Carbon dating exponential equation


The carbon-14 isotope would vanish from Earth's atmosphere in less than a million years were it not for the constant influx of cosmic rays interacting with molecules of nitrogen (N) into organic compounds during photosynthesis, the resulting fraction of the isotope 14C in the plant tissue will match the fraction of the isotope in the atmosphere.

After plants die or are consumed by other organisms, the incorporation of all carbon isotopes, including 14C, stops.

Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value.

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We can easily find an expression for the chance that a radioactive atom will "survive" (be an original element atom) to at least a time t.

Radiocarbon dating (usually referred to simply as carbon-14 dating) is a radiometric dating method.

Draw the log graph and deduce l (and hence half-life).

The experimental scatter should be obvious on the graph, and hence the value of a straight line graph can be pointed out.

However, now the "thin slice" is an interval of time, and the dependent variable is the number of radioactive atoms present, N(t). If we have a sample of atoms, and we consider a time interval short enough that the population of atoms hasn't changed significantly through decay, then the proportion of atoms decaying in our short time interval will be proportional to the length of the interval.