Half-Life of Radioactive Materials

Much like population problems, half-life problems concern a population, but one of atoms of radioactive materials where half the atoms change over time into atoms of a different substance. For example, Carbon-14 decays into Nitrogen-14, and it takes about 5,730 years for half the carbon to decay. This makes radiocarbon dating a crucial tool in everything from archaeology to detecting forged artworks.

Exercise 12.08: Measuring Radioactive Decay

Radium-226 has a half-life of 1,600 years. How much of the radium in a given sample will disappear in 800 years?

The differential equation meaning "the rate of decay of a substance is proportional to the amount of the substance" is expressed like this:

Figure 12.10: Differential equation for calculating rate of decay of a substance

The solution is similar to that for our population problems, except that the decay factor is negative, since the amount decreases:

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