Radioactive Decay Analysis

Statistical modeling of random nuclear events using Geiger-Muller counters to determine half-lives and verify Poisson distributions. 가이거-뮐러 계수기로 무작위 핵 사건을 통계적으로 모델링해 반감기를 구하고 포아송 분포를 검증합니다.

Nuclear Physics Statistical Analysis Distributions Error Analysis

Project Overview프로젝트 개요

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.방사성 붕괴는 개별 원자 수준에서는 예측 불가능한 확률 과정이지만, 큰 집단에서는 통계적으로 결정적인 거동을 보입니다. 이 프로젝트는 가이거-뮐러 계수기로 지수 붕괴 법칙 $N(t)=N_0 e^{-\\lambda t}$을 검증합니다.

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.붕괴 생성물의 도착 시간이 포아송 분포($\\sigma \\approx \\sqrt{N}$)를 따른다는 점을 확인해 신호와 배경 방사선을 구분했습니다. 또한 단수명 동위원소의 반감기 $t_{1/2}=\\ln(2)/\\lambda$를 계산했습니다.

Key Concepts Investigated탐구한 핵심 개념

Poisson Statistics포아송 통계

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 Determination반감기 추정

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 Subtraction배경 신호 보정

Implemented rigorous background radiation subtraction techniques to isolate the sample's activity, a critical step for low-activity signal processing.

Full Documentation전체 문서

This report details the statistical methods used to validate the stochastic nature of quantum decay events.