The photoelectric effect is taught in almost every physics class but we often forget to say why it is so important. In my opinion, the photoelectric effect is important because Einstein’s photoelectric effect equation was based on a revolutionary new view of light. And I use the word “revolutionary” because it was! Even at the time, Einstein wrote a friend that the paper he was writing deals with “the energy properties of light and is very revolutionary[1]”.
Not only were Einstein’s views radical, every statement in this paper is still considered correct well over 100 years after its publication! Why did Einstein think this way? And why and how did this kick-start the quantum revolution? And how did he do it in the middle of personal drama much of his own making? Well, I’ll tell you.
Table of Contents
Einstein, the Photoelectric Effect, and Mileva’s Child(ren)
Einstein and Lenard
How Quantum Mechanics Started and Flourished
Relativity
References
Einstein, the Photoelectric Effect, and Mileva’s Child(ren)
Let’s begin in April of 1901 when22-year-old Albert Einstein read a paper by a conservative German physicist named Max Planck on how certain heated objects radiate light. Planck included this wild math trick that assumed that light was created in little bundles with an energy equal to a constant, h, times it’s frequency (note, Planck used the Greek letter nu, which looks like a v for frequency, sorry for the confusion).
Einstein was not impressed and wrote his girlfriend, Mileva Marić, “About Max Planck’s studies on radiation, misgivings of a fundamental nature have arisen in my mind, so that I am reading his article with mixed feelings.[2]”Seven days later he was still complaining that Planck’s restriction that the vibrating objects that create light are limited in how they vibrate was, “an assumption I cannot really warm to,[3]” and because of Planck, “my views on the nature of radiation have again sunk back into the sea of haziness.[4]”
By May, Einstein read another paper more to his liking, a former professor of Mileva’s named Philipp Lenard had written about an experiment that proved that shining ultraviolet light on a metal plate would cause electrons to fly off of the plate (this was only a few years after the discovery that something called cathode rays in vacuum tubes were actually beams of electrons). Einstein wrote Mileva, “My dear kitten, I have just read a wonderful paper by Lenard on the generation of cathode rays by ultraviolet light. Under the influence of this beautiful piece I am filled with such happiness and joy that I absolutely must share it with you[5]”.
In the next few years, this phenomenon became known as the photoelectric effect, photo for light and electric for electric. There is no hint in Einstein’s letter of May that he saw any connection between the photoelectric effect and Planck’s energy elements. However, Albert and Mileva had bigger issues; Mileva was pregnant with Albert’s illegitimate child. Albert’s letter about Lenard’s paper abruptly switched from science to comfort, “Be happy and don’t fret darling,” Albert added, “I won’t leave you and will bring everything to a happy conclusion. You just have to be patient![6]”
Mileva had met Albert at the Zurich Polytechnic where she was the only woman studying Physics (and only one of 20 women studying Science or Math in all of Germany and Switzerland![7]). Three years older than Einstein, Mileva had come from Serbia to become a doctor but had switched to Physics. Her grades were fantastic until she fell for Albert. Then, well, not so fantastic.
By 1901, Mileva had failed her exams twice, was pregnant, and went home to confess her troubles to her parents. Meanwhile, Einstein was struggling to get a job (due to his knack and delight in flaunting authority and because of a dose of anti-Semitism) and he refused to marry Mileva without one. Mileva wrote a friend, “Albert has not yet found a job… [and] you know that my darling has a very wicked tongue and on top of it he is a Jew.[8]”
Don’t worry, Albert wrote, “I will look immediately for a position, no matter how humble. My scientific goals and personal vanity will not hinder me from accepting the most subordinate role. The moment I have obtained such a position I’ll marry you… And you, as my little wife can peacefully rest your little head in my lap and will not have to regret the slighted bit the love and devotion you have bestowed upon me.[9]”
But Albert couldn’t find a job and Mileva had her daughter, Lieserl, in secret in the beginning of 1902. Finally, in June, Einstein’s friend got him a job as a Swiss Patent clerk and in January of the following year Mileva went to Bern (leaving the baby with her parents) and married Albert.
