Simple experiments on diffraction by a grating or refraction by a prism are explained by the wave nature of light. Whereas interpretation of photo-electric effect is based on the particle nature of light (photons). Thus, light radiations have dual behavior and can be considered either as a wave motion or as a stream of photons. In 1924, de Broglie proposed a similar dual behavior for electrons and gave an expression relating their wavelength with mass (m) and velocity:
                                                              
Experimental proof of wave nature of electrons was provided by Davisson and Germer in 1927 by showing that electron beam is diffracted by a crystal in the same way as light radiation in diffracted.

Another fundamental difficulty arose form Heisenberg’s Uncertainty Principle which states that it is impossible to describe, simultaneously and precisely both the position and momentum of the electron. (Bohr model violates the uncertainty principle, as it describes simultaneously other the positing and momentum of the electron.)

These developments led to a completely different model of the atom-wave or Quantum Mechanical Model- based on the following postulates:

(i)    Heisenberg uncertainty principle governs atomic particles. The term probability distribution of mathematical wave function is used to describe motion of an electron.
(ii)    A stream of electron is associated with a wave whose wavelength is given by de Broglie relationship:
                                                             
(iii)    Electron wave is compared to a stationary or standing wave formed by a vibrating string fixed between two points.
(iv)    Energy values of the electron are quantized as postulated by Bohr.

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