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In this situation it is generally uncommon to talk about half-life in the first place, but sometimes people will describe the decay in terms of its "first half-life", "second half-life", etc., where the first half-life is defined as the time required for decay from the initial value to 50%, the second half-life is from 50% to 25%, and so on.
One of its great advantages is that any sample provides two clocks, one based on uranium-235's decay to lead-207 with a half-life of about 700 million years, and one based on uranium-238's decay to lead-206 with a half-life of about 4.5 billion years, providing a built-in crosscheck that allows accurate determination of the age of the sample ...
The age of a sample is given by the age equation: = (+) where λ is the radioactive decay constant of 40 K (approximately 5.5 x 10 −10 year −1, corresponding to a half-life of approximately 1.25 billion years), J is the J-factor (parameter associated with the irradiation process), and R is the 40 Ar*/ 39 Ar ratio.
Thorium-230 is itself radioactive with a half-life of 75,000 years, [4] so instead of accumulating indefinitely (as for instance is the case for the uranium–lead system), thorium-230 instead approaches secular equilibrium with its radioactive parent uranium-234. At secular equilibrium, the number of thorium-230 decays per year within a sample ...
The half-life of a radioactive isotope (usually denoted by t 1/2) is a more familiar concept than the mean-life, so although the equations above are expressed in terms of the mean-life, it is more usual to quote the value of 14 C 's half-life than its mean-life. The currently accepted value for the half-life of 14 C is 5,700 ± 30 years. [21]
A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. (If N(t) is discrete, then this is the median life-time rather than the mean life-time.) This time is called the half-life, and often denoted by the symbol t 1/2. The half-life can be ...
Given a sample of a particular radionuclide, the half-life is the time taken for half the radionuclide's atoms to decay. For the case of one-decay nuclear reactions: = = /, the half-life is related to the decay constant as follows: set N = N 0 /2 and t = T 1/2 to obtain
Since the exact rate at which uranium decays into lead is known, the current ratio of lead to uranium in a sample of the mineral can be used to reliably determine its age. The method relies on two separate decay chains , the uranium series from 238 U to 206 Pb, with a half-life of 4.47 billion years and the actinium series from 235 U to 207 Pb ...