Concept explainers
Radioactive Decay The half-life of a radioactive substance is the time H that it takes for half of the substance to change form through radioactive decay. This number does not depend on the amount with which you start. For example, carbon-14 is known to have a half-life of
Where H is the half-life, t is the elapsed time,
a. Uranium-228 has a half-life H of 9.3 minutes. Thus, the decay function for this isotope of uranium is
where t is measured in minutes. Suppose we start with grams of uranium-228.
i. How much uranium-228 is left after 2 minutes?
ii. How long will you have to wait until there are only 3 grams left?
b. Uranium-235 is the isotope of uranium that can be used to make nuclear bombs. It has a half-life of 713 million years. Suppose we start with 5 grams of uranium-235.
i. How much uranium-235 is left after 200 million years?
ii. How long will you have to wait until there are only 3 grams left?
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