730 years and print it in every question that needs it, so always use the value the question gives.
What is the decay constant?
The chance per second that one nucleus decays. It links to the half-life by λ = ln 2 ÷ t½, about 0.693 ÷ t½. The activity is A = λN, so with λ in s⁻¹ it comes out in becquerels. CBSE Class 12 meets the same idea in chemistry, as the first-order rate constant k: t½ = 0.693 ÷ k.
Can I give my class the same questions?
Yes. Share with class copies a link with the set code, and everyone who opens it gets the same graphs and numbers. To stop copying, print a class set: each copy asks the same kinds of question in the same order with different numbers, and each has its own key.
Sources, read October 27, 2026: IAEA LiveChart of Nuclides (evaluated half-lives, ENSDF); New York State Education Department, Reference Tables for Earth and Space Sciences, 2024 edition, radiometric dating table, and the August 2025 Earth and Space Sciences rating guide (uranium-238, 4.5 billion years); OpenStax Chemistry 2e, 21.3 (carbon-14, 5730 years); AQA GCSE Physics 8463 specification 4.4.2.3 (half-life from given information, net decline as a ratio); College Board AP Environmental Science course and exam description (cesium-137 activity in kBq/m²); NCERT Class 12 Chemistry, Unit 3 Chemical Kinetics (t½ = 0.693 ÷ k; exercises 3.14, 3.16, 3.17 and 3.19).