This simulation shows radioactive decay for the two most abundant uranium isotopes, U-235 and U-238. Use the sliders to set the initial number of atoms N0 and the generic decay constant k. Decay curves for U-235 (blue) and U-238 (orange) are plotted, together with a generic decay curve (green) for the selected decay constant. The red dots mark the half-life of each decay.
Radioactive decay has the form of exponential decay:
$$N(t) = N_0\, e^{-\lambda t}$$
where \(N(t)\) is the number of nuclei remaining at time \(t\) (in years) for an initial number \(N_0\) in the sample, and \(\lambda\) is the decay constant, which is specific to the individual isotope:
$$\lambda_{238} = 1.54\times10^{-10}\ \text{yr}^{-1}\ \ \text{for U-238}$$
$$\lambda_{235} = 9.90\times10^{-10}\ \text{yr}^{-1}\ \ \text{for U-235}$$
The half-life \(t_{1/2}\) is the time for half of the sample to decay:
$$N(t_{1/2}) = \frac{N_0}{2} = N_0\, e^{-\lambda t_{1/2}}$$
$$t_{1/2} = \frac{\ln 2}{\lambda}$$
where \(N_0\) is the initial number of nuclei.
The green curve is a generic decay for the decay constant \(\lambda\) set with the slider.
This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Anushka Dalvi, Mindy Huang, and Jack Rickle. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.