After reviewing Planck's solution to the ultraviolet catastrophe problem of blackbody radiation (one of Klevin's "dark clouds"), we started discussing the photo-electric effect. A metal is characterized by so-called "free electrons". Some electrons are held close (bound) to the nuclei, but others are freer to move about. These free electrons give metals some of the properties we associate with them, such as they conduct heat and electricity well and are shiny.

Still the nuclei and bound electrons have a residual positive charge, so the free electrons are still attracted to the metal as a whole. Described in energy terms, there is some energy -- a negative potential energy -- resulting from the negative electron's attraction to the positive array of nuclei. In this context, that energy is called the "work function." If we were to supply enough energy to one of these electrons (enough meaning more than the work function), then the electron could escape the confines of the metal and convert any residual energy into kinetic energy.

In the photoelectric effect, this additional energy is provided by light. Because of Young, Maxwell and others, light was understood to be a wave and the power (rate of energy) of a wave is related to the wave's amplitude and frequency. The frequency is related the wavelngth and the color of light; whereas the amplitude is associated with its brightness (or intensity). In the classical view, one would expect light of any frequency or intensity to eventually be able to deliver the needed energy to the electron. However, this expectation did not match the outcome of the experiments (first performed by Hertz, then Stoletov, and ultimately by Millikan). Instead they found that for a particular metal (particular work function) there was a cutoff in frequency; light below that frequency no matter how intense produced no escaping electrons. Above that cutoff, higher frequencies produced faster electrons, i.e. electrons with greater kinetic energy. The intensity affected only the number of electrons escaping.

Einstein, in 1905, his annus mirabilis (miraculous year), proposed that the quantization of light that Planck found for light radiating from a blackbody applied to the light shining onto the metallic surface. Thus the energy was only available in quantized units, given by the formula E=hf, where h is Planck's constant and f is the frequency of light. In other words, the energy does not continuously accumulate but comes in discrete amounts. If that discrete amount is insufficient (as it is with lower frequencies), no electrons are freed. In this situation then light is acting like a particle, behaving as a discrete unit rather than this spread out wave. In the context of light, that particle-like behavior is called a photon. Thus we have light which acts as both a wave (interfering as in Young's double slit experiment) and as a particle (photon) (exchanging energy is discrete amounts only as in the photoelectric effect). Then we said if things we thought were waves are behaving like particles, then perhaps the reverse is true and things we thought were particle can display wave-like behavior. This concept that things act like both waves and particles depending on the circumstances in known as wave-particle duality.

We started considering the nature of atoms or more particularly what we thought of atoms at the end of the 19th century and beginning of the 20th century. One model put forth at the time was the "Plum pudding model" (by yet another Thomson, J.J. in this case). At that time they knew about electrons but not nuclei. The Plum Pudding model had these discrete electrons sprinkling throughout a positive mass. Then Rutherford directed an experiment that shot alpha particles (basically positively charged Helium ions) at gold foil. Many were not deflected at all, but were deflected right back out -- inconsistent with the plum-pudding view. This led to the concept of the positive charge being concentrated -- or in other words -- atomic nuclei. This led to a solar system like model with electrons orbiting the nuclei. It is at this point that Bohr comes into the picture.