Einstein's papers on the photoelectric effect and Brownian motion
The photoelectric effect [1]
James Clerk Maxwell had shown that light is an electronic wave, and in the late 1800s it was noticed that when a charged metal plate was illuminated by ultraviolet light it would begin to emit electrons, but no one could quite determine why. According to the classical theory of light and matter, the strength or amplitude of a light wave was in proportion to its brightness: a bright light should have been easily strong enough to create a large current.
Yet, oddly, this was not so. The speeds of the electrons emitted didn’t change when you increase the brightness. Increasing the brightness of the light only increased the number of the low-energy photons, not their energy. Without quite knowing why, but adopting the statistical approach pioneered by Ludwig Boltzmann and basing his findings on his observations in his study of black body radiation, Planck had proposed that the atoms (electrons) ejected from a black body could only emit light energy in packets, the amount of energy in each packet increasing at shorter wavelengths. [2]
Light is a particle as well as a wave
In his paper on the photoelectric effect, for which he won the Noble Prize in 1922[3], Einstein resolved this unsolved puzzle by postulating that electrons can receive energy from an electromagnetic field only in discrete portions (quanta) rather than continuous levels. Building on Planck’s equation:
E=hf
where E = the photon's energy, h = Planck's constant (h = 6.6 x10-34) and f = the photon's frequency,
Einstein said that not just the energy released from the black body came in quanta as Planck hypothesised, but that light itself is not only a wave, but a collection of discrete wave packets (photons) each with energy hf. Photons with low frequencies, like radio waves, have lower energies than photons with high frequencies, like x-rays.
This explained why light can eject electrons from certain metals even if its intensity (brightness) is low, and why bright red light with very low frequencies caused no electrons to escape. At higher frequencies photons have more energy, and at lower frequencies they have less energy. In other words, unlike a wave which can give some or all of its energy to an object, photons can only give all their energy or none, so an electron in the metal can either absorb all the photon's energy (allowing it to escape the metal) or none. Making the photons more intense (in other words, more of them) would have no effect if the frequency wasn't high enough. "Because one photon effectively boots out one electron, Einstein realised that the photon behaves like a particle and not a wave".[4]
Because the frequency of the wave multiplied by Planck's constant, is a unit so small that it is beyond the capacity of the human mind to grasp (just as we can't appreciate the speed of light because it is so far out of the range of our own worldly experience), many physicists still find it easier to think in terms of light’s wavelength rather than its frequency.[5]
Einstein generalises from Planck’s insight
Einstein's methodology was to start by showing why existing equations couldn’t really be applied to the problem of the radiation of objects. The old equations worked fine in the low energy region, but they failed in the high energy region. Starting from basic physics principles, Einstein demonstrated that the radiation of hot objects behaves as if it were made up of separate quanta (bundles or packets) of energy and the shorter the wavelength, the larger the value of the energy. Einstein then declared that matter and radiation can interact only by exchanging these energy quanta.
In other words, light, and indeed all electromagnetic radiation, is made up of quanta of energy: bundles or packets with energies that are related to the wavelength of the light, and, again, the shorter the wavelength, the larger the amount of energy of a light quantum, or photon. These photons cannot be split.
With Einstein’s new view of the nature of light, Planck’s radiation law became the accepted explanation for the radiation of hot objects, postulating that the thermal energy emitted by an object comes from charged particles oscillating inside the object and that these oscillations have only some specific energies.
Planck’s great insight, validated by Einstein’s generalisation, was to realise that the energies are related to the different wavelengths of the light emitted by the oscillators, and instead of assuming that the energies are all equally distributed, light and all electromagnetic radiation are made up of quanta. Einstein went even further, concluding not only that light has the dual character of being a wave and a particle, but that matter also shows the same duality: matter should also have wavelike behaviour.
