Revision: Dual Nature of Matter and Radiation JEE Main Dual Nature of Matter and Radiation

The minimum frequency of incident radiation required to start photoemission in any photosensitive material is known as the threshold frequency. 

The phenomenon of emission of electrons from the metal surface is called "Electron Emission".

The minimum energy required by an electron to escape from the surface of a metal is called the work function (ϕ₀​) of that metal.

Unit: electron volt (eV).

The minimum energy needed for an electron to escape from the metal surface is called the work function of that metal. Its unit is electron volt (eV).

An electron volt is the energy gained by an electron when it is accelerated through a potential difference of 1 volt.

1 eV = 1.602 × 10⁻¹⁹J

The phenomenon of emission of electrons from a metal surface, when radiation of appropriate frequency is incident on it, is called the Photoelectric Effect.

The phenomenon of emission of electrons from a metal surface when radiation of appropriate frequency is incident on it is known as the photoelectric effect. 

It is a phenomenon where light falling on a material (usually a metal) causes it to emit electrons, generally called photoelectrons.

Electrons emitted from the metal during photoelectric emission are called photoelectrons.

The minimum frequency of incident radiation required to just cause photoelectric emission from a given metal is called the threshold frequency.

The emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency falls on it. This phenomenon is called the photoelectric effect.

Threshold frequency is the lowest frequency of electromagnetic radiation that will result in the emission of electrons from a specified metal surface.

The stopping potential is defined as the potential necessary to stop any electron from reaching the other side.

The photoelectric effect demonstrates that light behaves as if it consists of energy packets called quanta or photons.

The property by which light or matter can show both wave-like and particle-like behaviour depending on the experiment is called wave-particle duality.

The waves associated with a moving material particle are called matter waves or de Broglie waves.

According to de Broglie, every moving particle is associated with a wave whose wavelength depends on its momentum.

E = hν

where:

• E = energy of one photon
• h = Planck’s constant = 6.626 × 10^-34 J s
• ν = frequency of radiation

For a particle of momentum p, the associated wavelength is:

For a particle of mass m moving with speed v:

• Maxwell’s equations and Hertz’s experiments established the wave nature of light.
• Low-pressure discharge tube experiments led to important discoveries in atomic structure.
• Cathode rays were identified as fast-moving negatively charged particles.
• J. J. Thomson measured the specific charge of these particles and named them electrons.
• Millikan measured the elementary charge and established the quantisation of electric charge.

• When light of frequency ≥ threshold frequency (ν₀) falls on a metal surface, electrons are emitted.
• If ν < ν₀ → no emission, regardless of intensity.
• The threshold frequency (ν₀) varies with metal.
• Energy equation: \[h\nu=h\nu_0+\frac{1}{2}mv^2\]
• Maximum kinetic energy depends only on frequency, not on intensity.
• Number of emitted electrons depends on intensity (for ν ≥ ν₀).
• Emission of electrons is instantaneous (no time lag).
• Increasing frequency increases the kinetic energy of electrons.
• Increasing intensity increases the number of electrons, not their energy.
• The photoelectric effect proves the particle (quantum) nature of light.

• Photoelectric emission was discovered in 1887 by Heinrich Hertz.
• Hertz made this observation during electromagnetic wave experiments.
• High-voltage sparks across the detector loop were enhanced when the emitter plate was illuminated by ultraviolet light from an arc lamp.
• Light shining on the metal surface facilitated the escape of free, charged particles.
• These free, charged particles are electrons.
• Electrons near the metal surface absorb energy from incident radiation.
• If the absorbed energy is sufficient, electrons overcome the attraction of positive ions in the material.
• The electrons then escape from the metal surface into the surrounding space.

1.  The experiment verified the de-Broglie hypothesis.
2. In this experiment, the wave nature of electron particles was studied with the help of a nickel crystal.
3. Electrons undergo interference and diffraction phenomena and produce alternate bright and dark rings.
4. When accelerating potential V = 54 V:
   λ = 0.165 nm (Experimental value)
   λ = 0.167 nm (Theoretical value from de-Broglie hypothesis)

• Proposed by Louis de Broglie in 1924: just as light shows both particle and wave nature, matter in motion also exhibits wave-like behaviour.
• The wave associated with a moving particle is called the matter wave or de Broglie wave.
• de Broglie wavelength equation: \[\lambda=\frac{h}{mv}=\frac{h}{p}\]
  

  where m = mass of particle, v = velocity, p = momentum.

• For an electron: λ = h/mv or λ = h/p