Derive the de Broglie wavelength for a charged particle of charge q and accelerated through a potential difference of V volts.


The Required de Broglie Wavelength:

A photon of light of frequency  has the momentum,


But, . Therefore, the momentum of the photon can be expressed in terms of wavelength λ as,


The wavelength of a photon is, therefore, specified by its momentum according to the relation,




de Broglie suggested that the above equation is applicable for any material particles as well as photons. If the mass of a moving particle is m and velocity is v, then its momentum is p = mv and its de Broglie wavelength is accordingly,


If  is the kinetic energy of the material particle, then


Therefore, de Broglie wavelength of particle of K.E. = 

 ………….(ii)

If the particle is charged of charge q and accelerated through potential difference of volt V, the K.E.  

Thus, the de Broglie wavelength for a charged particle of charge q which accelerating through potential difference of volt V is,

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