Table of contents 
DeBroglie's Hypothesis: 
Derivation of De Broglie's Relationship : 
Heisenberg Uncertainty Principle: 
Wave mechanical model of an Atom: 
ψ2 [Probability Density] : 
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For a photon,
...(i)
...(ii)
He concluded that as electromagnetic radiation have some associated mass or associated momentum, in the same way every moving particle of mass `m' and velocity `v' is associated with waves and these associated waves are known as matter waves or De Broglie's waves.
Experimental verification of De Broglie's hypothesis : Given by Davission and Germer.
They observed that a beam of electrons are diffracted by nickel crystal just like the xrays. More over the wavelength of the electrons determined by the diffraction experiments are equal to the values calculated from De Broglie's relationship.
Derivation of Bohr's postulate of quantization of angular momentum from De Broglie's Equations
According to De Broglie, moving electron is associated with waves must be completely in phase and therefore, only those orbits are possible where circumference of the orbit is integral multiple of λ i.e.
, where n is the no. of waves
From the above expression it can be commented that
no of waves in a shell waves = shell no.
Calculation of De Broglie wavelength if K.E. of the particle is E
2E = mv^{2}; 2mE = m^{2} v^{2 }= p^{2}
If a charge particle at rest (having charge `q') is accelerated by potential difference'V' volt then,
,
(Only for electron).
Ex. Calculate λ_{dB} of electron having K.E. 3 eV.
Sol.
Fig: Uncertainty Principle.
Fig: Schrodinger wave equation.
Where , E = total energy of electron
U = potential energy of electron
= Laplacian operator =
and y = wave function of electron = amplitude of matter wave.
Schordinger equation can be solved completely for hydrogen atom and hydrogenlike species like He^{ }, Li^{2 }.
The Schordinger equation can also be written in terms of spherical polar coordinates (r, q, f) in addition to Cartesian coordinate x, y, z.
Since, Hatom possess spherical symmetry, it is easier to solve Schrodinger equation if it is represented in polar coordinate.
When Schrodinger equation in polar coordinate is solved for Hatom then the solution obtained can be expressed as:
represents radial wave function which depends on n, l.
→ Angular wave function which depends on m, l.
(Psi) : [Wave function or Amplitude of Electron Wave]
It is also known as atomic orbitals. It is a mathematical function whose value depends on coordinates of electron in an atom. It may be ve or ve depending upon value of coordinates and it has no physical significance.
According to electromagnetic wave theory, intensity of light is proportional to square of amplitude. In the same way gives an idea of intensity of electron wave i.e. probability of finding electron at that point.
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