The Hollow Chamber :

The hollow chamber is a good approximation of a black body. It has a tiny aperture through which radiation is emitted, and is immersed in a heat bath to keep it at constant temperature. The radiation emitted can be detected and analyzed with a spectrometer in order to obtain the spectral distribution of the emitted radiation energy.

Spectral Distribution of the black body:

The spectrum of the black body radiation is plotted for three different temperatures, 2000 K, 1750 K, and 1250 K. They appear as differently coloured solid curves with the radiation energy plotted as energy density per wavelength unit over wavelength (measured in nm).

Stefan-Boltzmann's Law of black body radiation:

The total emitted radiation energy of the black body at a given temperature, i.e. the integral, M, over the spectral distribution at each individual temperature setting, is proportional to the 4th power of T:

with the constant

Wien's Law of black body radiation:

If the wavelength of maximum emission of the spectral distribution of the black body is plotted over 1/T, one obtains a straight line.

This is an empirical law formulated by Wien in the late 19th century.

Wien's 2nd Law, Rayleigh-Jeans' Law, and Planck's Law:

Wien's second law:

is also empirical, and does a pretty good job of simulating the behavior of the black body spectrum at short wavelengths. It fails at longer wavelengths.

On the other hand, Rayleigh-Jeans' law:

was derived from classical physics. It simulates the spectrum well at long wavelengths (in the infrared) while failing at short wavelengths (in the visible and UV range). The radiation energy increase to very high energy levels at short wavelengths gave rise to the term "ultraviolet catastrophy", which is predicted from classical physics, but obviously not observed.

Planck's law of black body radiation:

is the one that describes the experimental observation best. It was based on the idea that the electrons, bound in the atoms of the wall of the hollow chamber act like little dipole oscillators (Hertzian oscillators) that absorb and emit electromagnetic radiation. A mechanical analog of this is a spring loaded with a mass. If one pulls the load down a bit it starts to oscillate up and down. Classical physics predicts that the amplitude of this oscillation can assume any arbitrary value (as long as it is not too large for anharmonic contributions of the spring to be taken into account). In order to derive the correct formula for black body radiation, Planck had to assume that the amplitude of his Hertzian dipole oscillators (i.e. their energy which is a function of their amplitude) can only assume discrete values, characterized by Planck's constant h:

Planck derived his black body radiation law by assuming that the energy of each Hertzian oscillator is a product of its inherent frequency, Planck's constant h, and a natural number n:

As it turned out later, in the correct equation a zero-point energy term has to be added:

Atomic Line Spectra:

The observation of line spectra out of electrical discharge tubes, loaded with low pressures of various gases, could also not be explained in the frame of classical physics. The plot shows a typical spectrum, measured in wavenumbers, the classical units of spectroscopists. Classical physics would rather predict a continous spectrum originating from the excited electrons that would spiral into the positively charged nuclei. The only way to explain line spectra was to assume that the electrons could occupy stationary states in the atom, and that radiation would only be emitted upon a transition between two stationary states at different energies, as seen in the energy level diagram. This assumption was one of the postulates with which Bohr set up his atomic model which was later superceded by the true quantum mechanical model.

Einstein's derivation of Planck's law:

With an elegant derivation of Planck's law, Einstein demonstrated the relationship between the quantum hypothesis and black body radiation. He assumed that the interaction between light and matter takes place in three fundamentally different forms. The three fundamental processes are: absorption, spontaneous emission, and induced emission. The latter was introduced by Einstein, and is the basis for light amplification by stimulated emission of radiation (the LASER principle). Einstein also claimed that light radiation came in quantized particles, called photons.

The photon hypothesis:

The photon hypothesis went against strongly held beliefs in classical electrodynamics. The success of Maxwell's equation to describe electromagnetic phenomena had virtually eradicated the belief that light consisted of particles. It was a revolutionary hypothesis by Einstein to reintroduce the photon concept. He was proven correct not only by the black body spectrum that was only explained in terms of Planck's Law, the derivation of which required the assumption of quantized light particles, but also by the photoelectric effect.

The Photoelectric Effect:

The photoelectric effect can be observed with a simple experimental set-up. An evacuated glass tube contains two electrodes. Light metals that give up electrons easily (e.g. alkaline or earth-alkaline metals) are deposited on the cathode (electron emitting). The anode collects the electrons that are emitted by the cathode. Electrons are ejected from the cathode when a light beam is falling on it, and their number as well as their kinetic energy can be measured by the current through the circuit. If the tube is reverse biased, i.e. the cathode is connected to the positive pole of the power source and the anode to the negative pole, the set-up can be used to measure the kinetic energy of the ejected electrons.

They loose their kinetic energy on their way up for the potential energy they gain by coming close to the (negatively biased) anode. By varying the reverse bias voltage until no current is flowing the maximum kinetic energy of the electrons can be measured. Classical physics would predict that the amplitude of the electric field of the electromagnetic wave causes the electrons to break away from their atoms and leave the cathode. Thus by varying the intensity of the light one would observe different kinetic energies of the electrons coming off the cathode, and measure different reverse bias voltages in the circuit reflecting these different energies. The experiment shows on the other hand that does not depend on the intensity of the incident light but rather on its frequency:

Below a certain frequency, no electrons will be emitted, no matter how high the amplitude of the electromagnetic field is given. depends linearly on the frequency of the incident light, with a threshold frequency,

that is material dependent.