Dual Nature of Radiation and Matter notes

This chapter connects two major ideas of modern physics: light behaves both as a wave and as a particle, and moving matter also shows wave nature. Electron emission explains how electrons can be liberated from metal surfaces by heat, light or strong electric field. The photoelectric effect proves the particle nature of light because electrons are emitted only when incident light has frequency above a threshold value. Einstein explained this using photons, each carrying energy hf. Photon theory gives energy and momentum of light particles. Finally, de Broglie proposed matter waves, assigning wavelength h/p to moving particles. NEET questions mainly test formula use, graph interpretation, threshold frequency, stopping potential and de Broglie wavelength.

Electron emission is the process by which electrons escape from the surface of a metal. In metals, free electrons move inside the material but cannot normally leave the surface because they are bound by surface forces. The minimum energy required to remove an electron from the metal surface is called work function, and it depends on the nature of the metal. If energy is supplied as heat, the process is thermionic emission. If energy comes from incident light, it is photoelectric emission. If electrons are pulled out by a very strong electric field, it is field emission. Electron emission is the foundation of photoelectric cells, vacuum tubes, electron guns and many detectors.

The photoelectric effect is the emission of electrons from a metal surface when light of suitable frequency falls on it. In the experimental setup, a photosensitive cathode and collecting anode are enclosed in an evacuated tube. When light frequency is above threshold frequency, photoelectrons are emitted and collected as current. The current increases with intensity because more photons eject more electrons. For a fixed frequency, current becomes maximum at saturation current when all emitted electrons are collected. A negative potential can stop even the fastest electrons; this is stopping potential. Wave theory failed because it predicted emission at any frequency if intensity was high enough, time delay at low intensity and kinetic energy depending on intensity, all contrary to observations.

Einstein explained the photoelectric effect by proposing that light energy is delivered in discrete packets called photons. A photon of frequency f carries energy hf. When a photon interacts with an electron in a metal, its energy is absorbed by a single electron. Part of the energy equal to the work function φ is used to liberate the electron from the surface. The remaining energy appears as the maximum kinetic energy of the photoelectron. Therefore, hf = φ + Kmax. If hf is less than φ, no electron is emitted. Since Kmax = eV0, stopping potential increases linearly with frequency. This equation successfully explains threshold frequency, instantaneous emission and intensity independence of maximum kinetic energy.

Photon theory describes light as a stream of discrete energy packets called photons. Planck introduced the idea that electromagnetic energy is emitted or absorbed in quanta of energy hf. Einstein used this idea to explain the photoelectric effect. A photon travels with the speed of light in vacuum, has zero rest mass, carries energy E = hf and momentum p = h/λ. The intensity of light depends on the number of photons crossing a unit area per second, while the energy of each photon depends on frequency. Photon theory explains particle-like effects such as photoelectric emission and Compton scattering, while wave theory explains interference and diffraction. Together they show wave-particle duality of light.

de Broglie proposed that just as light shows both wave and particle nature, moving material particles should also have wave nature. The wavelength associated with a particle is called de Broglie wavelength and is given by λ = h/p. For a non-relativistic particle of mass m and speed v, λ = h/mv. If a charged particle is accelerated through potential V, its kinetic energy becomes qV and wavelength can be written as h/sqrt(2mqV). Matter waves are significant for electrons, protons, neutrons and atoms, but negligible for macroscopic objects because their momentum is very large. Davisson-Germer experiment verified electron diffraction and confirmed the wave nature of matter.