By the late 19th century, classical physics could not explain the Blackbody Radiation spectrum (leading to the "Ultraviolet Catastrophe").
In 1900, Max Planck proposed that energy is not continuous but exchanged in discrete packets called Quanta.
Where h is Planck's constant (6.626 × 10-34 J·s) and ν is the frequency.
The Photoelectric Effect is the emission of electrons from a metal surface when light of a sufficient frequency shines on it. Classical theory failed because it predicted that emission should depend on intensity, not frequency.
Einstein applied Planck's idea, suggesting light itself consists of particles called Photons.
Where Φ (Work Function) is the minimum energy required to liberate an electron, and Kmax is the maximum kinetic energy of the emitted electron.
Arthur Compton observed that when X-rays are scattered by a material (like graphite), the scattered radiation has a longer wavelength than the incident radiation. This shift depends on the scattering angle.
This experiment proved that photons carry linear momentum and behave like particles during collisions.
In 1924, Louis de Broglie hypothesized that if light (a wave) can behave like a particle, then matter (particles) should also behave like waves.
This is known as the de Broglie wavelength. It suggests that every moving object has an associated "matter wave."
This experiment provided the first direct evidence for the wave nature of electrons. By scattering an electron beam off a Nickel crystal, they observed diffraction patterns similar to X-rays.
Key Result: The measured wavelength of the diffracted electrons perfectly matched the value predicted by de Broglie's formula.
A matter wave is represented by a Wave Packet (a superposition of many waves with slightly different frequencies).
In quantum mechanics, the group velocity of a particle's wave packet is equal to the classical velocity of the particle.
Tip: If asked to differentiate between Photoelectric and Compton effects, remember: Photoelectric involves complete absorption of the photon, while Compton involves scattering with energy transfer.