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Einstein and the photoelectric effect

Albert Einstein
Albert Einstein

Mention Albert Einstein and the first thing that springs to mind is the theory of relativity, that other extraordinary supernova that burst upon 20th-century physics. Yet, incredibly, Einstein never won a Nobel Prize for relativity. His one Nobel medal (he surely should have got at least two), awarded in 1921 and presented in 1922, was for his pioneering work in quantum theory. If Planck hadn't fathered quantum theory (see Max Planck and the origins of quantum theory) that role may well have fallen to Einstein. As it was, Einstein was the first person to take the physical implications of Planck's work seriously. The turning point came when he saw how Planck's idea of energy quanta could be used to account for some puzzling facts that had emerged about a phenomenon known as the photoelectric effect.

Early studies of the photoelectric effect

In 1887, Heinrich Hertz became the first person to observe the photoelectric effect during his experiments that confirmed Maxwell's theory of electromagnetism. Hertz found that by shining ultraviolet light onto metal electrodes, he could lower the voltage needed to make sparks hop between the electrodes. The light obviously had some electrical effect, but Hertz stopped short of speculating what that might be. "I confine myself at present," he said, "to communicating the results obtained, without attempting any theory respecting the manner in which the observed phenomena are brought about."

In 1899 the English physicist J. J. Thomson offered an important clue toward understanding the photoelectric effect. Thomson showed that ultraviolet light, falling onto a metal surface, triggered the emission of electrons. These were tiny charged particles whose existence Thomson had demonstrated a couple of years earlier and which he believed were the only material components of atoms. The photoelectric effect, it seemed to physicists at the time, must come about because electrons inside the atoms in a metal's surface were shaken and made to vibrate by the oscillating electric field of light waves falling on the metal. Some of the electrons would be shaken so hard, the theory went, that eventually they'd be tossed out altogether.

In 1902, Philipp Lenard, who'd earlier been an assistant to Hertz at the University of Bonn, made the first quantitative measurements of the photoelectric effect. He used a bright carbon arc light to study how the energy of the emitted photoelectrons varied with the intensity of the light and, by separating out individual colors, with the frequency of light. Increasing the frequency of light, by selecting light from the bluer end of the spectrum, caused the ejected electrons on average to be more energetic, as predicted – because it was assumed they'd been made to vibrate faster. Increasing the intensity of light (by moving the carbon arc closer to the metal surface) caused more electrons to be thrown out, also as expected. On the other hand, increasing the intensity had no effect at all on the average amount of energy that each ejected electron carried away. That came as a real shock. If, as physicists believed, the photoelectric effect followed from an interaction between electrons and electromagnetic waves, then intensifying the radiation ought to shake the electrons in the metal surface harder and so shoot them out with more energy. It was a mystery why this didn't happen.

Quanta of light

photoelectric effect
Photoelectric effect caused by light falling onto the metal sodium
Several years went by before Lenard's observations on the photoelectric effect and Planck's strange but neglected theory of the quantum, both puzzling in themselves, were seen as arrows pointing to a common solution. Looking back now, it seems clear enough, but it took the genius of Einstein to apply quantization, not to blackbody oscillators as Planck had done in a desperate effort to patch up classical theory, but to the actual radiation that's emitted or absorbed. Light itself is quantized, Einstein realized. All the light of a particular frequency comes in little bullets of the same energy, equal to the frequency multiplied by Planck's constant, and that's the key to understanding the photoelectric effect. An incoming light quantum smashes into an electron on the surface of a metal and gives up all of its energy to the electron. A certain amount of energy, called the work function, is needed simply to overcome the force of attraction between the electron and the metallic lattice in order to set the electron free; so there can't be any photoelectric effect unless this threshold is reached. Any energy left over from the exchange, above and beyond the work function, appears as kinetic energy (energy of motion) of the ejected electron. Increasing the intensity of radiation – the number of light quanta per unit area – has no effect on the energy of individual electrons because each electron is thrown out by one and only one parcel of light. Increasing the frequency of radiation, on the other hand, means that each light bullet packs a bigger wallop, which results in a more energetic photoelectron.

The fact that 16 years went by before Einstein won a Nobel Prize for his groundbreaking work on the photoelectric effect, reflects how long it took the scientific world to accept that radiant energy is quantized. That may seem like an age, but the idea that energy, including light, is granular ran counter to everything that physicists had been taught for several generations: matter is made of particles; energy is continuous and tradable in arbitrarily small amounts; light consists of waves; matter and light don't intermingle. These rules had been the mantras of physics for much of the 19th century and were now being overturned.

There was also the issue of experimental proof. It took a decade or so for the details of Einstein's photoelectric theory to be thoroughly tested and verified in the lab. The actual observation that the kinetic energy of electrons kicked out by the photoelectric effect is tied to the frequency of incoming light in exactly the way Einstein prescribed was finally made in 1916 by the American physicist Robert Millikan. Millikan had, in fact, long been expecting to prove Einstein wrong and thereby to uphold the wave theory of light. Instead he wound up giving powerful support to the particle theory and measuring Planck's constant to within 5 percent of its currently accepted value. Ironically, he won the Nobel Prize in 1923 for a superb series of experiments that dashed what earlier had been his greatest scientific hope.

