Activity, Half-Life and Radioactive Dating
Activity is the decay constant times the number of nuclei, so it falls on the same curve as the nuclei do, and the half-life is ln 2 divided by the decay constant. Comparing the activity left with the activity at the start dates a sample.
What a learner can do afterwards
- Converts between half-life and decay constant in both directions
- Calculates activity in becquerels from the number of nuclei present
- Dates a sample from a measured carbon-14 activity and names one assumption the method makes
1 · Read
Activity tells you how strong a sample really is right now, since it counts the decays per second. It equals the decay constant times the nuclei present, and one becquerel means one decay each second. As nuclei dwindle, activity slides down the same exponential curve, since fewer nuclei mean fewer decays.
Try the activity rule on clean numbers. A sample holds 4000 nuclei with lambda 0.5 per second. Multiply: 0.5 times 4000 gives 2000 decays per second, so the activity is 2000 Bq. Halve the nuclei and the activity halves too.
Carbon-14 dating turns this curve into a clock. Living wood keeps a steady share of carbon-14, which has a half-life of 5730 years. Charcoal with half the living activity died one half-life ago, so 5730 years. With a quarter, two half-lives passed, so 11460 years. The Shroud of Turin keeps 92 percent, giving about 690 years.
Name the assumption before you trust a date. The method needs the air level steady while the organism lived, and no carbon entering or leaving since death. Convert either way with lambda equals 0.693 over half-life, and check whether contamination could fake the ratio.
Activity tracks the nuclei downward, and the leftover fraction of carbon-14 converts straight into years.
The rewritten readings were written for this dataset.
More to read
From half-life to activity
Individual nuclear decays are unpredictable. Large populations follow a reliable statistical pattern. Half-life measures how long it takes for the expected remaining population to halve. Under ordinary conditions, it is characteristic of the isotope. A larger decay constant corresponds to a shorter half-life.
Activity measures decays per second in becquerels. It equals the decay constant multiplied by the remaining number of radioactive nuclei. As that population decreases, its activity drops proportionally. Knowing the half-life gives the decay constant, so dividing measured activity by that constant estimates the number of nuclei.
Dating material with radioactive decay
Radioactive isotopes provide clocks in rocks and once-living material. Living organisms exchange carbon with their surroundings, including a small amount of carbon 14. After death, this exchange stops. Carbon 14 then declines with a half-life of 5730 years.
Compare the remaining activity per gram of carbon with the expected activity per gram when the organism was alive to estimate its age. Dating must account for past changes in atmospheric carbon 14 and assumes no later addition or loss of carbon. Older rocks can be dated using slower decay systems, such as uranium becoming lead; these are not substitutes for carbon dating every old bone.
Ways unstable nuclei change
An unstable nucleus can release particles or electromagnetic radiation. Alpha emission ejects a group of two protons and two neutrons. In beta-minus decay, a neutron becomes a proton. Gamma emission releases excess energy as photons.
An isotope's decay rate is usually almost unaffected by ordinary changes in temperature, pressure or chemistry. This stability supports radioactive dating, although some decay processes are sensitive to their surroundings.
Some radioactive nuclei begin decay chains: each unstable daughter decays again until a stable nucleus remains. Long natural chains often finish with lead.
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