Quantum Physics

At the turn of the 20th century, classical physics, which had successfully described the macroscopic world, began to fail when applied to phenomena at the atomic and subatomic levels. This led to the development of Quantum Physics, a revolutionary theory that describes the dual wave-particle nature of energy and matter.

### The Photon: A Quantum of Light

Classical wave theory describes light as a continuous electromagnetic wave. However, phenomena like the photoelectric effect could not be explained by this model. In 1900, Max Planck proposed that energy is not continuous but is emitted and absorbed in discrete packets, or quanta. Building on this, Albert Einstein in 1905 suggested that light itself consists of these energy packets, which were later named photons.

The energy of a single photon is directly proportional to its frequency. This relationship is described by the Planck-Einstein relation:

E = hf

Where:

Since the speed of light (c) is related to frequency (f) and wavelength (λ) by c = fλ, the photon energy can also be expressed as E = hc/λ.

### The Photoelectric Effect

This is a key phenomenon that provides evidence for the particulate nature of light. The photoelectric effect is the emission of electrons (called photoelectrons) from a metal surface when electromagnetic radiation of sufficiently high frequency is incident upon it.

Classical wave theory incorrectly predicted that any frequency of light, if intense enough, could cause electron emission after a time delay. However, experiments showed:

Einstein's photon model explains these observations perfectly. He proposed a one-to-one interaction: one incident photon transfers all its energy to one electron. A part of this energy is used to overcome the electrostatic forces binding the electron to the metal; this minimum energy is called the work function (Φ) of the metal. The remaining energy becomes the kinetic energy of the photoelectron.

This is summarised by Einstein's photoelectric equation:

hf = Φ + KE_max

The work function is related to the threshold frequency by Φ = hf₀. If the incident photon's energy hf is less than Φ, no electron can escape.

### Wave-Particle Duality

Light exhibits properties of both waves (e.g., diffraction and interference) and particles (e.g., the photoelectric effect). This concept is known as wave-particle duality. In 1924, Louis de Broglie hypothesised that this duality is universal and that all matter, including particles like electrons, also possesses wave-like characteristics.

The wavelength of a particle is given by the de Broglie wavelength formula:

λ = h/p

Where p is the momentum of the particle (p = mv for a non-relativistic particle). The experimental confirmation for this came from the diffraction of electrons by a crystal lattice, proving that particles can indeed behave like waves.

### Discrete Energy Levels in Atoms

The quantum model of the atom, particularly the Bohr model and later Schrödinger's wave mechanics, posits that electrons in an atom cannot have just any amount of energy. Instead, they are restricted to specific, discrete energy levels. An electron occupying its lowest possible energy level is in the ground state. If it absorbs energy, it can jump to a higher energy level, an excited state.

This absorption or emission of energy happens via photons. An atom can only absorb a photon if the photon's energy (hf) exactly matches the energy difference (ΔE) between two allowed energy levels. Similarly, when an electron in an excited state falls back to a lower energy level, it emits a photon with an energy equal to the energy difference.

ΔE = E_final - E_initial = hf

This explains atomic line spectra. An emission spectrum, consisting of bright lines at specific frequencies, is produced when atoms in an excited gas de-excite. An absorption spectrum, showing dark lines in a continuous spectrum, is formed when light passes through a cool gas and atoms absorb photons at their characteristic frequencies.