The relative decay rate of naturally occurring uranium U-238 was given in Example 4. Scientists estimate the age of the earth to be about 4.55 billion yr. Determine the fraction of the U-238 present when the earth was formed that is still present as U-238.
A 1-G sample of pure uranium produces about 740,000 decays each minute. We can use these data to determine the relative rate of decay for uranium. Nearly a million decays in a minute may sound like a lot, but the units are misleading. The decay rate is given in atoms per min, but the amount is given in grams. There are about 2.53 X 10^21 atoms in 1 gram of uranium. If we divide the decay rate in atoms per min by the number of atoms, we get k = 2.9 X 10^-16 min^-1. We would get the same result if we ha instead converted the decay rate to grams per minute. Relative rates of decay are always reported with units of inverse time; it doesn't matter whether quantities are reported as atoms or grams. The decay rate of uranium is usually given in inverse years rather than inverse minutes, an the result is k = 1.537 X 10^-10 yr^-1. This is a very slow rate of decay, but it is typical for naturally occurring radioactive materials. Any radioactive materials with a much faster decay rate (and present at the time of earth's foundation) have all disappeared.
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This solution shows how to determine the fraction of uranium that was present when the earth was formed that is still present and has remained in the form U-238 in an attached Word document.