Question

What is Photoelectric effect? Write Einstein's photoelectric equation.
OR
What is de-broglie matter wave? Write de-broglie wave relation.

Hint:

The photoelectric effect and de-Broglie waves both demonstrate the dual nature of matter and light, supporting the concept that particles and waves are interconnected.

Answer 1

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 \( E \) of a photon is given by the equation:
\[ E = h\nu \]
where \( h \) is Planck's constant and \( \nu \) is the frequency of the incident light. The energy required to release an electron from the material's surface is the work function \( \phi \). Thus, the photoelectric equation is given by:
\[ E_k = h\nu - \phi \] where \( E_k \) 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 \( \lambda \) associated with a moving particle is given by the de-Broglie relation:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant and \( p \) is the momentum of the particle, given by \( p = mv \), where \( m \) is the mass and \( v \) is the velocity of the particle.