In August of 1903, Mileva went on a trip to Serbia and learned that her daughter had scarlet fever and that she had became pregnant again. Albert was mildly concerned about Lieserl but pleased with the pregnancy and told Mileva that, “I’m happy … that you get a new Lieserl.[10]”
Oy! Einstein, darling, you can’t just replace babies! He also told her to hurry home as “a good little wife shouldn’t leave her husband alone[11]” for too long. Also, the place was getting messy, but don’t worry, “You’ll be able to clean up in short order[12].” Sigh. Anyway, it seems that either Lieserl died from the scarlet fever or was secretly adopted away is that is the last anyone heard of her. In May of 1904, Mileva did not get another Lieserl as she had a boy, Hans Albert.
Despite what you might have read or seen, Einstein enjoyed his job as a patent clerk finding it “uncommonly diversified[13]” and easy. In fact, Einstein later recalled that he was able to “do a full day’s work in only one or two hours, [and] the remaining part of the day, I would work out my own ideas… Whenever anybody would come by, I would cram my notes into my desk drawer and pretend to work on my office work”[14].
Einstein and Lenard
In this way, the Einsteins kept up with the latest research and Albert, at least, had a lot of time for thinking of new ideas. At around this time, Einstein read that Phillip Lenard had conducted a new experiment on how ultraviolet light creates electrons in the photoelectric effect that Einstein called “pioneering”[15].
See, Lenard had the very clever idea of placing a counter voltage so that the electrons freed by the ultraviolet light would be pushed back towards the irradiated plate, as Lenard said, “in the same way as a stone thrown upwards falls back to the ground.[16]” Lenard also knew that the voltage to stop the electrons could tell him the top speed of the escaped electrons.
Lenard then found something truly startling, the top speed of the electrons was unaffected by the intensity of the light! Lenard decided that the energy of the electrons did not come from the light but instead the light acted like a trigger to release the inherent energy of the atoms like, “the fuse in firing a loaded gun.[17]”This “triggering” theory of atoms seemed like a good solution and even as late as 1909 it was written as one of the, “generally accepted truths in physics.”[18]
However, in 1904 or so Einstein had a quirky thought: what if the energy of the electrons did come from the light, but the light didn’t act like a typical wave? See, for a typical wave, like a sound wave or a water wave, the higher the intensity, the greater the energy, so more intensity ultraviolet light should be led to higher energy electrons, but that is not what Lenard had observed.
How Quantum Mechanics Started and Flourished
However, Einstein remembered Planck’s paper where Planck assumed that light was created in little energy packets with an energy that depended on the frequency of the light.
Now Planck just did this as a math trick but it got Einstein thinking, what if it was literally true? What if the light acted as a bunch of tiny particles that could only be created, move or absorbed as a whole? Einstein called these particles “quanta” which is a word for units that are indivisible, which is why this branch of Physics is called “Quantum Mechanics” (quantum being the singular of quanta).
In 1905 Einstein wrote, “The assumption to be contemplated here [is that] when a light ray is spreading from a point, the energy is not distributed continuously over ever-increasing spaces, but consists of a finite number of energy quanta that are localized in points in space, move without dividing, and can be absorbed or generated only as a whole.[19]”
This has been called, “the most revolutionary sentence written by a physicist of the twentieth century.[20]” Before this paper, items were either waves or particles, this is the first proposal that light could be both. Light has frequency and creates interference patterns like a wave but it is composed of little energy packets that cannot be split in two, just as electrons cannot be split in two, like particles.
