Physical Chemistry Lesson of the Day – Effective Nuclear Charge

Much of chemistry concerns the interactions of the outermost electrons between different chemical species, whether they are atoms or molecules.  The properties of these outermost electrons depends in large part to the charge that the protons in the nucleus exerts on them.  Generally speaking, an atom with more protons exerts a larger positive charge.  However, with the exception of hydrogen, this positive charge is always less than the full nuclear charge.  This is due to the negative charge of the electrons in the inner shells, which partially offsets the positive charge from the nucleus.  Thus, the net charge that the nucleus exerts on the outermost electrons – the effective nuclear charge – is less than the charge that the nucleus would exert if there were no inner electrons between them.

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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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