DUAL NATURE OF ELECTRON
Mechanical theory describes electron, protons as particles.
In 1905 Plank and Einstein proposed that energy radiation including those of heat and light are emitted discontinuously as little bursts called as quanta or Photons. This view is opposed to the wave theory of light and it gives particle like properties to waves.
According De-Broglie, the light exhibits both a wave and a particle nature under suitable condition.
In 1927 Davission and Germer discovered the diffraction of electrons. As Diffraction was one of the main properties supporting the wave like character of light, it also confirmed the electron’s wave behavior.
LOUIS- DE BROGUE EQUATION
According to plank, the energy of a photon is given by the equation.
 (1)
According to Einstein, the energy of photon with mass “m” can be given by the equation.
 (2)
Comparing equation 1 and 2
 (3)
As 
Or 
or
Therefore equation 3 can be arranged on
 (4)
Equation 4 is called as De- broglies equation. De-broglie predicted that all atomic particles have wave like properties.
According to him a moving object will have wave like motion. The wave of the moving body will have wavelength, which will be inversely related to the mass of the object. To explain these consider the following to examples.
1) Wave length of electron having the velocity of light :-
The velocity of electron= 
The Mass of electron= 
The plants constant h= 
According to De-Borglies equation
 
2) Wave length of an object of 1 kg moving with a velocity of 10m/s.
Velocity of object= 
Mass of the object= 
The plant’s constant,
According to De- broglies equation.
 .
From the above two examples we can conclude that:
- Each material object is associated with a wave length (l ) .
- There is inverse relationship between wavelength and mass of substance. When mass increases wavelength decrease.
X-rays has a wavelength of about 10-13m, and as wavelength decreases, its accurate measurement become difficult and has no significance.
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