The beginnings of quantum mechanics
The problem
At the beginning of the twentieth century, there were two rival theories to explain the phenomenon known as black body radiation - the hypothetical situation that a dark body absorbs all the electromagnetic radiation which falls upon it (in contrast say to a paler body) until it becomes a pure emitter of radiation - one theory was effective at longer wavelengths and lower energies, the other at shorter wavelengths and higher energies. However, neither theory could match the overall distribution of radiation measured from such a body in the laboratory. At this time, the prevailing view was that the thermal energy emitted by an object was formed by the continuous changes in energy of charged particles oscillating within the matter.[1]
The problem that physicists hadn’t been able to solve was in the short wave length, high-energy region, where their equations were giving them infinities or nonsense answers. What physicists were observing was that at short wavelengths, the energy distributions actually grew smaller and smaller. Because these very short wavelengths were in the ultraviolet part of the spectrum, this gave rise to what was known as the ultraviolet catastrophe, which predicted that black bodies should radiate more energy at short wavelengths, but the observations showed that these bodies emitted less energy. [2]
Enter Max Planck
In 1900, Max Planck, a professor of physics at the University of Munich, used Maxwell’s electromagnetism and Boltzmann’s technique of counting energy in discrete increments in his work on the second law of thermodynamics to develop a theory that connected the heat or thermal energy of the radiating body with the charged oscillating particles. To do this, he first had to split the total energy being radiated from an object into a number of arbitrarily small but finite bundles or packets all with the same energy, and then use the statistical methods that Ludwig Boltzmann had invented for the distribution of energies in molecular collisions by counting the possible ways of distributing these bundles among all the oscillating particles.[3]
Planck hypothesised that because the energy (E) released by a black body must ultimately come from within the body itself, it would not be released at any old frequency (f) but only at well-defined and separated or discrete wavelengths, in other words packets known as “quanta”, each related to a constant number called h known as Planck’s constant[4], the important feature of which is that, although almost infinitesimally small, it was a non-zero number. In the high frequency region of the black body curve, the quanta are so large that only a few vibration modes are excited and the radiation drops off to zero, so the ultraviolet catastrophe does not occur.[4.1]
In other words, what Planck did was to assume that atoms could only vibrate at certain frequencies that were whole number multiples of this base frequency, h: 2h, or 3h - but not 2.5h, and by choosing the size of the lumps appropriately, he was able to arrive at a formula which matched the data. In the process he correctly predicted blackbody emissions and h subsequently became known as the Planck Constant. A black body’s temperature is therefore related to the intensity of the energy radiated by it at a given wavelength: E = hf [5]. This is now known as Planck's law.
It's a bit like saying that you can't buy sugar loose in the supermarket, it has to be in kilogram bags, says Stephen Hawking. "The energy in the packets or quanta is higher for ultra-violet and X-rays than for infrared or visible light. It means that unless a body is very hot, like the Sun, it will not have enough energy to give off even a single quantum of ultra-violet or X-rays". [5.1]
Since 2019, the numerical value of the Planck constant has been fixed, with infinite significant figures.
Planck's legacy
At the time, Planck regarded the idea of quanta as just a mathematical trick, and not as having any physical reality.[5.2] However, what he had achieved was to encapsulate thermodynamics, electrodynamics and classical mechanics in the one package, giving birth to a whole new world, where light, energy and indeed matter itself were recognised as being composed of particles, quanta and waves at the same time. "Planck’s great insight, validated by Einstein’s (later) generalisation, was to realize that the energies are related to the different wavelengths of the light emitted by the oscillators, instead of assuming that the energies are all equally distributed, like previous theories had done. Einstein’s great insight was to make this idea a fundamental property of nature. Light and all electromagnetic radiation are made up of quanta; light is 'quantised.' [6]
Another illustration: the energy of the electron
One illustration of this new approach came in 1913, the year in which the Danish physicist Niels Bohr came up with a new model of the atom in which the electrons orbit the nucleus in very specific orbits that he called stationary orbits[7] Under this scenario, no intermediate orbits are allowed. Whilst in this stationary state, the electrons don’t radiate any energy.
