Energy in packets – What did Planck discover?

A piece of wire and a revolution in physics

Although the world is full of light-emitting bodies, for a long time we knew very little about the physical laws of the creation of light. Why does a piece of wire turn red at a certain temperature and white at another? Gustav Kirchhoff discovered in the mid-19th century that the general problem of radiation could be reduced to the study of black-body radiation. However, there were major experimental and theoretical obstacles to overcome, which represented an enormous challenge for contemporary physics.

It was 1900 before researchers succeeded in producing a comprehensive measurement of black-body radiation and the theoretician Max Planck established a radiation law that corresponded to these measurements. He unintentionally triggered a revolution in physics through his findings.

The black body

A black body completely absorbs all electromagnetic radiation that falls on it irrespective of its wavelength. When such a body is in a state of heat equilibrium, it emits radiation, such as light or thermal radiation, the intensity distribution of which is determined only by temperature, and not by the material of the body.

A perfect black body does not exist in nature. However, it can be approximately created experimentally using a large cavity, the inside walls of which are black. A black-body model of sufficiently high quality was first built and used for measurements in the 1890s at the Berlin-based Physikalisch-Technische Reichsanstalt (Imperial Institute for Physics and Technology).

Planck’s point of departure

Following his previous research into the irreversibility of thermal processes, Max Planck turned his attention to the problem of black-body radiation in 1897. He attempted to explain with Maxwell’s theory of electrodynamics why the radiation in the cavity unavoidably and irreversibly comes to a state of equilibrium, which could be described by a radiation law.

When Planck began his work, important conditions that the radiation law had to meet had already been established theoretically. In particular, it had to be independent of material and only dependent on universal constants. Establishing such a law and theoretical justification for it presented Planck, who saw the search for absolutes as the most important role of research, with a major challenge.

The problem

Gustav Kirchhoff discovered in the mid-19th century that “heat rays [are] ... the same in nature as light rays, in fact a particular type. Invisible heat rays are only different from light rays in their period of oscillation or wavelength.”

A black body not only emits radiation at a particular wavelength, but over the entire wavelength spectrum. The distribution of radiation over the spectrum depends entirely on temperature.

The challenge that faced experimental physicists was to create, as far as possible, an ideal black body and to measure its spectrum at various temperatures. In contrast, theoreticians attempted to discover the radiation law that would describe the measurements in all wavelength ranges.

The birth of quantum theory

Planck produced five publications by 1899 that dealt with black-body radiation. His aim was to derive the Wien law on the basis of the thermodynamics of electromagnetic radiation. He hoped to establish an explanation for the irreversibility of thermodynamic processes that did not rely on Boltzmann’s probability theory.

When Planck finally thought he had successfully derived Wien’s law, events started to unfold rapidly in 1900. New experimental results showed that Wien’s law was invalid. On October 19, 1900, Planck presented a new radiation law. In its derivation he set aside his reservations about the Boltzmann method and introduced “energy elements” of a specific size that we today refer to as quanta.

Planck’s act of desperation

Planck could see only one other way to derive his empirically correct radiation law – the “Boltzmann method”. It was based on a counting method from Boltzmann’s atomic gas theory. In order to “count” radiation, Planck had to divide the energy of the black-body radiation into energy elements. Boltzmann let the size of such packets go to zero at the end of the calculation, obtaining a continuous energy distribution. But this didn’t work for Planck. His energy elements had to have a definite size – the product of the frequency under consideration and a constant h, today known as Planck’s quantum of action.

Planck's formula and its consequences

Planck succeeded in deriving a radiation formula that stood up to all experimental tests. But what is the significance for physics of the energy elements in Planck’s derivation? This question took years to answer and many young scientists worked on it, most notably Albert Einstein. The belief that a complete overhaul of classical physics was needed gained more and more support. However, Planck himself remained sceptical about such a revolutionary idea.

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