Bio

Srinath is a rising senior at Nashua High School South. As an aspiring technologist, Srinath loves to explore the fields of mathematics, computer science, and physics. In his spare time, Srinath enjoys playing chess and playing table tennis. Other times, you can catch him learning about machine learning. He participates in various STEM-related activities throughout his school and his favorite subject is calculus.

Project: Exploring Lifetime Distributions for Nuclear Isotope Decay Cascades

Goal

The purpose of the project was to find a unique way to observe the decay patterns of any given isotope. An algorithm was written that would utilize various calculation methods in order to generate graphics that showcase the mathematics behind radioactive decay. This includes calculations developed by physicists Ernest Rutherford and Harry Bateman for one-decay, chain-decay and alternative-decay processes, including the Bateman model. In this project, the task will be creating a representation of how isotopes decay. There were two stages to the project. The first was to help visualize the isotopes so that the user can clearly see how the molecules transform into a new product. The second part was to take into consideration all of the calculation aspects. This involves developing new formulas to see how the atoms will behave over a period of time and calculating the probability of specific transformations. The program is able to create a system where the user can input any known isotope and time and then the program will create an interactive chart of the possible outcomes. This process happens through utilizing Wolfram databases on the decay properties of various molecules. This way, it is possible to explore a plethora of different examples and see how the molecules evolve over time using Bateman's equations.

Summary of Results

There were three major parts of the project. The first was generating the graphics and the plots for the decay series. Here, the atomic mass of the atoms were represented by a certain 3D graphic, and the user could observe how the ratios of the input isotopes changed by manipulating the half-lives. The second part was to construct a relation graph of any given isotope input. This included constructing automated nodes and vectors that showed the cascade patterns of the nuclear decay. The first two parts were intertwined by using generating buttons at each node. The final part was to create an information chat that gives a little bit more detail about each isotope in the decay chart. This involved information such as the type of decay.

Future Work

Some possible extensions that this program could have is improving the chain reaction functions. It doesn’t fully exploit the differential recursive functions outlined in the Bateman model. This way, for any potential given chain process, all the successive decays would be calculated. The graphical representations of the decay shown with the molecules’ behavior over a certain number of half-lives could be updated to showcase a variety of animations that help explain the behavior of the decay pattern.