Construction of the Electronic Radial Wave Functions and Probability Distributions of Hydrogen-like Systems©
Thomas S Kuntzelman
Department of Chemistry
Spring Arbor University
Spring Arbor, MI 49283
United States
mail to: tkuntzle@arbor.edu

This Mathcad document allows users to explore the characteristics of the components of the radial electronic wave function of the hydrogen atom, R(r) (where r is the distance of the electron from the nucleus). Within this exercise, R(r) is separated into four parts: a normalization constant, a polynomial function of r, an associated Laguerre polynomial of r, and an exponential function of r. After choosing quantum numbers n and l, users can evaluate graphically display the component functions of R(r) separately. After combining these components, the entire wave function is constructed and graphs of R(r) and its associated probability density are displayed. How each separate function of r affects the overall radial wave function can be investigated. Finally, users have an opportunity to discover some relationships between values of n, l and certain properties of the radial electronic wave function and its associated probability density (such as the number of nodes and the most probable distance from the nucleus).
Editor's Commentary
Audiences: Upper-Division Undergraduate
Pedagogies: Computer-Based Learning
Domains: Physical Chemistry
Topics: Chemometrics, Mathematics / Symbolic Mathematics, Quantum Chemistry
File NameDescriptionSoftware TypeSoftware Version
H_like_RadialFunctions11.mcd JCE Mathcad 11 Computational Document Mathcad 11
H_like_RadialFunctions.xmcd JCE Mathcad 12 XML Mathcad 12
H_like_RadialFunctions.pdf Read-Only Document
JCE JCE Subscribers only: name and password or institutional IP number access required.
Kuntzleman, Thomas S. J. Chem. Educ. 2007, 84 (7), 1231
Comments to: tkuntzle@arbor.edu
©Copyright 2007 Journal of Chemical Education