Quantisation of energy

In the 1800s, blackbodies were studied in this manner, and it was noted that the distribution of the electromagnetic spectrum was not dependent on the material; only the temperature played a role. With increasing temperature, the peak wavelength would shift left and move into the visible spectrum at around 4000K and above. Objects at these temperatures emit a lot of visible light.

Issues arose when scientists attempted to model this distribution using classical mathematical models. They were able to fit the experimental data accurately for the longer wavelengths; however, these models did not predict that the intensity would decrease in the UV portion of the spectrum, as observed in the experimental data. The maths, which followed Rayleigh-Jeans law, predicted that the intensity at shorter wavelengths would become infinitely large.

This did not align with what was observed in reality, and so the contradiction was dubbed ‘the Ultraviolet Catastrophe’. Here, we started to see some of the limitations of classical electromagnetism.

Comparison of Rayleigh-Jean’s law (classical theory) and the curve predicted by Planck’s radiation formula. [Ref: Ultraviolet catastrophe wiki ]

POV: Rayleigh-Jeans law holds true for even short wavelengths and you are incinerated with an infinitely intense blast of UV radiation every time you try to heat up a potato waffle.

Max Plank was able to solve this problem when he introduced the quantisation of energy. Heat is transfer of kinetic energy from one equilibrium to another. In the case of metals, this kinetic energy takes the form of atomic vibrations. These vibrations are what generate the light we see in the blackbody spectrum. Planck proposed that the vibrational energy of these atoms must be quantised, meaning that they can only take on specific discrete values, rather than continuous ones. He proposed an expression for blackbody radiation:

where $h$ is Planck’s constant ($6.626 \times 10^{-34} J \cdot s$) and $f$ is the frequency of radiation.

$n$ is always an integer, meaning that the resulting energies will be quantised, forming a set of specific values with anything in between being forbidden. This equation enabled a precise explanation of blackbody radiation across the entire spectrum.

Planck’s constant is super small, which is why the idea of the quantisation of energy had not been discovered previously. The energy difference between the allowed energy levels is so minute that there was no measurement tool or apparatus that could make such a measurement. Energy appears to be continuous on the macroscopic level, but fundamentally, it is quantised. While the quantisation of energy allowed us to solve some problems, it also created a whole new set of problems. The big question being: why is energy quantised? This marked the beginning of the quantum revolution.

References and further reading

Lumen Learning - radiation

Hyperphysics - blackbody radiation

Blackbody radiation wiki

Ultraviolet catastrophe wiki