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This time is called the half-life, and often denoted by the symbol t 1/2. The half-life can be written in terms of the decay constant, or the mean lifetime, as: / = = (). When this expression is inserted for in the exponential equation above, and ln 2 is absorbed into the base, this equation becomes:
The term "half-life" is almost exclusively used for decay processes that are exponential (such as radioactive decay or the other examples above), or approximately exponential (such as biological half-life discussed below). In a decay process that is not even close to exponential, the half-life will change dramatically while the decay is happening.
In principle a half-life, a third-life, or even a (1/√2)-life, could be used in exactly the same way as half-life; but the mean life and half-life t 1/2 have been adopted as standard times associated with exponential decay. Those parameters can be related to the following time-dependent parameters:
The relationship between the elimination rate constant and half-life is given by the following equation: = / Because ln 2 equals 0.693, the half-life is readily calculated from the elimination rate constant.
The integral solution is described by exponential decay: =, where N 0 is the initial quantity of atoms at time t = 0. Half-life T 1/2 is defined as the length of time for half of a given quantity of radioactive atoms to undergo radioactive decay:
Mercury (as methylmercury) in the body has a half-life of about 65 days. Lead in the blood has a half life of 28–36 days. [29] [30] Lead in bone has a biological half-life of about ten years. Cadmium in bone has a biological half-life of about 30 years. Plutonium in bone has a biological half-life of about 100 years.
The voltage (v) on the capacitor (C) changes with time as the capacitor is charged or discharged via the resistor (R) In electronics, when a capacitor is charged or discharged via a resistor, the voltage on the capacitor follows the above formula, with the half time approximately equal to 0.69 times the time constant, which is equal to the product of the resistance and the capacitance.
The half-life of this isotope is 6.480 days, [2] which corresponds to a total decay constant of 0.1070 d −1. Then the partial decay constants, as computed from the branching fractions, are 0.1050 d −1 for ε/β + decays, and 2.14×10 −4 d −1 for β − decays. Their respective partial half-lives are 6.603 d and 347 d.