# Chapter 9

# Understanding Hydrogen Atoms

In This Chapter

- The Schrödinger equation for hydrogen
- The radial wave functions
- Energy degeneracy
- Location of the electron

Not only is hydrogen the most common element in the universe, but it's also the simplest. And one thing quantum physics is good at is predicting everything about simple atoms. This chapter is all about the hydrogen atom and solving the Schrödinger equation to find the energy levels of the hydrogen atom. For such a small little guy, the hydrogen atom can whip up a lot of math — and I solve that math in this chapter.

Using the Schrödinger equation tells you just about all you need to know about the hydrogen atom, and it's all based on a single assumption: that the wave function must go to zero as *r* goes to infinity, which is what makes solving the Schrödinger equation possible. I start by introducing the Schrödinger equation for the hydrogen atom and take you through calculating energy degeneracy and figuring out how far the electron is from the proton.

## Coming to Terms: The Schrödinger Equation for the Hydrogen Atom

Hydrogen atoms are composed of a single proton, around which rotates a single electron. You can see how that looks in Figure 9-1.

Note that the proton isn't at the exact center of the atom — the center of mass is at the exact center. In fact, the proton is at a radius of *r*_{p} from the exact center, and the electron ...