Slow revolution

We talk about the quantum revolution – but it wasn't an overnight affair, this overthrow of the old worldview of matter and energy in favor of new one. It was more than two decades after Planck's first inkling of the existence of quanta when quantum theory was fully accepted and acknowledged as the reigning paradigm of the microcosmos. For the first part of this interregnum, Einstein was at the cutting edge of developments. Following his seminal 1905 photoelectric paper, he worked on meshing Planck's notion of the quantum with other areas of physics. For instance, he showed that some anomalies to do with how much heat substances have to absorb to raise their temperature by a certain amount are best explained if the energy of vibration of atoms is assumed to be quantized. This early quantum pioneering by Einstein now seems almost entirely overshadowed by his work on relativity, but it was instrumental at the time in persuading scientists of the validity of quantum theory when applied to matter.

His views on the quantum nature of electromagnetic radiation proved a harder sell. Yet, he insisted that the way ahead had to lie with some acceptance of light's particlelike behavior. In 1909 he wrote: "It is my opinion that the next phase in the development of theoretical physics will bring us a theory of light that can be interpreted as a kind of fusion of the wave and emission theory." In 1911, at the first Solvay Congress (an annual meeting of the world's top physicists) he was more forceful: "I insist on the provisional character of this concept, which does not seem reconcilable with the experimentally verified consequences of the wave theory." That apparent irreconcilability was a major stumbling block for all scientists. What kind of madness was it to argue that light could be both a particle and a wave?

Experimentalists railed at the prospect of what Einstein's equation of the photoelectric effect implied. Robert Millikan, the very man who showed that the equation really did work, would have nothing to do with its physical interpretation. In 1915, Millikan wrote: "The semicorpuscular theory by which Einstein arrived at his equation seems at present wholly untenable." Three years later, Ernest Rutherford, the great New Zealand physicist who probed the structure of the atom, said there appeared to be "no physical connection" between the energy and frequency in Einstein's hypothesis about light quanta. It didn't seem to make sense that a particle could have a frequency, or that a wave could act as if it were made of energetic particles. The two concepts seemed to rule each other out.

Final proof of the particle nature of light

Between 1911 and 1916, Einstein took a sabbatical from his quantum work to attend to another little problem – the general theory of relativity, which transformed our ideas on gravity. Upon his return to the physics of the very small, he quickly grasped a link between quantum theory and relativity that convinced him of the reality of the particle aspect of light. In earlier work, Einstein had treated each quantum of radiation as if it had a momentum equal to the energy of the quantum divided by the velocity of light. By making this assumption he was able to explain how momentum is transferred from radiation to matter – in other words, how atoms and molecules are buffeted when they absorb radiation. Although this buffeting was much too small to be seen directly, it had effects on properties, such as the pressure of a gas, that could be measured. These measurements fitted with the formula for quantized momentum. Einstein now realized, in coming back to his quantum studies, that exactly the same expression for the momentum of a light quantum fell straight out of a basic equation in relativity theory. This link between relativity and the earlier assumption about the momentum of a radiation quantum clinched the case for light particles in Einstein's mind. In 1917, he may have been the only major scientist alive who believed that light had a genuine particle aspect. But the fact that his theory now insisted that whenever these supposed light quanta interacted with particles of ordinary matter a definite, predictable amount of momentum should be transferred, paved the way for experimental tests. Six years later, the particle nature of light had been put virtually beyond dispute.

At the heart of lab work that ultimately proved the reality of radiation quanta was the American physicist Arthur Compton. In his early days at Princeton, Compton devised an elegant way of demonstrating Earth's rotation, but he soon launched into a series of studies involving X-rays that climaxed in the final victory of quantum physics over the old world order. In his mid-twenties Compton hatched a theory of the intensity of X-ray reflection from crystals that gave a powerful tool for studying the crystallographic arrangement of electrons and atoms in a substance. In 1918 he began a study of X-ray scattering that led inevitably to the question of what happens when X-rays interact with electrons. The key breakthrough came in 1922 and was published the following year. Compton found that when X-rays scatter from free electrons (electrons not tightly bound inside atoms) the wavelength of the X-rays increases. He explained this effect, now known as the Compton effect, in terms of radiation quanta colliding with electrons, one quantum per electron, and giving up some of their energy (or momenta) in the process. Energy lost translated to frequency decrease, or wavelength increase, according to the Planck formula. A further boost for this interpretation came from a device invented by Charles Wilson. Inspired by the wonderful cloud effects he'd seen from the peak of Ben Nevis, in his native Scotland, Wilson built a vessel in which he could create miniature artificial clouds. This cloud chamber proved invaluable for studying the behavior of charged particles, since water droplets condensing in the wake of a moving ion or electron left a visible trail. Wilson's cloud chamber revealed the paths of the recoil electrons in the Compton effect, showing clearly that the electrons moved as if struck by other particles – X-ray quanta – which, being uncharged, left no tracks. Final proof that the Compton effect really was due to individual X-ray quanta scattering off electrons came in 1927 from experiments based on the so-called coincidence method, developed by Walther Bothe. These experiments showed that individual scattered X-ray quanta and recoil electrons appear at the same instant, laying to rest some arguments that had been voiced to try and reconcile quantum views with the continuous waves of electromagnetic theory. To complete the triumph of the particle picture of light, the American physical chemist Gilbert Lewis coined the name "photon" in 1926, and the fifth Solvay Congress convened the following year under the title "Electrons and Photons."

Doubt had evaporated: Light could manifest itself as particles. But there was equally no doubt that, at other times, it could appear as waves. And that didn't seem to make any sense at all. As Einstein said in 1924, "There are ... now two theories of light, both indispensable ... without any logical connection."

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