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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.
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 ...
As an extreme example, the half-life of the isotope bismuth-209 is 2.01 × 10 19 years. The isotopes in beta-decay stable isobars that are also stable with regards to double beta decay with mass number A = 5, A = 8, 143 ≤ A ≤ 155, 160 ≤ A ≤ 162, and A ≥ 165 are theorized to undergo alpha decay.
Secular equilibrium can occur in a radioactive decay chain only if the half-life of the daughter radionuclide B is much shorter than the half-life of the parent radionuclide A. In such a case, the decay rate of A and hence the production rate of B is approximately constant, because the half-life of A is very long compared to the time scales ...
This is still a short half-life relative to many other known modes of radioactive decay and it is in the middle of the range of half lives for radiopharmaceuticals used for medical imaging. After gamma emission or internal conversion, the resulting ground-state technetium-99 then decays with a half-life of 211,000 years to stable ruthenium-99 ...