Calculus in Radioactive Decay Rates

by Tyler Paffenroth

Submitted : Fall 2013

18F-FDG (fluoro deoxyglucose) is often used as the radiolabelled tracer for positron emission tomography (PET) scans. PET scans show where the radioactive tracer is concentrated, based on the body's utilization of it. PET scans are helpful for diagnostics, within the medical field, and research in many fields, including psychology. In a study to test the safety of 18F-FDG (U.S. Food and Drug Administration, 2011), 200-740 megabecquerels of 18F-FDG were administered to participants prior to a PET scan, with the median and mean dosage at 370 MBq. This mean value was used to model radioactive decay, and integration was used to demonstrate how the standard radioactive decay formula, N = N₀e^-kt, originated from the first-order rate law.

Through converting the first order rate law, rate = kN, into the standard formula, the time necessary for the mean dosage of 18F-FDG to decay to 1 MBq was found to be approximately 15.6 hours. Calculus is necessary to Chemistry as it is the source of most of the formulas utilized to describe the activity of atoms, and subatomic particles. Familiarity with Calculus allows one to ground the formulas given in a Chemistry textbook in an understanding of what the formula truly means.

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