Bohr’s concept of stationary states provided a means of understanding both the stability of atoms and the quantum jumps that lead to discrete spectra. Yet, as we have seen, the Bohr model was not successful for any neutral atom other than hydrogen. This chapter is an overview of how quantum mechanics finally provides us with an understanding of atomic structure and atomic properties.
Let’s begin with a quantum-mechanical model of the hydrogen atom. As you learned in Chapter 40, the problem-solving procedure in quantum mechanics consists of two basic steps:
Specify a potential-energy function.
Solve the Schrödinger equation to find the wave functions, allowed energy levels, and other quantum properties.
The first step is easy. The proton and electron are charged particles with , so the potential energy of a hydrogen atom as a function of the electron distance is
The difficulty arises with the second step. The Schrödinger equation of Chapter 40 was for one-dimensional problems. Atoms are three-dimensional, and the three-dimensional Schrödinger equation turns out to be a partial differential equation whose solution is outside the scope of this textbook. Consequently, we’ll present results without derivation or proof. The good news is that you have learned enough quantum mechanics to interpret and use the results.