While a radioactive isotope decays almost perfectly according to so-called "first order kinetics" where the rate constant is a fixed number, the elimination of a substance from a living organism usually follows more complex chemical kinetics.
The biological half-life of caesium in human beings is between one and four months.
Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value.
Instead, the half-life is defined in terms of probability: "Half-life is the time required for exactly half of the entities to decay on average".
In other words, the probability of a radioactive atom decaying within its half-life is 50%.
The half-life of carbon-14 is approximately 5,730 years, and it can be reliably used to measure dates up to around 50,000 years ago.
Solving Half Life Problems
The process of carbon-14 dating was developed by William Libby, and is based on the fact that carbon-14 is constantly being made in the atmosphere.
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This is the exact solution; evaluate the natural log with a calculator to get the decimal approximation k = -0.000436 .
A typical "half-life problem" might be worded: Tungsten 181 has a λ value of 0.005723757/days. Half-Life = ln(2) ÷ λ Half-Life = .693147 ÷ 0.005723757 Half-Life = 121.1 days Scroll down for 4 more half-life problems.