# 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.

- What is the shape of a p orbital?
- What are the similarities and differences between the p
_{x}, p_{y}, and p_{z} orbitals (for a given *n*)?
- For a given value of
*n*, how many nodal surfaces are present?
- What is(are) the shape(s) of the nodal surface(s) for the 2p
_{x}, 2p_{y}, and 2p_{z} orbitals?
- What is(are) the shape(s) of the nodal surface(s) for the 3p
_{x}, 3p_{y}, and 3p_{z} orbitals?
- Why does the program prevent you from using
*n* = 1 in this exercise?

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