Overview: Dual Nature of Radiation and Matter

Electromagnetic radiation consists of mutually perpendicular oscillating electric and magnetic fields, both perpendicular to the direction of propagation of the wave.

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

A surface that emits electrons when illuminated with suitable radiation is called a photosensitive surface.

Electrons emitted from a metal surface due to incident light are called photoelectrons.

When the anode is at positive potential with respect to the cathode, it accelerates the emitted electrons. This potential is called accelerating potential.

When the anode is at negative potential with respect to the cathode, it opposes the motion of electrons. This is called retarding potential.

• Electrons are emitted only if the light frequency is greater than a minimum value, the threshold frequency (ν₀), which differs for different metals.
• Emission of electrons is instantaneous; there is no time delay between light falling and electrons coming out.
• At a fixed frequency, photocurrent increases with increasing light intensity.
• Photocurrent increases with accelerating potential and then becomes constant; this maximum value is called the saturation current.
• Saturation current depends on light intensity, not on its frequency (if ν > ν₀).
• The maximum kinetic energy of emitted electrons depends only on the frequency of light, not on its intensity.
• Stopping potential is the minimum negative potential needed to stop the photocurrent; it depends on frequency, not on intensity.

\[
K_{\text{max}} = eV_0
\]

             or

\[
K_{\text{max}} = h\nu - \phi_0
\]

Linear Form:

\[
V_0 = \frac{h}{e}\nu - \frac{\phi_0}{e}
\]

The minimum energy required to remove an electron from the surface of a metal is called the work function of the metal.
It is denoted by ϕ₀.

\[
1\,\text{eV} = 1.602 \times 10^{-19}\,\text{J}
\]

\[
e = 1.602 \times 10^{-19}\,\text{C}
\]

\[
\frac{e}{m} = 1.76 \times 10^{11}\,\text{C/kg}
\]

• Wave theory could not explain the instant emission of electrons; it predicted a time delay.
• It said higher intensity should give higher kinetic energy, but actually, kinetic energy depends on frequency, not intensity.
• Wave theory predicts emission at any frequency when intensity is high, but emission occurs only when the frequency is above the threshold frequency (ν₀).
• Even very low intensity light causes immediate emission, which contradicts wave theory.
• Hence, the photoelectric effect supported the particle (quantum) nature of light rather than the wave theory.

The quantum (bundle) of electromagnetic radiation having energy E = hν is called a photon.

\[
p = \frac{h\nu}{c} = \frac{h}{\lambda}
\]

The relation E = hν, which connects the energy of a photon with its frequency, is called Einstein’s relation.

The minimum frequency of incident radiation required to eject electrons from a metal surface (ν₀ = ϕ₀/h) is called the threshold frequency.

\[
\nu_0 = \frac{\phi_0}{h}
\]

The minimum negative potential applied to the collector to reduce the photocurrent to zero is called the stopping potential (cut-off potential).

The maximum kinetic energy of emitted photoelectrons given by KE_max⁡ = hν − ϕ₀​ is called Einstein’s photoelectric equation.

• Einstein extended Planck’s idea and proposed that light behaves as particles called photons, each carrying energy hνh\nuhν.
• A photon gives all its energy to a single electron; emission occurs only if this energy is equal to or greater than the work function of the metal.
• Photoelectric emission is instantaneous because energy transfer from photon to electron occurs in a single interaction.
• The intensity of light controls the number of emitted electrons (photocurrent), while the frequency controls the maximum kinetic energy of the electrons.
• Einstein’s photon theory successfully explained threshold frequency, stopping potential, saturation current, and all experimental observations of the photoelectric effect.

The property of electromagnetic radiation to exhibit both wave nature and particle nature is called wave–particle duality of electromagnetic radiation.

The change in wavelength of X-rays after scattering from electrons is called the Compton shift.

\[\Delta\lambda=\lambda^{\prime}-\lambda=\frac{h}{m_ec}(1-\cos\theta)\]

A device that uses the photoelectric effect to convert light energy into electrical energy is called a photocell.

The hypothesis that matter, like radiation, exhibits both wave and particle nature is called the de Broglie hypothesis.

The waves associated with moving material particles are called matter waves.

The wavelength associated with a moving material particle is called the de Broglie wavelength.

λ = \[\frac {h}{p}\]

\[
\lambda = \frac{h}{mv}
\]

The emission of electrons from a metal surface by heating it to high temperature is called thermionic emission.

The emission of electrons from a metal surface by applying a strong electric field is called field emission.

A microscope that uses accelerated electron beams instead of visible light to obtain high-resolution images is called an electron microscope.