Dual Nature Of Matter

The energy of a photon is related to its frequency by the equation , where is energy, is Planck's constant, and is frequency.

a. Photoelectric Effect:
The photoelectric effect is the phenomenon in which electrons are ejected from the surface of a material (typically metal) when it is exposed to light of certain frequency. This phenomenon provided experimental evidence for the particle nature of light.
Einstein's Photoelectric Equation:
The energy of a photon is given by the equation:

where is Planck's constant and is the frequency of the incident light. The energy required to release an electron from the material's surface is the work function . Thus, the photoelectric equation is given by:
where is the kinetic energy of the emitted electron.
b. de-Broglie Matter Waves:
de-Broglie proposed that particles, such as electrons, exhibit wave-like properties. The wavelength associated with a moving particle is given by the de-Broglie relation:

where is Planck's constant and is the momentum of the particle, given by , where is the mass and is the velocity of the particle.

De Broglie waves refer to the wave-like behavior of particles, and they are not electromagnetic waves. These waves are related to matter, unlike electromagnetic waves, which are related to electric and magnetic fields.