The Bohr Atom Revisited

Once again, the energy of the electron can only take certain values; energy is quantized. This happens because only certain wave functions satisfy the Schroedinger equation and all boundary conditions, and these Eigenfunctions each have their own energy Eigenvalues. The great thing for fans of quantum physics is that the spacing of these energies that Schrodinger first derived corresponded exactly to the energy levels deduced by observing emission spectra of hydrogen!

The different wave function solutions take the place of the different electron orbits in the old Rutherford-Bohr model of the hydrogen atom. In many ways, though, they play the same roles. A photon coming in with just the right energy can promote an electron from one of the standing waves to a different one with a higher energy. If an electron is already in a higher energy state, it can emit a photon and make the transition to a lower energy state. The energy of the emitted photon is then exactly equal to the difference between the energies of the two electron states.

Quantum mechanics gives us an entirely new way of visualizing the atom. Rather than the old picture of electrons whizzing around in circular orbits, we can think about the electron jumping from one resonance to another as photons are absorbed or emitted, like notes being plucked on a cello string or bellowing from a pipe organ.

The old models weren’t so far off on the topic of angular momentum, either. If you recall from the previous generation of quantum physicists postulated that quantization of angular momentum was somehow responsible for the different electron states. Sure enough, the different solutions to the Schroedinger equation have quantized values of angular momentum as well as energy. And higher values of angular momentum tend to go with higher energy levels.

Since the solutions to Schroedinger’s equation are standing waves, the distribution of electron probability does not change in time. It is therefore a little puzzling to imagine how these states have any angular momentum at all. But the quantum math says they do Instead of orbits, we now prefer to call these electron states “orbitals.”