Checking the Goodness of Fit of the Poisson Distribution in R for Alpha Decay by Americium-241

Introduction

Today, I will discuss the alpha decay of americium-241 and use R to model the number of emissions from a real data set with the Poisson distribution.  I was especially intrigued in learning about the use of Am-241 in smoke detectors, and I will elaborate on this clever application.  I will then use the Pearson chi-squared test to check the goodness of fit of my model.  The R script for the full analysis is given at the end of the post; there is a particularly useful code for superscripting the mass number of a chemical isotope in the title of a plot.  While there are many examples of superscripts in plot titles and axes that can be found on the web, none showed how to put the superscript before a text.  I hope that this and other tricks in this script are of use to you.

smoke detector

 

Smoke Detector with Americium-241

Source: Creative Commons via Eric Mason’s Coursework for Physics 241 at Stanford University

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The Gold Foil Experiment and The 250-Million-Ton Pea: The Composition of the Atom

This Atom Is Not To Scale

In a recent post about isotopic abundance, I used a prototypical image of a lithium atom to illustrate the basic structure of an atom.  However, the image was deliberately not drawn to scale to make the protons, neutrons, and electrons visible.  Let’s look at the basic composition of the atom to see why, and we owe this understanding to Ernest Rutherford.  First, let’s give some historical background about what motivated Rutherford to conduct this experiment; we first turn to the Plum Pudding Model by J.J. Thomson.

The Plum Pudding Model

Before 1911, the dominant theory of atomic composition was J.J. Thomson‘s “plum pudding” model.  Thomson hypothesized that an atom consisted of electrons as negatively charged particles (the “plums”) “floating” in a “pudding” of positive charge.

plum pudding model

Plum Pudding Model of the Atom

Source: Wikimedia Commons

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