Molecules and photonsThis page supports the multimedia tutorial The Nature of Light.
A clean metal surface, often in vacuum, is exposed to light whose wavelength or frequency may be controlled. A nearby electrode can receive the emitted electrons and so allow a current, which may be measured. A variable potential difference may be applied to stop the current. For a given metal, there is a minimum frequency f_{o} (ie a maximum wavelength) of light that will cause electrons to be emitted. For light (or UV radiation) with higher frequency, the stopping voltage increases linearly with frequency f, as sketched. More reactive metals have lower f_{o}. This phenomenon was investigated experimentally by Philipp Lenard and then later and more precisely by Robert Millikan. Both received Nobel prizes for the work. The photoelectric effect was explained by Albert Einstein in work for which he received the Nobel prize in 1921. The quantisation of emitted radiation and black body radiationBlack body radiation is (by definition) radiation in thermal equilibrium with its container. So let us think of a box with hot walls giving off and receiving photons at an equal rate. If we open a small window in the box, the radiation coming out will have the same spectrum, and this is what we measure with our spectrometer to determine the black body radiation spectrum. The spectral radiancy is given by Planck's radiation law, which was initially empirical.
On the left is a sketch of the experimental apparatus used to observe black body radiation. An object of controlled temperature T contains a cavity, joined to the outside by a small hole. If the hole is very small, the radiation in the cavity comes to equilibrium with the walls. The hole allows a small fraction of the radiation to pass to a spectrometer. On the right is a plot of Planck's radiation law for two temperatures. Note that the wavelength for maximum emission becomes shorter (higher frequency) for higher temperature. Note also the strong dependence on temperature of the total emission. The radiancy is the power emitted per unit area per increment of wavelength and so has units of W.m^{3}. Note that the peak of the curve moves to the left as the temperature increases: hotter objects output a larger fraction of their electromagnetic radiation at shorter wavelengths. This displacement of the peak of the curve is called Wien's displacement law. After taking the derivative of Planck's radiation law and setting it to zero, one finds an expression for the wavelength λ_{max} at which the radiation is a maximum. It is related to the temperature T of the black body by the simple equation
At low frequencies, the wavelengths are long. There are relatively few ways in which standing waves can fit into the box if their wavelengths are long. So, if the energy is shared among the different possible standing waves, we should expect the radiation intensity to go to zero at low frequency and to increase with increasing frequency. This is the classical result. But now let's add the quantum hypothesis, that radiation energy is quantised and comes in photons that have an energy hf. In thermal equilibrium, the atoms and electrons of the wall have thermal motion. At sufficiently high frequency, few atoms or electrons will have enough energy to emit a photon with energy hf. Note how this depends on the quantisation hypothesis: if you could have radiation with frequency f and an energy less than hf, then the walls would emit high frequencies like crazy. They don't because they have to emit only whole photons. So, at low frequency, the long wavelength limits the number of possible photons. At high frequency, the high energy makes emission unlikely. So the distribution goes to zero at both f = 0 and f = infinity, and has a maximum in between. Incidentally, the frequency for maximum energy is proportional to the temperature of the walls. Wien's Law. The typical energy of any motion is kT/2, where k is Boltzmann's constant and T is the temperature. (k = R/N_{A} where R is the gas constant and N_{A} is Avagadro's number.) There is more discussion and many more examples in The electromagnetic spectrum. The following link takes you back to the multimedia tutorial The Nature of Light. 
