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Matter Waves (de-Broglie Waves)

According to de-Broglie a moving material particle sometimes acts as a wave and sometimes as a particle.
The wave associated with moving particle is called matter wave or de-Broglie wave and it propagates in the form of wave packets with group velocity.
de-Broglie wavelength According to de-Broglie theory, the wavelength of de-Broglie wave is given by
where h = Planck’s constant, m = mass of the particle, v = Speed of the particle, E = energy of the particle.
The smallest wavelength whose measurement is possible is that of γ -rays.
The wavelength of matter waves associated with the microscopic particles like electron, proton, neutron, α-particle etc. is of the order of 10–10 m.
de-Broglie wavelength associated with the charged particles The energy of a charged particle accelerated through potential difference V is 99961.png
Hence, de-Broglie wavelength,
99977.pngÅ, 99983.pngÅ,
99994.pngÅ, 100000.pngÅ
de-Broglie wavelength associated with uncharged particles For neutron, de-Broglie wavelength is given as
Energy of thermal neutrons at ordinary temperature,
where T = absolute temperature, k = boltzman’s constant = 1.38 × 10–23 Joule/kelvin,
So, 100023.png

Ratio of wavelength of photon and electron The wavelength of a photon of energy E is given by λph = hc / E. While the wavelength of an electron of kinetic energy K is given by 100035.png. Therefore, for the same energy, the ratio 100041.png

Characteristics of Matter Waves

  • Matter wave represents the probability of finding a particle in space.
  • Matter waves are not electromagnetic in nature.
  • de-Brogile or matter wave is independent of the charge on the material particle. It means matter wave of de-Broglie wave is associated with every moving particle (whether charged or uncharged).
  • Practical observation of matter waves is possible only when the de-Broglie wavelength is of the order of the size of the particles.
  • Electron microscope works on the basis of de-Broglie waves.
  • The phase velocity of the matter waves can be greater than the speed of the light.
  • Matter waves can propagate in vacuum, hence they are not mechanical waves.
  • The number of de-Broglie waves associated with nth orbital electron is n.
  • Only those circular orbits around the nucleus are stable whose circumference is integral multiple of de-Broglie wavelength associated with the orbital electron.

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