This Mathcad document allows students to explore the characteristics of the components of the angular electronic wave function of the hydrogen atom, Ylm(Θ, φ). Within this exercise, Ylm(Θ, φ) is separated into three parts: the normalization constant, a polynomial function and an exponential function. After choosing quantum numbers l and m, users can evaluate and graphically display the component functions of Ylm(Θ, φ) separately. After combining these components, the entire wave function is constructed and a graph of its associated probability density is displayed. Users have the opportunity to discover when, why and how linear combinations of the exponential portion of Ylm(Θ, φ) are used in constructing orbital plots that are normally displayed in textbooks. In addition, students gain a mathematical understanding of why the quantum number m can only vary from −l to l.
The first five Legendre Polynomials, Leg(order,x) as a function of x.
Our Secondary School editors work hard to distill all the JCE materials to produce a fraction of particular interest to high school teachers. We call it CLIC.
In recent years we have worked hard to better match our advertisers with our readers. When shopping for chemistry education materials, visit our advertisers' WWW sites first.
Take JCE along on your outreach missions. Copies of the Journal, guest access to JCE Online, our publications catalog, and more are available for your participants.
