ultra-violet catastrophe | A History of Science

1900 – Germany

‘Energy is not a continuous quantity but it is quantised; it flows in discrete packets or quanta. When particles emit energy they do so only in quanta’

According to Quantum theory, the energy (E) of one quantum (photon) is given by E = hf where f is the frequency of radiation and h is Planck’s constant.
Its value is 6.63 x 10^-34 joules per second

h is a tiny number, close to zero, but it is has a finite value. This implies energy is released in discrete chunks, a revolutionary notion.

MAX PLANCK

By the late 1800s the science of thermodynamics was developing to the point that people were beginning to understand the nature of energy.
The traditional view was that energy was released in a continuous stream and that any amount of energy could be indefinitely divided into smaller and smaller ‘lumps’. Planck’s work on the laws of thermodynamics and black body radiation led him to abandon this classical notion of the dynamic principles of energy and formulate the quantum theory, which assumes that energy changes take place in distinct packages, or quanta, that cannot be subdivided. This successfully accounted for certain phenomena that Newtonian theory could not explain.

The basic laws of thermodynamics recognised that energy could not be created or destroyed, but was always conserved. The second law was drawn from an understanding that heat would not pass from a colder body to a hotter body.
The study of thermodynamics was based on the assumption that matter was ultimately composed of particles. LUDWIG BOLTZMAN had proposed an explanation of thermodynamics, saying the energy contained in a system is the collective result of the movements of many tiny particles rattling around. He believed the second law was only valid in a statistical sense; it only worked if you added up all the bits of energy in all the little particles.
Among his detractors was Max Karl Ernst Ludwig Planck.

Planck began his work on the second law of thermodynamics and the concept of entropy. He investigated how materials transform between solid, liquid and gaseous states. In doing so he found explanations for the laws governing the differing freezing and boiling points of various substances.
He also looked at the conduction of electricity through liquid solutions (electrolysis).

In the mid 1890s Planck turned his attention to the question of how heated substances radiate energy. Physicists were aware that all bodies radiate heat at all frequencies – although maximum radiation is emitted only at a certain frequency, which depends on the temperature of the body. The hotter the body, the higher the frequency for maximum radiation. (Frequency is the rate per second of a wave of any form of radiation).

Planck had been considering formulae for the radiation released by a body at high temperature. Using ideas developed by ROBERT KIRCHOFF, he knew it should be expressible as a combination of wavelength frequency and temperature. For a theoretical ‘black body’, physicists could not predict expressions that were in line with the behaviour of hot bodies at high frequencies and were in agreement with other equations showing their nature at low frequencies. Thus no law could be found which fitted all frequencies and obeyed the laws of classical physics simultaneously.
Plank resolved to find a theoretical formula that would work mathematically, even if it did not reflect known physical laws. His first attempts were partially successful, but did not take into account any notion of particles or quanta of energy, as he was certain of the continuous nature of energy. In an ‘act of despair’ he renounced classical physics and embraced quanta.

The final straw had been a concept developed by John Rayleigh and James Jeans that became known as the ‘ultraviolet catastrophe’ theory. They had developed a formula that predicted values for radiation distribution and worked at low frequencies, but not at high frequencies. It was at odds with Planck’s formula, which worked for high frequencies but broke down at low frequencies. In June 1900 Rayleigh had pointed out that classical mechanics, when applied to the oscillators of a black-body, leads to an energy distribution that increases in proportion to the square of the frequency. This conflicted with all known data.

Planck’s answer was to introduce what he called ‘energy elements’ or quanta and to express the energy emitted as a straightforward multiplication of frequency by a constant, which became known as ‘Planck’s constant’ (6.6256 x 10^-34 Jsec^-1). This only works with whole number multiples which means for the formula to have any practical use one must accept the radical theory that energy is only released in distinct, non-divisible chunks, known as ‘quanta’, or for a single chunk of energy, a ‘quantum’. This completely contradicts classical physics, which assumed that energy is emitted in a continuous stream. The individual quanta of energy were so small that when emitted at the everyday large levels observed, it appears that energy could seem to be flowing in a continuous stream.
Thus classical physics was cast into doubt and quantum theory was born.

Planck announced his theory on December 14 1900 in his paper ‘On the Theory of the Law of Energy Distribution in the Continuous Spectrum’. Planck said ‘energy is made up of a completely determinate number of finite equal parts, and for this purpose I use the constant of nature h = 6.55 x 10^-27(erg sec)’

When ALBERT EINSTEIN was able to explain the ‘photoelectric’ effect in 1905, suggesting that light is emitted in quanta called ‘photons’, by applying Planck’s theory – and likewise NIELS BOHR in his explanation of atomic theory in 1913 – the abstract idea was shown to explain physical phenomena.

Planck was awarded the Nobel Prize for Physics in 1918.