In other words, light, and all forms of radiation and matter itself are “quantised”, and the “step size” of these quanta is determined by Planck’s constant: radiations of shorter wavelengths carry more energy (larger steps) and are identical to each other, but those radiations are different from the ones that consist of larger wavelengths [6].
[1] From Brian Koberlein’s, The photoelectric effect, https://briankoberlein.com/2015/05/06/bit-by-bit/ 6 May 2015 and other sources. See also "Einstein's explanation of the photoelectric effect": en.wikipedia.org/wiki/Wave%E2%80%93particle_duality
[2] Carlos I, Calle Einstein For Dummies (Kindle Location 4132-4151). Wiley. Kindle Edition.
[3] “On a heuristic point of view concerning the production and transformation of light”, "heuristic" meaning essentially “serving to guide, valuable for empirical research, but unproved or incapable of proof”: Carlos I Calle, Einstein for Dummies, 9Kindle Locations 4125-4126), Wiley, Kindle edition.
[4] Journeyman Philosopher site: http://journeymanphilosopher.blogspot.com.au/2011/05/trying-to-understand-schrodingers.html ; Carlos I Calle, op cit, Locs 4080-4085.
[5] Associate Professor Michael Box WEA lecture series What are atoms made of?, Session 1, 26 October 2016.
[6] The foregoing is an edited summary from Carlos I Calle's Einstein for Dummies, (Kindle Locations 4062-4124; Locations 4168-4169, Wiley, 2005, Kindle edition.
Brownian motion
Einstein’s second paper on Brownian motion[1] explained why tiny pollen grains in water, each only about 1/5000 of an inch in size, constantly jiggled about, remaining in motion indefinitely no matter how much time the solution was given to settle. This, said Einstein, is because, viewed under a microscope, they are constantly being knocked about by large numbers of molecules in the water. The heat in the water at room temperature causes the molecules to move about, and Einstein found that he could estimate the number of molecules hitting a single pollen grain, the size of the individual molecules and how fast they moved about[2].
The same thing happens when you put drops of food colouring in water: it spreads out over time. This is due to the fact that the colouring is bouncing around with the water molecules. Since the molecule collisions are random, the colouring also moves in a random pattern, something like taking a step, then turning randomly in a different direction and taking another. On average the position of the colouring stays the same, but by chance some drifts outward, and over time the colouring becomes more diffuse[3], something like the image at right:
At the time many scientists did not believe water was composed of molecules, and did not believe matter was composed of atoms either. Einstein demonstrated their existence and showed that he could measure the size of a sugar molecule, even if inaccurately, in another paper “A new determination of molecular dimensions” submitted to the Annalen der physik in April 1905[4].
Einstein’s two “lesser” papers, one on Brownian motion, which became the foundation stone for his Ph D thesis and the other on the viscosity of sugar molecules, are among the most frequently cited of Einstein papers[5]. In his commentary, Carlos Calle says that Einstein confronted the Brownian motion issue by exploring “the erratic, zigzag motion of the individual particles of smoke”, rather than the diffusion of particles in a fluid. Either way, Einstein’s methodology provided direct evidence of the existence of molecules and atoms, and “by exploring the zigzagging of the smoke specs and the diffusion of sugar in water”, he managed to come up with an equation that he then applied to the already developed molecular theory to obtain the sizes of atoms and molecules and also found a value for the number of molecules in a certain mass of any substance (Avogadro’s number). With this number, he was then able to calculate the mass of any atom.
As Calle goes on to note, although not revolutionary, these two papers have practical applications in the mixing of sand in cement, the motion of certain important proteins in cow’s milk, and the motion of aerosol particles in the atmosphere[6].
[1] Named after the Scottish botanist Robert Brown’s discovery in 1827 - a botanist be it noted, not a chemist: see Bill Bryson, A Short History of Nearly Everything, Broadway Books, 2003, 102.
[2] See Lisa Wade McCormick, Albert Einstein, Angus & Robertson, 47-49; Gary Moring, The Complete Idiot’s Guide to Understanding Einstein, 159-161, Penguin; also available as an eBook.
