- Interference, diffraction and polarization establishes the wave nature of light and can be explained on the basis of wave theory
- photoelectric effect and compton effect are explained on the basis of quantum theory of light which establishes that quanta behaves like corpescules.
- Louis de Brogli proposed that idea of dual nature i.e., wave particle duality should be extanded to all micro particlesi.e., wave and corpescular nature should be associated with each particle.
- According to him material particles might have dual nature same as that of light.
- He suggested that moving particle whatever is its nature , has wave properties associated with it.
- Wavelength λ associated with any particle of momentum p is given by

λ=h/p=h/mv

where h is the Plank's constant. - From Plank's theory of radiation , energy of photon is given by

E=hν = hc/λ

therefore λ=hc/E

From special theory of relativity

E=mc^{2}

mass of photon is m=hν/c^{2}

momentum of photon is

mc=p=hν/c = h/λ

therefore p=h/λ

or, λ=h/p - Thus what is true for energy packet (photon) is also true for material particle. Thus, for particle of mass m moving with velocity v , we have p=mv and de Brogli wavelength associated with it is

λ=h/mv

where m is the relativistic mass of the particle - If m or v is large the de Brogli wavelength associated with a material particle would be small.
- The de Brogli wave associated with a material particle or photon of any charge associated with it can also be calculated. Thus we know that

K=mv^{2}/2

therefore mv=√(2mK)

λ=h/√(2mK) - If a charged particle carrying a charge q is accelerated through a potential difference V volts, then kinetic energy K=qV

Therefore be Brogli wavelength of charge particle for charge q and accelerated through a potential difference of V volts is given by

λ=h/√(2mqV)

## Thursday, December 30, 2010

### de Brogli wavelength

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