By measuring the ratio, R, in a sample we can then calculate the age of the sample: T = -8033 ln(R/A) Both of these complications are dealt with by calibration of the radiocarbon dates against material of known age.
Further complications arise when the carbon in a sample has not taken a straightforward route from the atmosphere to the organism and thence to the measured sample.
This discussion is a simplified introduction to radiocarbon dating.
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Because the radiocarbon is radioactive, it will slowly decay away.
Obviously there will usually be a loss of stable carbon too but the proportion of radiocarbon to stable carbon will reduce according to the exponential decay law: R = A exp(-T/8033) where R is C ratio of the living organism and T is the amount of time that has passed since the death of the organism.
Carbon-14 is produced in the atmosphere when neutrons from cosmic radiation react with nitrogen atoms: C ratio of 0.795 times that found in plants living today. Solution The half-life of carbon-14 is known to be 5720 years. Radioactive decay is a first order rate process, which means the reaction proceeds according to the following equation: is the quantity of radioactive material at time zero, X is the amount remaining after time t, and k is the first order rate constant, which is a characteristic of the isotope undergoing decay.