Introduction To Quantum Mechanics - The First Quantum Theory: Max Planck and Black Body Radiation

The First Quantum Theory: Max Planck and Black Body Radiation

Thermal radiation is electromagnetic radiation emitted from the surface of an object due to the object's temperature. If an object is heated sufficiently, it starts to emit light at the red end of the spectrum — it is red hot. Heating it further causes the colour to change from red to yellow to blue to white, as light at shorter wavelengths (higher frequencies) begins to be emitted. It turns out that a perfect emitter is also a perfect absorber. When it is cold, such an object looks perfectly black, because it absorbs all the light that falls on it and emits none. Consequently, an ideal thermal emitter is known as a black body, and the radiation it emits is called black body radiation.

In the late 19th century, thermal radiation had been fairly well-characterized experimentally. How the wavelength at which the radiation is strongest changes with temperature is given by Wien's displacement law, and the overall power emitted per unit area is given by the Stefan–Boltzmann law. However, classical physics was unable to explain the relationship between temperatures and predominant frequencies of radiation. In fact, at short wavelengths, classical physics predicted that energy will be emitted by a hot body at an infinite rate. This result, which is clearly wrong, is known as the ultraviolet catastrophe. Physicists were searching for a single theory that explained why they got the experimental results that they did.

The first model that was able to explain the full spectrum of thermal radiation was put forward by Max Planck in 1900. He modeled the thermal radiation as being in equilibrium, using a set of harmonic oscillators. To reproduce the experimental results he had to assume that each oscillator produced an integer number of units of energy at its single characteristic frequency, rather than being able to emit any arbitrary amount of energy. In other words, the energy of each oscillator was "quantized." The quantum of energy for each oscillator, according to Planck, was proportional to the frequency of the oscillator; the constant of proportionality is now known as the Planck constant. The Planck constant, usually written as h, has the value 6.63×10−34 J s, and so the energy E of an oscillator of frequency f is given by

Planck's law was the first quantum theory in physics, and Planck won the Nobel Prize in 1918 "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta." At the time, however, Planck's view was that quantization was purely a mathematical trick, rather than (as we now know) a fundamental change in our understanding of the world.