The Birth Of Quantum Mechanics - The Ultraviolet Catastrophe
The Ultraviolet Catastrophe
At the end of the 1900s, a Physicist called Lord Rayleigh wanted to figure out how things glowed. Hot objects emit electromagnetic waves and he wanted to understand what was going on and how to predict what colours of light would be emitted.
If you turn on an oven and heated it to 500°C, it would mostly emit long wavelength electromagnetic waves. Using classical physics, Rayleigh and his colleage James Jeans calculated that the total energy carried by the electromagnetic radiation in this oven would be infinite. A strange answer considering we don't get blasted by gamma rays each time we use our ovens...
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| This Graph shows that as the wavelength of light decreases, the light intensity approached infinity |
James Clerk Maxwell's electromagnetic theory meant that the waves generated by an oven must have a whole number of peaks and troughs. This means you can only have complete waves and no half waves, quarter waves or anything in between. If the oven is 1 metre wide. There can be waves with a wavelength of 1m, 0.5m, 0.3m, 0.25m, 0.2m etc... (1/1m, 1/2m, 1/3m, 1/4m etc...). The wavelengths can get shorter and shorter which means the frequencies get higher and higher. 19th century thermodynamics meant that Physicists thought that the amplitude of an electromagnetic wave determined its energy. If you consider a baseball swing this is only logical. The energy given to each ball is determined by the amplitude of the swing (how hard you swing) and not the frequency of your swings (how often you swing). This means each wavelength carried an equal amount of energy if they all had the same amplitude.
This results in a huge issue. You can always decrease the wavelength of the EM wave and so there are an infinite number of available waves to put in the oven. All waves carry the same energy, since they have the same amplitude, and so there is an infinite amount of energy.
It is called the ultraviolet catastrophe because the assumptions they made worked for long wavelengths of EM waves, but as the wavelengths shortened, the predictions diverged away from observations. By the time the wavelengths were in the ultraviolet part of the spectrum, it was predicted that there would be infinite energy.
In 1900 Max Planck was studying why heat flowed from hot to cold. In this work he guessed that EM waves in the oven would have to come in chunks. When he assumed this, he solved the ultraviolet catastrophe.
He predicted that there is a smallest amount of energy and that energy from EM waves can only come in multiples of this. This is like having a smallest denomination of money. You can't have half a penny. You can't have a quarter of a penny. You can only have money in multiples of the penny,e.g, 5p, 10p, 50p, £1 etc... He also suggested that the minimum energy of a wave is proportional to its frequency. This guess which seemed wild at the time managed to solve the problem.
The number used to describe the smallest amount of energy was h (Planck's constant - 6.63 x 10-34). This multiplied by the frequency of the wave would give the minimum energy a wave of any wavelength could have.
Imagine energy as a debt. You and an infinite number of friends each owe £10 to a bank that can't give change. Using classical physics, all of you carry £5, you all pay £5 and the bank collects infinite money. This is analogous to each EM wavelength carrying the same amount of energy and so each contributes one contributes. This is because the energy was supposedly determined by the amplitude.
If we use Plank's guess we can solve the problem however. Instead lets redistribute the money so one person has all the pennies, one with the 2ps, one with the 5ps, one with the 10ps etc... Everyone carrying money in denominations equal to and less than £10 (1ps, 2ps, 5ps, .... £10s) can pay the bank exactly £10. Everyone else can't pay since the bank doesn't give change and they can't split their money. This means the bank does not receive infinite money. The bank only collects money from people who carry their money in £10's or less.
This is what happens with EM waves. High frequency waves carry too much energy in each photon. These photon's can't be split further once the waves are reduced to one photon and so they can't contribute to the total energy in the oven. High frequency waves lie dormant in the oven while low frequency, low energy waves "pay most of the debt".
Planck did not know what his discovery meant immediately however. If we liken the problem to one in the maths homework you can't do; he looked at his wrong answer and performed multiplication and addition until he reached the right answer. 18 years later Einstein discovered the photoelectric effect and realised that the discrete packets of energy that Planck said EM waves came in was the photon.
Seeing that light was seemingly a particle, even though previous Physicists said it was a wave, was the start of quantum mechanics.
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Seeing that light was seemingly a particle, even though previous Physicists said it was a wave, was the start of quantum mechanics.
Thanks for reading. If you enjoyed this post or any of my others, follow and subscribe to my blog. Feel free to discuss anything related to this post or ask questions in the comments below.
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