However, under Bohr’s theory the electrons are allowed to move between orbits. When they jump to a lower orbit, they give off energy, but if they gain energy, they jump to a higher orbit. The energies that the electrons give off or gain when they jump around in their orbits are Planck’s bundles or quanta. Electrons are allowed to give off or gain energy only in the form of these quanta. Bohr used Planck’s theory to calculate the energies of the allowed stationary orbits for the atom, and when he compared his calculations with experimental data, his theory agreed exactly.[8]
[1] For the foregoing, see Adam Hart-Davis, Science – The Definitive Visual Guide, DK, London , 2009, 314. Also Crease, op cit, 125. For what follows, the topic "Wave-particle duality" on the site en.wikipedia.org/wiki/Wave%E2%80%93particle_duality is also worth a look, especially the section on "Radiation quantization".
[2] Carlos I. Calle, Einstein For Dummies (Kindle Locations 3977-4071). Wiley, 2005. Kindle Edition
[3] Ibid, loc 4023; JP McEvoy, Introducing Quantum Theory: A Graphic Guide, Icon Books Ltd. Kindle Edition, location 423.
[4] (h = 6.6 x 10-34)
[4.1] JP McEvoy, op cit, loc 424ff.
[5] The ‘lumpiness of energy’ is explained by Brian Greene in The Elegant Universe (1999) at 88 ff.
[5.1] Posthumous memoire, Brief Answers to the Big Questions, John Murray, London, 2018, 92.
[5.2] Ibid.
[6] Carlos I Calle, Einstein For Dummies (Kindle Locations 4119-4122). Wiley, 2005 . Kindle Edition.
[7] See his paper "On the Constitution of Atoms and Molecules", Philosophical Magazine and Journal of Science, Series 6, Volume 26, Issue 151, July 1913. Bohr won the Noble Prize in Physics for his insight. See also Particles and Forces.
[8] Calle, op cit, Locs 4035-4052.
At the beginning of the twentieth century, there were two rival theories to explain the phenomenon known as black body radiation - the hypothetical situation that a dark body absorbs all the electromagnetic radiation which falls upon it (in contrast say to a paler body) until it becomes a pure emitter of radiation - one theory was effective at longer wavelengths and lower energies, the other at shorter wavelengths and higher energies. However, neither theory could match the overall distribution of radiation measured from such a body in the laboratory. At this time, the prevailing view was that the thermal energy emitted by an object was formed by the continuous changes in energy of charged particles oscillating within the matter.[1]
The problem that physicists hadn’t been able to solve was in the short wave length, high-energy region, where their equations were giving them infinities or nonsense answers. What physicists were observing was that at short wavelengths, the energy distributions actually grew smaller and smaller. Because these very short wavelengths were in the ultraviolet part of the spectrum, this gave rise to what was known as the ultraviolet catastrophe, which predicted that black bodies should radiate more energy at short wavelengths, but the observations showed that these bodies emitted less energy. [2]
Enter Max Planck
In 1900, Max Planck, a professor of physics at the University of Munich, used Maxwell’s electromagnetism and Boltzmann’s technique of counting energy in discrete increments in his work on the second law of thermodynamics to develop a theory that connected the heat or thermal energy of the radiating body with the charged oscillating particles. To do this, he first had to split the total energy being radiated from an object into a number of arbitrarily small but finite bundles or packets all with the same energy, and then use the statistical methods that Ludwig Boltzmann had invented for the distribution of energies in molecular collisions by counting the possible ways of distributing these bundles among all the oscillating particles.[3]
Planck hypothesised that because the energy (E) released by a black body must ultimately come from within the body itself, it would not be released at any old frequency (f) but only at well-defined and separated or discrete wavelengths, in other words packets known as “quanta”, each related to a constant number called h known as Planck’s constant[4], the important feature of which is that, although almost infinitesimally small, it was a non-zero number. In the high frequency region of the black body curve, the quanta are so large that only a few vibration modes are excited and the radiation drops off to zero, so the ultraviolet catastrophe does not occur.[4.1]
In other words, what Planck did was to assume that atoms could only vibrate at certain frequencies that were whole number multiples of this base frequency, h: 2h, or 3h - but not 2.5h, and by choosing the size of the lumps appropriately, he was able to arrive at a formula which matched the data. In the process he correctly predicted blackbody emissions and h subsequently became known as the Planck Constant. A black body’s temperature is therefore related to the intensity of the energy radiated by it at a given wavelength: E = hf [5]. This is now known as Planck's law.
