Radioactive Decay
Radiocarbon dating depends on the assumption that the relative abundance of the radioactive carbon isotope in the atmosphere has been constant throughout earth's history. This concentration is used to estimate the initial concentration in living material. Once something dies it no longer gets fresh radioactive carbon from its environment and the radioactive carbon it has continues to decay. We measure the amount of radioactive carbon, [X]', and then can use the equation above to calculate time, t, since the decay rate constant, k, is known There are many methods of radioactive dating, of which carbon dating is only one. It turns out that carbon dating doesn't work very well on old things, because carbon-14's half life is too short. It can be used reliably only for artifacts younger than about 40,000 years. There are several mechanisms of radioactive decay. The most common ones are alpha and beta decay, in which a nucleus gives off a helium nucleus and an electron, respectively. These mechanisms are completely insensitive to the environment: the rate of decay is constant and invariant. The rate of decay (i.e., half-life) is characteristic of a radioactive element and "for all practical purposes" it is unaffected by temperature, pressure, atmospheric conditions, vacuum, space, etc. I hope that someone else would comment on this question for "non practical purposes", i.e., small influences that other forces in nature may have on radioactive decay. In radioactive dating, one compares the ratio of carbon 14 to carbon 12. This ratio in the earth's atmosphere is known. When a living being dies and ceases to take in air, the ratio of carbon 14 to carbon 12 in its body begins to fall because of carbon 14 decay. While carbon 14 decay is independent of the environment it is in, if we are going to use it for dating, we need to have a reference. On the Earth, atmosphere is the reference because its ratio of C14/C12 is almost constant over the time scales for which carbon dating is appropriate. Since C14's half life is over 5000 years, we can probably estimate age in samples in the 1000-100,000 year-old range using this technique. Older specimen would probably have too few C14 left in them to give us accurate estimates. We could then use other elements or techniques.
