Hydrogen Atom
Construction of the Electronic Angular Wave Functions and Probability Distributions of the Hydrogen Atom JCE
Mark David Ellison, Wittenberg University
Thomas S Kuntzelman, Spring Arbor University
John Tippin, Spring Arbor University
A Mathcad template that provides guided inquiry practice with angular functions used as parts of the solutions to the Hydrogen atom Schrodinger equation.
Construction of the Electronic Radial Wave Functions and Probability Distributions of Hydrogen-like Systems JCE
Thomas S Kuntzelman, Spring Arbor University
A Mathcad template that provides guided inquiry practice with radial functions used as parts of the solutions to the Hydrogen atom Schrodinger equation.
Graphing Orbitals in Three Dimensions with Rotatable Density Plots JCE
Louis Kijewski, Monmouth University
This Mathcad document uses symmetry to simplify the evaluation of an eigenvalue problem by reducing a matrix to sparse form. The sparse matrix is then transformed to block diagonal form. Group theory is used to set up the calculations without going through the proofs of the methods. The ability to use symmetry principles to get the vibrational frequencies and other information about molecules with symmetry is an important asset to any chemist.
Orbital Graphing JCE
Mark David Ellison, Wittenberg University
This document provides three-dimensional graphs of the angular parts of hydrogen-like atomic orbitals. Linear combinations of orbitals result in the familiar px and py orbitals. The process is repeated for some of the d orbitals. The second part of the document shows linear combinations of s and p orbitals to construct hybrid sp, sp2, and sp3 orbitals.
Properties of the Radial Functions
George M. Shalhoub, La Salle University
This Mathcad document provides exercises exploring the radial functions of the hydrogen atom. The document concludes with Slater Rules practice exercises for heavier atoms and an application to inorganic chemistry, SF6.
Radial Distributions Functions for Hydrogen-like Orbitals
Flick Coleman, Wellesley College
This document permits students to explore some of the properties of the radial distribution functions of hydrogen-like one-electron orbitals. The document includes the plots of the ns radial functions which students can change to view the np and nd functions. The calculus is used to demonstrate how to find the maximum and minimum for the functions. Other exercises include exploring the effect of nuclear charge on the function and extent (size) of the radial distribution function.
sp3dn Orbital Hybrids and Molecular Geometry JCE
Mark David Ellison, Wittenberg University
A Mathcad document that gives students the opportunity to explore hybrid orbitals that give rise to octahedral, trigonal bipyramidal, square planar, and square pyramidal shapes. LCAO is use to generate the hybrid shapes.
Symbolic Math Approach To Solve Particle-in-the-Box and H-Atom Problems JCE
Todd M. Hamilton, Georgetown College
After practicing with the particle-in-a-box problem, students solve the H atom symbolically using the derivatives feature in MathCad. The result is an expression for the energy levels of the hydrogen atom. Students will also prove that the radial part of the wavefunction is normalized and explore the concept of an orbital.