It's a bit like saying that you can't buy sugar loose in the supermarket, it has to be in kilogram bags, says Stephen Hawking. "The energy in the packets or quanta is higher for ultra-violet and X-rays than for infrared or visible light. It means that unless a body is very hot, like the Sun, it will not have enough energy to give off even a single quantum of ultra-violet or X-rays". [5.1]
Since 2019, the numerical value of the Planck constant has been fixed, with infinite significant figures.
Planck's legacy
At the time, Planck regarded the idea of quanta as just a mathematical trick, and not as having any physical reality.[5.2] However, what he had achieved was to encapsulate thermodynamics, electrodynamics and classical mechanics in the one package, giving birth to a whole new world, where light, energy and indeed matter itself were recognised as being composed of particles, quanta and waves at the same time. "Planck’s great insight, validated by Einstein’s (later) generalisation, was to realize that the energies are related to the different wavelengths of the light emitted by the oscillators, instead of assuming that the energies are all equally distributed, like previous theories had done. Einstein’s great insight was to make this idea a fundamental property of nature. Light and all electromagnetic radiation are made up of quanta; light is 'quantised.' [6]
Another illustration: the energy of the electron
One illustration of this new approach came in 1913, the year in which the Danish physicist Niels Bohr came up with a new model of the atom in which the electrons orbit the nucleus in very specific orbits that he called stationary orbits[7] Under this scenario, no intermediate orbits are allowed. Whilst in this stationary state, the electrons don’t radiate any energy.
However, under Bohr’s theory the electrons are allowed to move between orbits. When they jump to a lower orbit, they give off energy, but if they gain energy, they jump to a higher orbit. The energies that the electrons give off or gain when they jump around in their orbits are Planck’s bundles or quanta. Electrons are allowed to give off or gain energy only in the form of these quanta. Bohr used Planck’s theory to calculate the energies of the allowed stationary orbits for the atom, and when he compared his calculations with experimental data, his theory agreed exactly.[8]
[1] For the foregoing, see Adam Hart-Davis, Science – The Definitive Visual Guide, DK, London , 2009, 314. Also Crease, op cit, 125. For what follows, the topic "Wave-particle duality" on the site en.wikipedia.org/wiki/Wave%E2%80%93particle_duality is also worth a look, especially the section on "Radiation quantization".
[2] Carlos I. Calle, Einstein For Dummies (Kindle Locations 3977-4071). Wiley, 2005. Kindle Edition
[3] Ibid, loc 4023; JP McEvoy, Introducing Quantum Theory: A Graphic Guide, Icon Books Ltd. Kindle Edition, location 423.
[4] (h = 6.6 x 10-34)
[4.1] JP McEvoy, op cit, loc 424ff.
[5] The ‘lumpiness of energy’ is explained by Brian Greene in The Elegant Universe (1999) at 88 ff.
[5.1] Posthumous memoire, Brief Answers to the Big Questions, John Murray, London, 2018, 92.
[5.2] Ibid.
[6] Carlos I Calle, Einstein For Dummies (Kindle Locations 4119-4122). Wiley, 2005 . Kindle Edition.
[7] See his paper "On the Constitution of Atoms and Molecules", Philosophical Magazine and Journal of Science, Series 6, Volume 26, Issue 151, July 1913. Bohr won the Noble Prize in Physics for his insight. See also Particles and Forces.
[8] Calle, op cit, Locs 4035-4052.