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Radiometric dating in CALCULA

A radioactive isotope decays at a constant rate, summarised by its half-life T: the time after which half of the atoms have transformed.

The decay law

N = N₀ · (1/2)^(t / T)  ⟺  t = T · log₂(N₀ / N)

After one half-life 50 % of the isotope remains, after two 25 %, after three 12.5 %. Measuring the remaining proportion gives the elapsed time.

Example

A wood sample contains 25 % of the carbon-14 expected for living matter. With T ≈ 5,730 years, two half-lives have passed: about 11,460 years.

Choosing the isotope for the timescale

Carbon-14 (T ≈ 5,730 years) dates organic remains up to about 50,000 years. Beyond that too little is left to measure, and other pairs take over: potassium-argon (T ≈ 1.25 billion years) and uranium-lead (T ≈ 4.5 billion years) for rocks and the age of the Earth.

Example

The oldest terrestrial rocks dated by uranium-lead approach 4 billion years; Solar System meteorites, 4.57 billion.

Limits

Real dating happens in a laboratory and corrects for contamination, calibration, and past variations of atmospheric carbon-14. CALCULA gives the order of magnitude from the ideal decay law.

Typing it into CALCULA

“≡” menu → dating: choose the isotope (or a custom half-life), enter the remaining proportion to get the age, or the age to get the proportion. The decay curve places the result. See also chemistry.