The carbon-14, a radioactive isotope of carbon, is often used to date archaeological, geological, an — Analytical Chemistry Chemistry Question
Radiocarbon dating
The carbon-14, a radioactive isotope of carbon, is often used to date archaeological, geological, and hydrogeological samples. The half-life of 14C is t1/2 = 5730 years, but in calculations of the age of samples, a different value of half-life, t’1/2 = 5568 years, is used. The 14C is produced from nitrogen in the atmosphere under the action of cosmic rays. It can be included in the organisms of plants and animals through the photosynthesis and the food chains. The radiocarbon content in living organisms is nearly constant with the activity of 14C being 230 Bq per kg of carbon. After death of an organism, the carbon exchange stops and the 14C content starts decreasing continually.
Give the balanced reaction equations of formation and decay of 14C.
Model Answer
14_7N + 1_0n → 14_6C + 1_1H
14_6C → 14_7N + 0_-1β
Activity of radiocarbon in a sample of cloth from an Egyptian pyramid corresponds to 480 disintegrations per hour per gram of carbon. What is the age of the cloth?
Model Answer
Dependence of the activity (a) on time:
a = a0 e^(-λt)
λ = ln 2 / t'1/2 = ln 2 / 5568 = 1.245 × 10^-4 years^-1;
t = ln(a0 / a) / λ = ln(230 / (480 × 1000 / 3600)) / (1.245 × 10^-4) = 4380 years
In another pyramid, a white powder was found. Analysis showed it was a pure phenoxymethylpenicillin (Penicillin V):
Commercial phenoxymethylpenicillin is produced by microorganisms cultured in a medium containing carbohydrates (lactose, glucose, sucrose), cornsteep liquor, mineral salts and phenoxyacetic acid.
It was decided to determine the radiocarbon content to estimate the age of the powder. The 14C/12C ratio determined from mass-spectrometry measurements amounts to 6.0×10–13.
The archaeologists estimated the age of the powder from the radioactive decay law. What was the production date they obtained?
Model Answer
Activity 230 Bq/kg corresponds to the following 14C / 12C ratio:
a = N_A k (m / M(12C)) w = N_A (ln 2 / t_1/2) (m / M(12C)) w
(neglecting 13C content)
w(14C) = (a t_1/2 M(12C)) / (N_A m ln 2) = (230 × 5730 × 365 × 24 × 3600 × 12) / (6.02×10^23 × 1000 × ln 2) = 1.20 × 10^-12.
Since 6.0×10^-13 / 1.20×10^-12 = 1/2, one half-life time elapsed (we use the value 5568 year for the age determination). The archaeologists thought that the powder was made approximately in 3560 BC.
Explain this result. When was the powder produced in reality?
Constants were taken from: Lloyd A. Currie. The Remarkable Metrological History of Radiocarbon Dating. // J. Res. Natl. Inst. Stand. Technol. 109, 185-217 (2004)
Model Answer
In fact, the phenoxyacetyl group is formed from phenoxyacetic acid synthesized in industry from the products of petroleum and coal processing. It does not contain radiocarbon. Only 8 carbon atoms of 16 are natural (formed from living matter), so the 14C content is twice that in a natural part, and w = 1.2×10–12, that is the powder is present-day.