Now we are ready to study an electron trapped in an atom. For simplicity, we choose the simplest atom—hydrogen--which contains only one electron. To define the problem we must identify the potential energy function for this electron, for a finite well. In that case the motion of the electron was on dimensional. The electron in the hydrogen atom, however, can move in three dimension. Its potential energy, conveniently, involves only a single variable—namely, the radial distance r from the nucleus to the electron.

The potential energy function follows from Coulomb’s law and is:-

In which +e is the charge of the central proton and –e is that of the electron. It too, is a potential well. In the figure we have expressed the radial separation as a dimensionless ratio r/a₀. The constant a₀ called the Bohr radius. Is a convenient unit of length for distances on the atomic scale. Its numerical value, as we discuss later in this section is 52.9 pm, which is approximately the radius of a typical atom.

In the next section we will begin to consider the solutions to Schrodinger’s equation for the hydrogen atom. First, however, we give a brief review of the historical background.