Einstein later described it, “as a kind of fusion of the wave and particle theories of light.[21]” If that makes your brain hurt, you are not alone. Even Einstein never felt comfortable with this and in 1951 wrote his friend Besso, “all these fifty years of pondering have not brought me any closer to answering the question, What are light quanta?[22]”
Despite not really getting what light quanta are, Einstein found that the odd counter-intuitive idea of waves acting like particles could be used to explain all sorts of phenomena, including the photoelectric effect. Einstein decided that in the photoelectric effect electrons on the plate are “stuck” to the metal by electric forces and can only be removed by giving them a certain amount of energy, which they get from absorbing the energy of the incoming light. [Side note: some electrons are under the surface and some are on the surface so that the freed electrons have varying energy but the metal needs a minimum amount of energy to free even the surface electrons.]
Einstein then postulated that the light comes in little packets of energy where the brighter the light, the more packets, but the individual light packets (photons) have the same energy. If the frequency is too low, the light photons have less energy then the binding energy of the surface electrons to the metal and no electrons will be freed from the plate, no matter how many packets you throw at the plate.
This is why you need high frequency light to create the photoelectric effect (also why UV light causes sunburns and visible light does not). Above this threshold, the more intense the light, the more electrons are freed, but the electrons all have the same maximum energy (the energy of the photon of light minus the minimum energy to free the electron).
According to Planck’s equation, the energy of light is Planck’s constant, h, times the frequency, and, according to Einstein, the minimum energy to be free of the metal is a constant of the metal. Einstein also knew from energy conservation that the voltage to stop all the electrons from moving times the charge on the electron equals the maximum kinetic energy of the electrons.
Thus, Einstein created the equation for the photoelectric effect. Interestingly, for any metal there are only two variables in this equation, the stopping voltage and the frequency. Therefore, if you graph the stopping voltage vs. the frequency of the light you should get a straight line no matter what material you use for the plate!
Even more impressively, the slope of that line can give you Planck’s constant, h. Einstein found a way to prove that light comes in little packets with energy equal to Planck’s constant times the frequency of the light and found a new experiment that would find a fundamental constant of nature! You might think that some experimentalists would have jumped at this.
However, the experiment was notoriously difficult to accurately conduct and at the time and no one was that interested in what an annoying patent clerk (third class) had to say on the subject anyway. In fact, it took nine years for any scientist to successfully attempt this experiment, whereupon the scientist, Robert Millikan, of the oil drop experiment fame, found his results were a “complete success of the Einstein equation[23]” (although Millikan continued to reject what he called the “bold not to say reckless[24]” theory behind it.)
A comment about Mileva in all this. It is clear that she helped her husband with his papers at this time and sometimes both Albert and Mileva had called it “our work” in letters to each other andAlbert had also told Mileva’s friends, “I need my wife, she solves all the mathematical problems for me.[25]”
There are no mentions, however, of Albert attributing any idea to his wife. Is this because she did not contribute or because he was pretty sexist and considered her basically his “student” (as he affectionately called her) and her contributions did not need to be mentioned? That was how it was portrayed in the mostly excellent 2017 TV show “Genius”. It also should not be discounted that Einstein was attempting to be noticed by the academic community of 1900s Germany, not a place where he would be respected for acknowledging the intellectual support of ones wife!
Anyway, as I said in the beginning, Einstein thought correctly that this paper was “very revolutionary” and was not surprised to find that it did not go very far at first. He had higher hopes for his next paper on Brownian motion that proved the existence of atoms but that too was published but didn’t get him much recognition.
Relativity
His next paper was on a strange idea called relativity. That was the paper that got the attention of some prominent scientists, like Lorentz and oddly enough Planck (who loved relativity and fought against quantum mechanics that Planck himself accidentally initiated). In addition, that same year, Einstein published an addendum to his relativity paper, an “amusing and seductive” thought that the “relativity principle, together with Maxwell’s equations, requires that mass be a direct measure of the energy contained in a body[26].” In other words, Einstein published that E = mc^2.
