Visualization of Atomic Orbitals

p Orbitals

Unlike the spherically symmetric s orbitals, a p orbital is oriented along a specific axis. All p orbitals have l = 1, and there are three possible values for m (-1, 0, +1). Whenever m does not equal zero, the wave function is complex, which makes visualization of the wave function difficult. Chemists generally combine the complex wave functions to create new wave functions that are real. (The Schroedinger equation for the hydrogen atom is a linear differential equation. One consequence is that any linear combination of wave functions is also a valid wave function.) For l = 0, the m = 0 wave function is designated p_z. The m = -1 and +1 are combined to produce two new wave functions, which are designated p_x and p_y.

Exercise

Carefully examine the p orbitals for various values of n and the various orientations (p_x, p_y, and p_z) and answer the following questions.

1. What is the shape of a p orbital?
2. What are the similarities and differences between the p_x, p_y, and p_z orbitals (for a given n)?
3. For a given value of n, how many nodal surfaces are present?
4. What is(are) the shape(s) of the nodal surface(s) for the 2p_x, 2p_y, and 2p_z orbitals?
5. What is(are) the shape(s) of the nodal surface(s) for the 3p_x, 3p_y, and 3p_z orbitals?
6. Why does the program prevent you from using n = 1 in this exercise?