SYNOPSIS

An electromagnetic wave has dual (wave–particle) nature. 

• The wave nature of light can be observed in the phenomena of interference, diffraction and polarisation.
• While photoelectric effect and Compton effect involve energy and momentum transfer, radiation behaves as if it is made of a bunch of particles-photons show particle nature of a wave.

Wave nature of matter

• De Broglie said that wave nature was symmetrical and that the two basic physical entities—matter and energy-must have symmetrical character. If radiation shows dual aspects, so should matter.
• De Broglie proposed that wavelength λ is associated with a particle of momentum p.
• This wavelength is so small that it is beyond any measurement. This is the reason why macroscopic objects in daily life do not show wave-like properties.
  
  
• De Broglie hypothesis
• Matter shows dual character like electromagnetic radiation does. It also shows wave-like properties.
• Apart from being a particle, a wavelength associated with matter is called de Broglie
  wavelength. It is given by the relation,
• where m is the mass of the particle, v is speed and h is Planck’s constant.
• On the left-hand side of the above equation, λ is the attribute of a wave, while on the right-hand side, the momentum p is a typical attribute of a particle.

• Substituting the numerical values of h, m and e,
  

Davison and Germer experiment

Davisson–Germer electron diffraction arrangement

Result

• It was noticed that a strong peak appeared in the intensity (I) of the scattered electron for an accelerating voltage of 54 V at a scattering angle θ = 50°.

• This is due to the constructive interference of electrons scattered from different layers of the regularly spaced atoms of the crystals.

• From the electron diffraction measurements, the wavelength of matter waves was found to be 0.165 nm.

                      

Photoelectric effect

• When light falls on a metal surface, some electrons near the surface absorb enough energy from the incident radiation to overcome the attraction of the positive ions in the material of the surface.
• After gaining sufficient energy from the incident light, the electrons escape from the surface of the metal into the surrounding space.
• The photoelectric emission is an instantaneous process without any apparent time lag (〖~10〗^(-9)s or less) even when the incident radiation is made exceedingly dim.

Photoelectric effect

• When light of an appropriate frequency (or correspondingly of an appropriate wavelength) is incident on a metallic surface, electrons are liberated from the surface. These photo- or light-generated electrons are called photoelectrons.
• The incident light photon should be greater than or equal to the work function of the metal.
  E ≥ W
  hν ≥ W
  ν ≥ W/h

Effect of potential on photoelectric current

• The photoelectric current increases with an increase in accelerating (positive) potential.
• The maximum value of the photoelectric current is called saturation current.
• At saturation current, all the photoelectrons emitted by the emitter plate reach the collector plate.

Intensity of incident radiation

• The photocurrent is found to decrease rapidly until it drops to zero at a certain critical value of the negative potential V0, which is called the retarding potential V0.
• The minimum negative (retarding) potential given to the plate for which the photocurrent stops or becomes zero is called the cut-off or stopping potential.
• Photoelectric current is zero when the stopping potential is sufficient to repel even the most energetic photoelectrons with the maximum kinetic energy (Kmax).
  K max = e V0

Einstein’s photoelectric equation

• The electron is emitted with maximum kinetic energy given by K max = hν – φ0.
• Kmax depends linearly on ν and is independent of the intensity of radiation.
• Photoelectric emission is possible only if h ν > φ0.
• Greater the work function φ0, higher the minimum or threshold frequency ν0 needed to emit photoelectrons.
  Photoelectric equation can be written as eV0 = h ν – φ0, for ν ≥ ν0.