When the radial Schrodinger equation for the hydrogen atom is written in dimensionless form, the natural length and energy scales to emerge are the Bohr radius, a_o, (0.52 Angstroms; 1 Angstrom = 10^-10m) and the Rydberg, E_I (13.6 eV), respectively. Asymptotically, the function u(r) decays exponentially at large distances for energies less than zero. Solving the differential equation by a series solution, the normalizable solutions for u(r) are polynomials times the exponentially decaying factor. These solutions are only valid at certain energies E = -E_I/n² for n= 1, 2, 3, ... At other energies less than zero, the solutions to the radial Schrodinger equation grow exponential at infinity.