Thermal Radiation, Black Bodies, Photoelectric Effect, and Photons
Thermal Radiation and Black Bodies
Electromagnetic energy emitted by a body due to its temperature is called thermal radiation. This thermal radiation varies with both temperature and the composition of the body. However, there is a set of bodies for which thermal radiation depends only on its temperature. They are called black bodies. The total power P emitted by a surface of temperature Ts satisfies the Stefan-Boltzmann law. The wavelength for which the maximum power output occurs is inversely proportional to the temperature.
Planck’s Hypothesis
Two English physicists used the principles of electromagnetism and classical thermodynamics to describe black-body radiation. They obtained a mathematical expression in which the energy of radiation decreases with increasing wavelength but increases indefinitely. In contrast, the energy tends to zero for very small wavelengths. This failure of classical theory was so important that it was called the ultraviolet catastrophe. In late 1900, Planck formulated the following hypothesis as a starting point to try to explain black-body radiation: The radiation-emitting atoms behave as harmonic oscillators. Each oscillator absorbs or emits radiation energy in an amount proportional to its frequency of oscillation f: Eo = hf. The total energy absorbed or emitted by each oscillator atom can only have an integer n lots of energy Eo: E = nEo, E = nhf. hf power packs were called quanta, so that the energy of the oscillators is quantized and n is a quantum number.
The Photoelectric Effect
In the late 19th century, experiments were carried out. During these experiments, an effect was observed that would be used by Einstein to contradict other aspects of classical electromagnetic theory. It was found that when light was shone on certain metal surfaces, these gave off electrons (called photoelectrons). This phenomenon is called the photoelectric effect.
Einstein’s Quantum Theory
Einstein questioned the classical theory of light. He proposed a new theory and used the photoelectric effect to test which of the two theories was correct. According to Einstein, the energy emitted by a radiant source is quantized in packets called photons. To explain the photoelectric effect, Einstein assumed: The amount of energy of each photon is related to its frequency f by the expression E = hf. A photon is absorbed completely by a photoelectron. The kinetic energy (KE) of the photoelectron is KE = hf – W. The electron is more weakly bound to escape with Ecmax, which is determined by the expression of the photoelectric equation: Ecmax = hf – Wo. When Einstein published his theory, not enough experimental data existed to confirm it. Millikan had to wait for sufficient data. At this point, it was demonstrated that Einstein’s photoelectric equation was correct.
Features of Photons: The Compton Effect
While Millikan’s experiments corroborated Einstein’s hypothesis, the confirmation of the existence of photons was given by the physicist Compton. He directed a beam of wavelength λ onto a sheet of graphite and observed that the scattered radiation had two wavelengths, one equal to the incident, λ, and a larger one, λ’. According to classical theory, the scattered wave should have the same wavelength as the incident wave. Compton considered electromagnetic radiation as a set of relativistic particles, photons, each with zero rest mass (Mo = 0), with energy E = hf, and a momentum p: p = E / c = hf / c = h / λ. The Compton effect confirms both the validity of relativistic mechanics and the existence of photons.