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Derive de-Broglie wave equation (wavelength) for a material particle. |
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Answer» Solution :The momentum of photon of frequency v is given by `p = (h upsilon)/(c) = (h)/(lambda)` since `c = upsilon lambda` The wavelength of a photon in TERMS of its momentum is `lambda = (h)/(p)""...(1)` According to de Broglie, the above equation is completely a GENERAL one and this is applicable to material particles as well. Therefore, for a particle of mass m travelling with speed v, the wavelength is given by `lambda = (h)/(mv) = (h)/(p)""...(2)` This wavelength of the matter waves is known as de Broglie wavelength. This equation RELATES the wave character (the wave length `lambda`) and the particle character (the momentum p) through Planck.s CONSTANT. |
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