Tuesday, December 30, 2014

De-Broglie wavelength



According to de-Broglie a moving material particle sometimes acts as a wave and sometimes as a particle.The waves associated with moving particle is called matter waves 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 De-Broglie wavelength, λ=h/mv; where h = Plank's constant, m = Mass of the particle, v = Speed 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 m. 
 De-Broglie wavelength associated with the charged particles 
The energy of a charged particle accelerated through potential difference V is
            E = 1/2 mv2 = q(pd)
 Hence De-Broglie wavelength
de-brogly-wavelength
 De-Broglie wavelength associated with uncharged particles 
For Neutron De-Broglie wavelength is given as 
de-brogly-wavelengthÅ

Energy of thermal neutrons at ordinary temperature 3/2kT; where k = Boltzman's constant = 1.38 x 10-23 Joules/kelvin, T = Absolute temp.
So de-brogly-wavelengthÅ
 Some Important Graphs: 
de-brogly-wavelength
Characteristics of matter waves:
  • Matter waves are not electromagnetic in nature.
  • Practical observation of matter waves is possible only when the de-Broglie wavelength is of the order of the size of the particles is nature.
  • 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.
  • 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.

Photoelectric Effect


It is the phenomenon of emission of electrons from the surface of metals, when light radiations (Electromagnetic radiations) of suitable frequency fall on them. The emitted electrons are called photoelectrons and the current so produced is called photoelectric current.
This effect is based on the principle of conservation of energy.
Terms related to photoelectric effect
(i) Work function (or threshold energy) (W0) : The minimum energy of incident radiation, required to eject the electrons from metallic surface is defined as work function of that surface. 
v0 = Threshold frequency; l0 = Threshold wavelength
Work function is often stated in electron volt W0(eV).
(ii) Threshold frequency (n0) : The minimum frequency of incident radiations required to eject the electron from metal surface is defined as threshold frequency.
If incident frequency n < n0 Þ No photoelectron emission
(iii) Threshold wavelength (&lambda0) : The maximum wavelength of incident radiations required to eject the electrons from a metallic surface is defined as threshold wavelength.
If incident wavelength &lambda > &lambda0 Þ No photoelectron emission
Einstein's photoelectric equation: 
According to Einstein, photoelectric effect is the result of one to one inelastic collision between photon and electron in which photon is completely absorbed. So if an electron in a metal absorbs a photon of energy E (= hn), it uses the energy in the following ways:
(i)  Some energy (say W0) is used in making the surface electron free from the metal.
(ii) Rest energy will appear as kinetic energy (K) of the emitted photoelectrons. Hence E = W0 + K This is the Einstein's photoelectric equation