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Thursday, December 30, 2010

de Brogli wavelength

  • Interference, diffraction and polarization establishes the wave nature of light and can be explained on the basis of wave theory
  • photoelectric effect and compton effect are explained on the basis of quantum theory of light which establishes that quanta behaves like corpescules.
  • Louis de Brogli proposed that idea of dual nature i.e., wave particle duality should be extanded to all micro particlesi.e., wave and corpescular nature should be associated with each particle.
  • According to him material particles might have dual nature same as that of light.
  • He suggested that moving particle whatever is its nature , has wave properties associated with it.
  • Wavelength λ associated with any particle of momentum p is given by
    where h is the Plank's constant.
  • From Plank's theory of radiation , energy of photon is given by
    E=hν = hc/λ
    therefore λ=hc/E
    From special theory of relativity
    mass of photon is m=hν/c2
    momentum of photon is
    mc=p=hν/c = h/λ
    therefore p=h/λ
    or, λ=h/p
  • Thus what is true for energy packet (photon) is also true for material particle. Thus, for particle of mass m moving with velocity v , we have p=mv and de Brogli wavelength associated with it is
    where m is the relativistic mass of the particle
  • If m or v is large the de Brogli wavelength associated with a material particle would be small.
  • The de Brogli wave associated with a material particle or photon of any charge associated with it can also be calculated. Thus we know that
    therefore mv=√(2mK)
  • If a charged particle carrying a charge q is accelerated through a potential difference V volts, then kinetic energy K=qV
    Therefore be Brogli wavelength of charge particle for charge q and accelerated through a potential difference of V volts is given by

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