Revise Energy and momentum of a photon for Cambridge 9702 (22.1)

A photon is fundamentally a discrete, individual packet or quantum of electromagnetic energy. Think of it as the smallest possible unit of light, carrying a specific amount of energy. Light itself can be described as a stream of these photons, demonstrating both wave-like properties (like diffraction) and particle-like properties (like discrete energy transfers).

While classical physics describes light as a wave, explaining phenomena like diffraction and interference, this model fails to explain other observations. Quantum mechanics introduces the concept of wave-particle duality, where light behaves as both a wave and a stream of particles (photons) depending on the experiment.

The most compelling evidence for the particle nature of light comes from the photoelectric effect. In this phenomenon, electrons are ejected from a metal surface when light shines on it, but only if the light's frequency is above a certain minimum value (the threshold frequency). This suggests that energy is transferred in discrete packets, or photons, and a single photon must have enough energy to eject an electron.

The energy a single photon carries is directly linked to its frequency. Higher frequency light (like blue light or UV) means more energetic photons. This relationship is governed by a fundamental constant of nature, known as Planck's constant.

E = hf

• E = Photon energy (Joules, J)
• h = Planck's constant (6.63 × 10⁻³⁴ Js)
• f = Frequency of the electromagnetic radiation (Hertz, Hz)

Since the speed of light (c), frequency (f), and wavelength (λ) are related by $c = fλ$, we can also express the photon's energy in terms of its wavelength.

E = hc/λ

• c = Speed of light in a vacuum (3.00 × 10⁸ m s⁻¹)

Surprisingly, even though photons have no rest mass (they only exist when moving at the speed of light), they still carry momentum. This momentum allows light to exert a tiny force when it reflects off or is absorbed by a surface, a concept important in solar sails or radiation pressure.

p = E/c

• p = Photon momentum (N s or kg m s⁻¹)

By substituting our energy formulas, we can also express photon momentum directly in terms of frequency or wavelength.

p = hf/c

p = h/λ

In quantum physics, energy values are often incredibly small when expressed in Joules. To make calculations and discussions more manageable, we frequently use a unit called the electronvolt (eV). It's especially useful for energies of individual particles like electrons or photons.