[3] Brian Koberlein, Einstein’s theory of Brownian Motion, https://briankoberlein.com/2015/05/05/shake-rattle-and-roll/ 5 May 2015. Illustrative source from the same article: Wikipedia
[4] Lisa Wade McCormick, op cit, 46-47. On the inaccuracy of Einstein’s calculations, see Philip Ball, Claiming Einstein for Chemistry, http://www.rsc.org/chemistryworld/Issues/2005/September/einstein.asp
[5] Dr Carlos I. Calle, Einstein For Dummies, Wiley, 2005. Kindle Edition, Loc 972-1002.
[6] Ibid.
Einstein’s second paper on Brownian motion[1] explained why tiny pollen grains in water, each only about 1/5000 of an inch in size, constantly jiggled about, remaining in motion indefinitely no matter how much time the solution was given to settle. This, said Einstein, is because, viewed under a microscope, they are constantly being knocked about by large numbers of molecules in the water. The heat in the water at room temperature causes the molecules to move about, and Einstein found that he could estimate the number of molecules hitting a single pollen grain, the size of the individual molecules and how fast they moved about[2].
The same thing happens when you put drops of food colouring in water: it spreads out over time. This is due to the fact that the colouring is bouncing around with the water molecules. Since the molecule collisions are random, the colouring also moves in a random pattern, something like taking a step, then turning randomly in a different direction and taking another. On average the position of the colouring stays the same, but by chance some drifts outward, and over time the colouring becomes more diffuse[3], something like the image at right:
At the time many scientists did not believe water was composed of molecules, and did not believe matter was composed of atoms either. Einstein demonstrated their existence and showed that he could measure the size of a sugar molecule, even if inaccurately, in another paper “A new determination of molecular dimensions” submitted to the Annalen der physik in April 1905[4].
Einstein’s two “lesser” papers, one on Brownian motion, which became the foundation stone for his Ph D thesis and the other on the viscosity of sugar molecules, are among the most frequently cited of Einstein papers[5]. In his commentary, Carlos Calle says that Einstein confronted the Brownian motion issue by exploring “the erratic, zigzag motion of the individual particles of smoke”, rather than the diffusion of particles in a fluid. Either way, Einstein’s methodology provided direct evidence of the existence of molecules and atoms, and “by exploring the zigzagging of the smoke specs and the diffusion of sugar in water”, he managed to come up with an equation that he then applied to the already developed molecular theory to obtain the sizes of atoms and molecules and also found a value for the number of molecules in a certain mass of any substance (Avogadro’s number). With this number, he was then able to calculate the mass of any atom.
As Calle goes on to note, although not revolutionary, these two papers have practical applications in the mixing of sand in cement, the motion of certain important proteins in cow’s milk, and the motion of aerosol particles in the atmosphere[6].
[1] Named after the Scottish botanist Robert Brown’s discovery in 1827 - a botanist be it noted, not a chemist: see Bill Bryson, A Short History of Nearly Everything, Broadway Books, 2003, 102.
[2] See Lisa Wade McCormick, Albert Einstein, Angus & Robertson, 47-49; Gary Moring, The Complete Idiot’s Guide to Understanding Einstein, 159-161, Penguin; also available as an eBook.
[3] Brian Koberlein, Einstein’s theory of Brownian Motion, https://briankoberlein.com/2015/05/05/shake-rattle-and-roll/ 5 May 2015. Illustrative source from the same article: Wikipedia
[4] Lisa Wade McCormick, op cit, 46-47. On the inaccuracy of Einstein’s calculations, see Philip Ball, Claiming Einstein for Chemistry, http://www.rsc.org/chemistryworld/Issues/2005/September/einstein.asp
[5] Dr Carlos I. Calle, Einstein For Dummies, Wiley, 2005. Kindle Edition, Loc 972-1002.
[6] Ibid.