Quantum physics

At the start of the 20th century, classical physics viewed light purely as a wave. However, some phenomena, like the photoelectric effect, couldn't be explained this way. Max Planck proposed a revolutionary idea: electromagnetic energy is not continuous but is emitted and absorbed in discrete packets, or 'quanta'. Albert Einstein later named these packets 'photons'. The energy of a single photon is directly proportional to the frequency of the electromagnetic radiation. A higher frequency (like UV light) means higher energy photons, while a lower frequency (like red light) means lower energy photons. Because energy comes in these distinct chunks, we say it is 'quantised'. A common unit of energy at this scale is the electronvolt (eV), which is the energy gained by an electron when it is accelerated through a potential difference of 1 volt.

The photoelectric effect is the emission of electrons from a material (usually a metal) when light shines on it. These emitted electrons are called photoelectrons. Classical wave theory predicted that any frequency of light, if intense enough, should eventually provide enough energy to free an electron. However, experiments showed something different. For a given metal, there is a specific minimum frequency, called the 'threshold frequency' (f₀), below which no photoelectrons are emitted, no matter how intense the light is. The minimum energy required to free an electron from the surface is a property of the metal called the 'work function' (Φ). A single photon must have enough energy to overcome this work function. If the photon's energy (hf) is less than the work function (Φ), no electron is emitted.

Einstein's photoelectric equation is a beautiful application of the principle of conservation of energy to the photoelectric effect. It states that the energy of the incoming photon (hf) is used for two things: first, to provide the energy needed to free the electron from the metal (the work function, Φ), and second, any remaining energy is given to the emitted electron as kinetic energy. The equation refers to the *maximum* kinetic energy (KE_max) because some electrons may be liberated from deeper within the metal and lose some energy in collisions on their way out. The electrons that escape with the most KE are those from the very surface.

The photoelectric effect provides compelling evidence for the particle nature of light. The classical wave model fails to explain key experimental observations.

1. Existence of a Threshold Frequency: The wave model suggests any frequency of light, if intense enough, would eventually transfer enough energy to an electron. The particle model explains this perfectly: a single photon must have energy hf > Φ. If not, no emission occurs, regardless of how many photons (intensity) arrive.
2. Instantaneous Emission: Experiments show electrons are emitted the moment light of sufficient frequency hits the metal. The wave model predicts a time delay, as energy would need to accumulate over a region of the surface. The particle model explains this as a one-to-one, instantaneous interaction between a photon and an electron.
3. KE vs. Intensity: Increasing the light intensity (brightness) increases the number of photoelectrons emitted per second (the photoelectric current), but does not change their maximum kinetic energy. The particle model explains this because higher intensity means more photons arriving per second, leading to more one-to-one interactions, but the energy of each individual photon (and thus the KE_max) remains the same as long as frequency is constant.

Quantum physics reveals a strange truth: entities like light and electrons exhibit both wave-like and particle-like properties. This is called wave-particle duality. While the photoelectric effect shows light behaving as particles (photons), phenomena like diffraction and interference show it behaving as a wave. In 1924, Louis de Broglie proposed that this duality wasn't just for light. He suggested that all matter has wave-like properties. A moving particle, like an electron, has an associated wavelength, now called the de Broglie wavelength (λ). This wavelength is inversely proportional to the particle's momentum (p). This was a radical idea, but it was confirmed experimentally by observing electron diffraction. When a beam of electrons is passed through a thin crystal lattice (like graphite), they produce a diffraction pattern of concentric rings, just as waves would. This confirmed that particles can behave like waves. A photon, despite having no rest mass, also has momentum, which is related to its energy.

In an isolated atom, electrons can't just have any amount of energy. They are restricted to specific, discrete energy levels. Think of it like a staircase: you can stand on step 1, or step 2, but not on step 1.5. You can't be 'in between' levels. The lowest possible energy level is called the ground state (n=1). Higher levels are called excited states (n=2, n=3, etc.). By convention, the energy of a free electron (one that has escaped the atom completely, n=∞) is defined as 0 eV. Since energy must be supplied to an electron to move it to a higher level and eventually free it, all the energy levels within the atom have negative values. For example, the ground state of a hydrogen atom is -13.6 eV. An electron can 'jump' to a higher energy level if it absorbs the exact amount of energy corresponding to the difference between the levels. This energy is typically supplied by absorbing a photon or through a collision.

Atomic energy levels provide a perfect explanation for line spectra. When a gas is heated or has a high voltage passed through it, its atoms become excited. Electrons jump to higher energy levels but are unstable there. They quickly fall back down to lower, more stable levels. As an electron de-excites, it loses a specific amount of energy (ΔE = E_initial - E_final). This energy is released as a single photon. The photon's energy is exactly equal to the energy lost by the electron, so hf = E_initial - E_final. Since only certain energy transitions are possible, only photons of specific frequencies (and therefore specific colours) are emitted. When viewed through a spectrometer, this produces a series of bright coloured lines on a dark background, known as an emission line spectrum. Conversely, if white light (containing all frequencies) is passed through a cool gas, atoms will absorb photons that have the exact energies needed to excite their electrons to higher levels. These specific frequencies are then missing from the light that passes through. This creates a continuous spectrum with dark lines on it, known as an absorption line spectrum. The dark lines in a gas's absorption spectrum are at the exact same frequencies as the bright lines in its emission spectrum.