Radioactive Decay Analysis
Statistical modeling of random nuclear events using Geiger-Muller counters to determine half-lives and verify Poisson distributions.
Project Overview
Radioactive decay is an inherently stochastic process, impossible to predict for a single atom but statistically deterministic for large populations. This project investigates the exponential decay law $N(t) = N_0 e^{-\lambda t}$ using a Geiger-Muller counter.
I focused on verifying that the random arrival times of decay products followed a Poisson Distribution ($\sigma \approx \sqrt{N}$), distinguishing true signal from background radiation noise. The experiment also determined the half-life $t_{1/2} = \ln(2)/\lambda$ of a short-lived isotope.
Key Concepts Investigated
Poisson Statistics
Proved that nuclear decay events are independent and random by fitting experimental histograms to Poisson and Gaussian curves, validating the $\sqrt{N}$ error approximation.
Half-Life Determination
Used linear regression on semi-log plots ($\ln(Activity)$ vs. Time) to extract the decay constant $\lambda$ and calculate the precise half-life of the sample.
Background Subtraction
Implemented rigorous background radiation subtraction techniques to isolate the sample's activity, a critical step for low-activity signal processing.
Full Documentation
This report details the statistical methods used to validate the stochastic nature of quantum decay events.