http://www.ck12.org Chapter 23. Quantum Physics
FIGURE 23.4
The observed rate of different wave-
lengths of light from the Sun, compared
to the classical prediction.Planck’s Equation
In 1900, at the same time as the classical prediction was made, the German physicist Max Planck (1858-1947)
derived a mathematical equation that correctly matched the experimental results. However, at the time, he had no
physical explanation for what the equation meant. The mathematics implied that the energy given off by a blackbody
was not continuous, but given off at certain specific wavelengths, in regular increments. If Planck assumed that the
energy of blackbody radiation was in the form
E=nh f, where
- nis an integer (now called a quantum number),
- h, a constant, (now known asPlanck’s constant), with the valueh= 6. 626 × 10 −^34 J−s
- andfis the frequency of the light emitted,
then he could explain what the mathematics represented. This was indeed difficult for Planck to accept, because at
the time, there was no reason to presume that the energy should only be radiated at specific frequencies. Nothing in
Maxwell’s laws suggested such a thing. It was as if the vibrations of a mass on the end of a spring could only occur
at specific energies. Imagine the mass slowly coming to rest due to friction, but not in a continuous manner. Instead,
the mass jumps from one fixed quantity of energy to another without passing through the intermediate energies.
To use a different analogy, it is as if what we had always imagined as smooth inclined planes were, in fact, a series
of closely spaced steps that only presented the illusion of continuity.
Nature, it seemed, was quantized (non-continuous, or discrete). If this was so, how could Maxwell’s equations
correctly predict this result? Planck spent a good deal of time attempting to reconcile the behavior of electromagnetic
waves with the discrete nature of the blackbody radiation, to no avail. It was not until 1905, with yet another paper
published by Albert Einstein, that the wave nature of light was expanded to include the particle interpretation of light
which adequately explained Planck’s equation. To learn more about blackbody radiation, follow the link below.