Analysis of Radioactive Decay

by Charles Suleskey

Submitted : Fall 2013

The objective of this project was to determine the identity and quantitative presence in a radioactive sample given the starting material, the number of atoms, the elapsed time, and the mechanism by which the substance undergoes nuclear decay. The mechanism in question is the decay of Uranium-238 to the stable isotope Lead-206, taken from Polonium-218

The problem was first modeled in Microsoft Excel using by performing Euler integration. This gave a second-by-second estimation of the number of atoms of each isotope present in the sample. The second method, which shall be shown in full in the proof section, defined the rate laws of each reaction in series in terms of Bernoulli’s differential equation and solved using said equation’s general solution. This approach was further simplified by applying practical reasoning to the integration process.

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