Question

Derive an expression for the de-Broglie wavelength associated with an electron accelerated through a potential V. Draw a schematic diagram of a localised-wave describing the wave nature of the moving electron.

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Answer 1

Expression for de Broglie Wavelength associated with Accelerated Electrons The de Broglie wavelength associated with electrons of momentum p is given by

where m is mass and v is velocity of electron. If E_k is the kinetic energy of electron, then

If V volt is accelerating potential of electron, then Kinetic energy,

This is the required expression for de Broglie wavelength associated with electron accelerated to potential of V volt. 

The diagram of wave packet describing the motion of a moving electron is shown.

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