One would think that any of these four papers would be enough to catapult Einstein into scientific stardom. After all, that year 1905 is considered so influential from him that it is called a “miracle year” in science (like 1666 for Newton). However, it was a really slow burn. It took until 1909 for Einstein to even get a professorship and it wasn’t until the following year, 1910 that Einstein became famous among scientists, and at the time mostly famous for quantum mechanics, not relativity.
In fact, his 1911 talk at the first Solvay conference was on quantum mechanics. How did Einstein become famous? And what did it have to do with the third law of thermodynamics and absolute zero temperature? That is next time on the Lightning Tamers.
References
[1] Albert Einstein to Conrad Habicht (June/Sept 1905) (found in Isaaccson, W Einstein (2008) p. 138)
[2] Einstein, A to Maric, M (April 4, 1901) found in Einstein, A The Collected Papers of Albert Einstein: The early years, 1897-1902 (1987) Princeton University Press p. 162
[3] Einstein, A to Maric, M (April 10, 1901) found in Einstein, A The Collected Papers of Albert Einstein: The early years, 1897-1902 (1987) Princeton University Press p. 163
[4] Einstein, A to Maric, M (April 10, 1901) found in Einstein, A The Collected Papers of Albert Einstein: The early years, 1897-1902 (1987) Princeton University Press p. 163
[5] Einstein, A to Maric, M (May 28, 1901) translated and found in Highfield, R and Carter, R The Private Lives of Albert Einstein (1994) Macmillan p. 77
[6] Einstein, A to Maric, M (May 28, 1901) translated and found in Highfield, R and Carter, R The Private Lives of Albert Einstein (1994) Macmillan p. 77
[7]p 21 “Mileva Maric Einstein: Life with Albert Einstein” RadmilaMilentjevic
[8]Maric, M to Savic, H 1901, translated and found in Maric, M In Albert’s Shadow: The Life and Letters of Mileva Maric, Einstein’s First Wife (2001) p. 79
[9] Einstein, A to Maric, M (July 7, 1901) found in Einstein, A The Collected Papers of Albert Einstein: The early years, 1897-1902 (1987) Princeton University Press p. 176
[10]as recounted p 88 “Einstein” Walter Isaacson
[11]as recounted p 88 “Einstein” Walter Isaacson
[12]as recounted p 88 “Einstein” Walter Isaacson
[13] Albert Einstein to Hans Wolhwend (1902) Found in Isaacson, W Einstein (2008) p. 78
[14] Albert Einstein to Peter Bucky found in Bucky, P, Einstein, A, Weakland, A The Private Albert Einstein (1992) p. 28
[15]Einstain, A “On a Heuristic Point of View Concerning the Production and Transformation of Light” Translated and found in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 2 Princeton University Press p. 99
[16] Lenard, P “On Cathode Rays” Nobel Lecture (May 28, 1906) p. 122
[17]p 123 “On Cathode Rays” Nobel Prize Speech 1905 Lenard
[18] Ladenburg, R translated by Wheaton, B “Philipp Lenard and the Photoelectric Effect, 1889-1911” Historical Studies in the Physical Sciences Vol. 9 (1978) p. 319
[19]Einstain, A “On a Heuristic Point of View Concerning the Production and Transformation of Light” Translated and found in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 2 Princeton University Press p. 87
[20]Folsing, ?Albert Einstein p. 143
[21] Einstein, A (1909) found in Stone, A Einstein and the Quantum (2013) p. 137
[22] Einstein, A to Besso, M (Dec 12, 1951) from the Albert Einstein Archives vol 7 p. 401 (found in Isaaccson, W Einstein (2008) p. 101)
[23] Millikan, R “A Direct Photoelectric Determination of Planck’s “h”” Physical Review Vol 7, No. 3 p. 384
[24] Millikan, R “A Direct Photoelectric Determination of Planck’s “h”” Physical Review Vol 7, No. 3 p. 355
[25]p 135 “Einstein” Walter Isaacson
[26] Albert Einstein to Conrad Habicht (June/Sept 1905) (found in Isaaccson, W Einstein (2008) p. 138)