Spectroscopy Is Applied Quantum Mechanics, Part II: The Quantum Revolution

Jan 01, 2008


David W. Ball
Blackbody radiation, spectroscopy (especially of hydrogen), the photoelectric effect, low-temperature heat capacities — these phenomena were a puzzle to scientists of the 19th century. Well-entrenched theories of nature, including Newton's laws of motion and Maxwell's laws of electrodynamics, which were so successful in understanding the behavior of matter and radiation, did not help explain these behaviors completely.

As I've said before, if there is a disagreement between theory and nature, we've got to change either nature or theory. Because every attempt to change the universe has failed, our only choice is to get a new theory. That's what eventually happened, and it started with a thermodynamicist.

Max Planck's Quantum Theory


Figure 1
Max Planck (1858–1947) was a German theoretical physicist who was trained in thermodynamics. This was fortunate, for when Planck began to consider the issue involving blackbody radiation, he realized that Wien's law (1) would apply only if the entropy of the light depended upon its energy. Planck realized that if this were true in the high-frequency portion of the electromagnetic spectrum (where Wien's law applied), it had to be true in the low-frequency portion of the spectrum, where the Rayleigh-Jeans law was approximately correct.




Thus, Planck sought to combine the two laws into one mathematical framework. He was able to do this and derived a formula that did predict the nature of blackbody radiation — but he realized that this mathematical expression had to have some physical justification. So Planck looked into what physical basis was needed to justify his equation. Apparently, he did not like the conclusions he arrived at: that entropy was a statistical concept, not a deterministic or absolute one. In addition, Planck had to assume that the vibrating atoms in the blackbody could not absorb energy continuously, but only in certain amounts that were proportional to their vibrational frequency ν, not their amplitude A (Figure 1):




To make this proportionality an equality, a proportionality constant is needed:

where h is now known as Planck's constant.




The formula for the intensity of blackbody radiation that Planck derived was




where h is Planck's constant, c is the speed of light, k is Boltzmann's constant, and T is the absolute temperature. This equation is known by several names: Planck's law, the radiation distribution law, the law of blackbody radiation, and so forth. In terms of wavelength λ, Planck's law is