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Dual Nature Of Matter And Radiation

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Dual Nature of Matter and Radiation PDF Notes, Important Questions and Synopsis

 

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,begin mathsize 12px style straight lambda equals straight h over straight p end style
  • 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.
  • De Broglie wavelength for a photon
  • De Broglie’s idea that matter also exhibits duality and has wave properties can be expressed quantitatively by first considering electromagnetic radiation.
  • A photon of frequency v and wavelength λ has energy:begin mathsize 12px style straight E equals hv equals hc over straight lambda end style
  •  De Broglie wavelength for an electron
    If an electron (charge = e) is accelerated by potential difference of volts, then it acquires kinetic energy of
    K=eV
  • Therefore, the formula can be written as 
    begin mathsize 12px style straight lambda equals straight h over mn equals straight h over straight p equals fraction numerator straight h over denominator square root of 2 Km end root end fraction equals fraction numerator straight h over denominator square root of 2 eVm end root end fraction end style
  • Substituting the numerical values of h, m and e,
    Error converting from MathML to accessible text.

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.

    Error converting from MathML to accessible text.                    

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

Work function

  • The minimum energy required by an electron to escape from the metal surface is called the work function of the metal. It is generally denoted by W and measured in electron volt (eV).

Threshold frequency

  • The minimum frequency W/h required for emission of electrons is called threshold frequency. It is denoted by ν0.
    ν0 = W/h (threshold frequency)

Effect of intensity of light on photocurrent

  • Photocurrent increases linearly with the intensity of incident light when accelerating potential is fixed.

 

 

 

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.
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