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# Kinetics of Nuclear Decay - AP Chemistry

Radioactive nuclides have been used in various applications, ranging from biology to medicine. The rate of radioactive decay of a material can be understood using a first-order rate law from kinetics: $ln(N/N_o)=-kt$), where $N_o$=the original number of nuclides, N=the number of nuclides remaining at time t, and k=rate constant. This equation can be used to understand the negative of the change in the number of particles per unit of time. The first-order rate law that relates to nuclear decay can be rearranged to determine half-life, written as follows:$t_{1/2}=ln(2)/k=0.693/k$.

The equations above have long-ranging consequences, in that they can be used when considering how quickly a material will decay, as well as how long it should be stored. In medicine, a physician might use a short-lived radioactive nuclide to diagnose a patient with a certain disease, so long as the sample is manufactured in a nearby area. A long-lived radioactive nuclide, on the other hand, must be stored in a faraway area, so that it does not decay significantly. Other applications of the kinetics of nuclear decay include using radioisotopes like carbon-14 for dating of fossils and bones. Since carbon-14 has a half-life on the order of thousands of years, it can be used to trace how old fossils are.

In this lesson, you will learn about the kinetics of radioactive (nuclear) decay and how to solve problems involving the kinetics of radioactive decay. First, try the practice questions to determine what you already know about the kinetics of nuclear decay. Then, watch the video lesson to learn more about the kinetics of nuclear decay.

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