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Photons are quanta of electromagnetic radiation, each carrying discrete energy and momentum. A photon has energy E = hf (where h is Planck's constant and f is frequency) and momentum p = E/c = h/λ. Photons have zero rest mass but carry both energy and momentum, behaving as particles in interaction with matter while exhibiting wave properties in propagation.
You've studied electromagnetic waves and know they are oscillating electric and magnetic fields propagating at speed c, characterized by frequency f and wavelength λ = c/f. Classical wave theory describes these fields as continuous — you can dial the intensity up or down to any value. But this continuity breaks down in experiments like blackbody radiation (your prerequisite) and the photoelectric effect. The resolution is that electromagnetic radiation is quantized: light comes in discrete packets called photons, each carrying a definite energy fixed by its frequency.
A photon's energy E = hf = hc/λ, where h = 6.626 × 10⁻³⁴ J·s is Planck's constant, means higher-frequency light carries more energy per photon. Violet light (f ≈ 7.5 × 10¹⁴ Hz) has photons roughly twice as energetic as red light (f ≈ 4 × 10¹⁴ Hz). This quantization explains the photoelectric effect cleanly: electrons are ejected from a metal surface only if individual photons carry enough energy to overcome the work function φ. No matter how intense the light, if hf < φ, no electrons are emitted — ever. Intensity (photon count rate) determines how many electrons are ejected per second; frequency determines whether any are ejected at all. This is utterly impossible to explain with continuous waves.
A photon also carries momentum p = E/c = h/λ, linking the wave property λ to the particle property p. Photons have zero rest mass — they cannot exist at rest and always travel at c — yet they carry real, measurable momentum that transfers in collisions. The Compton effect (1923) confirmed this precisely: X-ray photons scatter off electrons and emerge with longer wavelengths (lower energy), transferring momentum to the recoiling electron exactly as predicted by relativistic particle mechanics applied to a zero-rest-mass particle. The wavelength shift Δλ = (h/m_ec)(1 − cos θ) depends on the scattering angle and involves the Compton wavelength h/m_ec, a combination of h, c, and the electron mass.
The conceptual revolution here is that wave and particle descriptions are not contradictions — they are complementary. A photon propagates as a wave (producing interference and diffraction) but interacts as a particle (depositing a discrete quantum of energy and momentum). The E = hf relation bridges both: it links frequency (a wave property) to energy (a particle property). This wave-particle duality extends to matter through the de Broglie relation λ = h/p — the same h appears, making photons not a bizarre exception but the first demonstration of a universal principle: all quantum objects are neither purely waves nor purely particles, but something new that has features of both depending on how they are measured.