Einstein and the Photoelectric Effect
This discovery is so important — and Nobel Prize worthy — because Einstein suggested for the first time that light is both a wave and a particle. This phenomenon, known as the wave-particle duality of light, is fundamental to all of quantum mechanics and has influenced the development of electron microscopes and solar cells.
When you think of Albert Einstein; what do you think of? General relativity? Black holes? Crazy hair? While he certainly made significant contributions to all of those topics during his lifetime, Albert Einstein was perhaps even more well known in his time for his work to understand the Photoelectric Effect. In fact, when he was awarded the Nobel Prize in Physics in 1921, the honor was stated to be “for his services to Theoretical Physics, and especially for his discovery of the law of the Photoelectric Effect.”
What is Photoelectric Effect?
Photoelectric Effect, phenomenon in which electrically charged particles are released from or within a material when it absorbs electromagnetic radiation. The effect is often defined as the ejection of electrons from a metal plate when light falls on it. In a broader definition, the radiant energy may be infrared, visible, or ultraviolet light, X-rays, or gamma rays; the material may be a solid, liquid, or gas; and the released particles may be ions (electrically charged atoms or molecules) as well as electrons.
When light with energy above a certain threshold hits a metal surface, an electron that was previously bound to the metal is knocked loose. Each particle of light, called a photon, collides with an electron and uses some of its energy to dislodge it from the metal. The rest of the photon’s energy is transferred to the now free-roaming negative charge, called a photoelectron.
So why does this happen? What determines the energies (and speeds) of the emitted electrons? To understand the answers to these questions, we need to dig a little into the history of the discovery of the Photoelectric Effect.
History of the Discovery
In 1905 Einstein extended Planck’s hypothesis to explain the Photoelectric Effect, which is the emission of electrons by a metal surface when it is irradiated by light or more-energetic photons. The Kinetic Energy of the emitted electrons depends on the frequency ν of the radiation, not on its intensity; for a given metal, there is a threshold frequency νₒ below which no electrons are emitted. Furthermore, emission takes place as soon as the light shines on the surface; there is no detectable delay. Einstein showed that these results can be explained by two assumptions: (1) that light is composed of corpuscles or photons, the energy of which is given by Planck’s relationship, and (2) that an atom in the metal can absorb either a whole photon or nothing. Part of the energy of the absorbed photon frees an electron, which requires a fixed energy W, known as the work function of the metal; the rest is converted into the kinetic energy mₑu²/2 of the emitted electron (mₑ is the mass of the electron and u is its velocity). Thus, the energy relation is
hv = W + ᵐₑᵘ ²/2
If ν is less than ν0, where hν0 = W, no electrons are emitted. Not all the experimental results mentioned above were known in 1905, but all Einstein’s predictions have been verified since.
Discovery and early work
The Photoelectric effect was discovered in 1887 by the German physicist Heinrich Rudolf Hertz. In connection with work on radio waves, Hertz observed that, when ultraviolet light shines on two metal electrodes with a voltage applied across them, the light changes the voltage at which sparking takes place. This relation between light and electricity (hence photoelectric) was clarified in 1902 by another German physicist, Philipp Lenard. He demonstrated that electrically charged particles are liberated from a metal surface when it is illuminated and that these particles are identical to electrons, which had been discovered by the British physicist Joseph John Thomson in 1897.
Further research showed that the Photoelectric effect represents an interaction between light and matter that cannot be explained by classical physics, which describes light as an electromagnetic wave. One inexplicable observation was that the maximum kinetic energy of the released electrons did not vary with the intensity of the light, as expected according to the wave theory, but was proportional instead to the frequency of the light. What the light intensity did determine was the number of electrons released from the metal (measured as an electric current). Another puzzling observation was that there was virtually no time lag between the arrival of radiation and the emission of electrons.
Consideration of these unexpected behaviors led Albert Einstein to formulate in 1905 a new corpuscular theory of light in which each particle of light, or photon, contains a fixed amount of energy, or quantum, that depends on the light’s frequency. In particular, a photon carries an energy E equal to hf, where f is the frequency of the light and h is the universal constant that the German physicist Max Planck derived in 1900 to explain the wavelength distribution of blackbody radiation — that is, the electromagnetic radiation emitted from a hot body. The relationship may also be written in the equivalent form
E = hc/λ ,
where c is the speed of light and λ is its wavelength, showing that the energy of a photon is inversely proportional to its wavelength.
