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The ratio of λ is a constant that depends on the particular isotope; for a given isotope it is equal to the reciprocal of the mean-life – i.e.
Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon.
Additional complications come from the burning of fossil fuels such as coal and oil, and from the above-ground nuclear tests done in the 1950s and 1960s.
Because the time it takes to convert biological materials to fossil fuels is substantially longer than the time it takes for its in the atmosphere, which attained a maximum in about 1965 of almost twice what it had been before the testing began.
Measurement of radiocarbon was originally done by beta-counting devices, which counted the amount of beta radiation emitted by decaying atoms in the sample and not just the few that happen to decay during the measurements; it can therefore be used with much smaller samples (as small as individual plant seeds), and gives results much more quickly.
The development of radiocarbon dating has had a profound impact on archaeology.