How Einstein’s theory of light shaped quantum theory.
First Observations of the Photoelectric Effect
Maxwell’s theory predicted the existence of electromagnetic waves, stating that light itself was one such wave. This greatly excited fellow scientists, who sought to prove his assertions experimentally. In 1887, German physicist Heinrich Hertz was toying around with a ‘spark gap’ when he noticed something peculiar…
Hertz’ set-up was a pair of conducting electrodes separated by a tiny gap across which a spark was generated upon detection of electromagnetic waves. After covering his apparatus in a dark box to see the sparks better, he noticed that a glass box decreased the spark length whereas a quartz box had no effect.
Little did he know that it was ultraviolet radiation which was interacting with the electrons in the current and supplying them with energy to jump across the gap. Hertz couldn’t explain his findings, but it soon became clear that the phenomenon occurred because glass absorbs UV and quartz doesn’t. He had accidentally witnessed the first example of the ‘Photoelectric Effect’.
The Discovery of the Electron and Metallic Structure
In 1897, British physicist J.J. Thomson made one of the most significant discoveries in scientific history, the electron. Using cathode ray tubes, he demonstrated that all atoms contain tiny, negatively charged particles. The electrons he identified inspired Thomson to conceive his ‘plum pudding model’ of the atom, in which negatively charged “plums” were embedded within a positively charged “pudding”.
Before moving on, it’s worth examining what constitutes a metal. At the atomic level, a metal is a closely packed lattice of metal ‘ions’, which are simply atoms with a net positive or negative charge.
The structure of a solid metal consists of charged ions because each atom has donated at least one of its outermost electrons to form a “sea” of ‘delocalised electrons’. The electrostatic force of attraction between the metal ions and delocalised electrons is what imparts metals with their rigidity and strength. In theory, if given enough energy, these delocalised electrons could become liberated from the metal’s surface.
The Incompatibility of Classical Physics and the Photoelectric Effect
In 1902, another German physicist Philipp Lenard demonstrated that illuminating a metal surface with light or another form of electromagnetic radiation could cause electrons in the material to be expelled or ‘liberated’. The electrons absorbed incoming ‘radiant energy’, allowing them to break free from the electrostatic forces binding them to the metallic ions. Unfortunately, this ‘photoelectric effect’ represented an interaction between light and matter which couldn’t be explained by classical physics, or by viewing light as an electromagnetic wave.
If light were only a wave, the energy of the released electrons would depend on the light source’s intensity. Except it didn’t! It was actually dependent on the light’s frequency, which according to wave theory should have zero effect. The intensity instead determined the number of electrons released from the metal’s surface. What was made clear is that classical ideas and the wave picture of light simply weren’t cutting it in explaining this puzzling effect.
Einstein’s Dazzling Idea
Albert Einstein made his mark in 1905 by formulating a startling new theory of light. He did this by expanding upon Planck’s idea of quantization to conjecture that light itself is made up of discrete packets or ‘quanta’. Each of these quanta contained a fixed amount of energy directly related to the light’s frequency. Their name? Photons!
This is where things took a strange turn, as Einstein was not only suggesting that light is composed of what are essentially particles, but that it also possesses wave-like properties such as frequency and therefore also an effective ‘wavelength’.
It became apparent from that point onwards that light isn’t fully described by a wave or a particle. This was the first example of ‘wave-particle duality’, a prominent concept in quantum mechanics stating that every particle may be described as either a particle or a wave. Neither description alone nor their classical interpretations are sufficient to fully describe the behaviour of any quantum system.
What is a Photon?
Like all forms of electromagnetic radiation, light transports energy across space. Einstein was able to convincingly show that the energy transmitted by light arrives at a receiver not continuously but in discrete units called ‘photons’. Instead of the energy being continuously distributed over a wavefront, it was now carried in neat, quantized packages. Therefore, we can view photons as effective “particles” of light! So what do we know about them?
Following on from Maxwell’s work, we know that photons always move at the speed of light. We also know that they are electrically neutral and have zero mass, but still carry an energy proportional to the light’s frequency. The higher the frequency or shorter the wavelength, the more energetic the photon. Lastly, photons can be created or destroyed. When a source emits electromagnetic waves, photons are created. When photons encounter matter, they can be absorbed and transfer their energy to the atoms and molecules.
The Energy of a Photon
When Planck derived an equation that described black body radiation curves with tremendous accuracy and resolved the ultraviolet catastrophe, he defined a universal constant ‘h’ in his calculations. This ‘Planck constant’ is unfathomably small – approximately 6.63 × 10^-34 – and just like the speed of light or the charge of an electron, it is a fundamental, unchanging quantity that has profound importance in quantum mechanics. In fact, this constant appears in any equation in which the phenomenon under consideration exhibits quantum mechanical behavior.
In Einstein’s quantum theory of light, he carried the Planck constant forward, capturing the relationship between the energy of a photon and its frequency via the straightforward equation E = h × f or E = hc / λ where ‘c’ is the speed of light and ‘λ’ is its wavelength. Therefore, according to Einstein’s work, red light photons possess lower energy than blue light photons due to the former having a relatively longer wavelength or lower frequency.
Photoelectric Effect Problem 1: The Cut-off Frequency
When light is shone on a metal surface, sometimes no electrons are emitted regardless of the light’s intensity. But if light were a wave, even a low intensity light source should continually transfer energy to the electrons until they absorb enough to escape from their metallic bonds. In quantum physics, it’s the light source’s frequency which matters. It turns out that every material has a unique ‘cut-off frequency’ below which no electrons are released and above which photoelectric effects are witnessed.
The quantum view of light states that intensity only affects the rate of electron emission, not whether they will be emitted. In other words, a greater number of photons transmitted per unit area and time means more opportunities for electrons to be liberated, assuming each photon has sufficient energy! When a photon with sufficient energy impacts an electron, it causes it to be liberated. Nothing happens if the photon lacks sufficient energy, regardless of how many there are!
Photoelectric Effect Problem 2: Electron Energy Independence of Intensity
To liberate an electron from a metal surface the incoming radiation needs to have energy surpassing Φ, which is related to the cut-off frequency fc by Φ = h × fc and known as the ‘work function’ of the metal. This work function is the minimum energy required to induce ‘photoemission’ of electrons, and it depends on the specific metal being illuminated. If an incoming photon’s energy exceeds the work function of the material, an electron can be freed, and any excess energy appears as kinetic energy of the electron.
It was established that the maximum kinetic energy of liberated electrons was independent of the light’s intensity, which only makes sense when light is quantized into photons. Each photon has a fixed energy based on frequency only, meaning that electrons will have a maximum kinetic energy – calculated as the difference between the energy of the photon and the work function of the metal – that doesn’t vary with intensity.
Photoelectric Effect Problem 3: No Time Lag
According to classical wave theory, a measurable time lag should exist between the time when light first starts to illuminate a surface and the subsequent ejection of electrons. However, no detectable time lag has ever been measured in the photoelectric experiment. In other words, when a single photon with sufficient energy interacts with a single electron the photoelectric emission process is instantaneous.
Classically, the time scale of the interaction should be measurable as the incoming wave continuously supplies energy until the electron has enough to escape, but this is not what was observed. The lack of a time lag in the photoelectric effect was another finding in favor of the quantum view.