Einstein assumed that a photon would penetrate the material and transfer its energy to an electron. As the electron moved through the metal at high speed and finally emerged from the material, its kinetic energy would diminish by an amount ϕ called the work function (similar to the electronic work function), which represents the energy required for the electron to escape the metal. By conservation of energy, this reasoning led Einstein to the Photoelectric equation :
Eₖ = hf − ϕ,
where Eₖ is the maximum kinetic energy of the ejected electron.
Although Einstein’s model described the emission of electrons from an illuminated plate, his photon hypothesis was sufficiently radical that it was not universally accepted until it received further experimental verification. Further corroboration occurred in 1916 when extremely accurate measurements by the American physicist Robert Millikan verified Einstein’s equation and showed with high precision that the value of Einstein’s constant h was the same as Planck’s constant. Einstein was finally awarded the Nobel Prize for Physics in 1921 for explaining the photoelectric effect.
In 1922 the American physicist Arthur Compton measured the change in wavelength of X-rays after they interacted with free electrons, and he showed that the change could be calculated by treating X-rays as made of photons. Compton received the 1927 Nobel Prize for Physics for this work. In 1931 the British mathematician Ralph Howard Fowler extended the understanding of Photoelectric emission by establishing the relationship between photoelectric current and temperature in metals. Further efforts showed that electromagnetic radiation could also emit electrons in insulators, which do not conduct electricity, and in semiconductors, a variety of insulators that conduct electricity only under certain circumstances
Theoretical Explanation
In 1905, Einstein proposed a theory of the Photoelectric Effect using a concept first put forward by Max Planck that light consists of tiny packets of energy known as photons or light quanta. Each packet carries energy hv of the corresponding electromagnetic wave. The proportionality constant h has become known as the Planck constant. The maximum Kinetic energy Kₘₐₓ of the electrons that were delivered this much energy before being removed from their atomic binding is
Kₘₐₓ = hv - Wₒ ,
where W is the minimum energy required to remove an electron from the surface of the material. It is called the work function of the surface and is sometimes denoted Φ or φ. If the work function is written as W=𝒉𝑣, the formula for the maximum kinetic energy of the ejected electrons becomes
Kₘₐₓ = h(v - v ₒ).
Kinetic energy is positive, and v>v is required for the photoelectric effect to occur. The frequency vₒ is the threshold frequency for the given material. Above that frequency, the maximum kinetic energy of the photoelectrons as well as the stopping voltage in the experiment
V ₒ= ʰ/ₑ (v - vₒ)
rise linearly with the frequency, and have no dependence on the number of photons and the intensity of the impinging monochromatic light. Einstein’s formula, however simple, explained all the phenomenology of the photoelectric effect, and had far-reaching consequences in the development of quantum mechanics.
Observation & How it Works?
Einstein observed that when light is exposed to metal, electrons fly out of the metal surface, which is very unusual if light was only a wave. The strange thing about the photoelectric effect is that the energy of the electrons (photoelectrons) that fly out of the metal does not change, regardless of whether the light is weak or strong (If light were a wave, strong light should cause photoelectrons to fly out with great power.)
Einstein then proposed that light is actually made up of tiny packets of energy that travel or propagate in a wave-like manner. The particle he conceived was a photon, and he speculated that when electrons within matter collides with photons, the former takes the latter’s energy and flies out. He went on to argue that the higher the oscillation frequency of the photons that strike, the greater the electron energy that will come flying out. This fact is perfectly illustrated through the double-slit experiment.
Using the same method as the single slit, the only modification is that the screen with the slit now has two parallel slits and light behavior is again observed on the screen placed behind the double-slit plate. The wave-like nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen — a result that would not be expected if light consisted of classical particles. However, the light is always found to be absorbed at the screen at discrete points, meaning as individual particles (not waves). Later, when detectors were installed at the slits, it was observed that each photon only passed through one of the slits, which is again a particle behavior, rather than a wave-like behavior.
The phenomenon was fundamentally significant in the development of modern physics because of the puzzling questions it raised about the nature of light — particle versus wavelike behavior — that were finally resolved by Albert Einstein in 1905. The effect remains important for research in areas from materials science to astrophysics, as well as forming the basis for a variety of useful devices.