To arrive at his result, Planck followed many of the same steps, which we described above, that other physicists had taken. He, too, assumed the emitted radiation came from thermally excited charges, each oscillating at a particular frequency. In addition, he assumed that the energy emitted at any particular frequency was given by the number of oscillators at that frequency multiplied by their average energy. However, he introduced two new hypotheses that amounted to nothing less than the opening shot of the quantum revolution.
First, whereas the classical approach assumed the charges could take on any possible energy as they oscillated, Planck hypothesized that they could assume only certain fixed energy levels. He imagined that the permissible energy levels were spaced evenly apart just like the rungs of a ladder. The classical view, by contrast, assumed that any energy between the rungs was also permitted.
DEFINITION
An energy level for a physical system is a particular amount of energy that the system is allowed to possess.
A quantum of energy is a little packet of energy whose size is determined by the spacing between one energy level and the next.
A second hypothesis that Planck made was that an oscillating charge could only emit energy by dropping from one rung of the energy ladder down to the next. A simple application of the conservation of energy tells us that the radiated energy must therefore equal the difference between one energy level and the one immediately below. As a result, only a certain quantity, or quantum, of energy could be radiated. No more, no less.
This is an illustration of Planck’s quantum hypotheses: the lines represent the permissible energy levels of oscillating charges, while the equal spacing between the energy levels represents the exact amount of energy that an oscillating charge can emit.
Finally, Planck argued that the spacing between the rungs was fixed by a simple formula: E = hf, where f is the oscillation frequency and h is a constant value that he defined, equal to 6.626 × 10-34 joules-seconds. Little did he know at the time, but this little letter would soon be embroidered into every aspect of quantum physics yet to come. Given its monumental importance, h is now named “Planck’s constant” in his honor. It also goes by the pithy name of “quantum of action” because its dimensional units are energy times time—a unit that physicists call “action.”
Planck’s model provides us with an intuitive understanding for the peaked shape of the blackbody spectrum. For high frequencies (low wavelengths), a single quantum of energy would be quite large. So large that, statistically speaking, only a few oscillating charges in the solid would have so much energy. Their total contribution to the overall energy emission would therefore be small.
Conversely, there would be many oscillating charges at the low frequency (long wavelength) end of the spectrum; however, each would contribute only a small amount of energy to the overall emitted energy. Only at the frequencies in between would there be a sufficient number of oscillating charges with sufficiently large quanta of energy to make a noticeable addition to the blackbody curve.
The takeaway points are that the permissible energy levels of his heated electrons were restricted to whole-number increments of a fundamental value. And that fundamental value was given by Planck’s constant times their oscillation frequency.
QUANTUM QUOTE
Moreover, it is necessary that [the energy from a single charge] not be regarded as a continuous, infinitely divisible quantity, but as a discrete quantity composed of an integral number of finite equal parts.
—Max Planck in his trailblazing publication (Annalen der Physik, vol. 4, 1901)
It is important to note that Planck’s hypotheses about the discrete nature of permissible energies came not from any underlying physical principle or physics-based intuition. He made these assumptions, quite simply, because they made the math work. He could offer no explanation as to why the energy levels were restricted. But when they were, he ended up with his blackbody radiation formula that so closely matched experimental observations.
Planck could be described as a true devotee to classical physics. And because his hypotheses were so contradictory to the notions of classical physics, he would spend many years trying to come up with a way of explaining them in classical terms. It is likely that this fixation prevented him from recognizing their broader implications. It was left to another great physicist—perhaps the greatest of all time—to fully appreciate the significance of what Planck had uncovered.
MAX PLANCK
Early on, Max Planck was advised against a career in physics, on the grounds that there was little left to discover. He was also an excellent pianist who seriously contemplated a career in music instead. Fortunately for us, he opted for physics. And discover he did, enough to earn him the 1918 Nobel Prize in physics.
Planck was a highly esteemed man known for his integrity and strong moral principles. As a witness to the Third Reich’s toll on Germany and German science, he intervened directly, though unsuccessfully, with Adolf Hitler. Undeterred, he advocated until his death against the slow and steady decimation of German physics.
Although he celebrated many triumphs in life, he suffered even greater adversity. He endured the death of his first wife and each of their four children, the last at the hands of the Gestapo for allegedly plotting to assassinate Hitler.
He was a classical physicist to the core and vigorously opposed many of the counterintuitive implications that emerged during the development of quantum physics. For years, he even questioned the validity of his own contributions. For this reason, historians often refer to him as a “reluctant” and “unlikely” scientific revolutionary.
Leave a Reply