Question

Write the expression for the de Broglie wavelength associated with a charged particle of charge q and mass m, when it is accelerated through a potential V.

Answer 1

An electron of mass m is accelerated through a potential difference of V volt. The kinetic energy acquired by the electron is given by `1/2` mv² = eV

Therefore, the speed v of the electron is v = `sqrt((2"eV")/"m")`

Hence, the de Broglie wavelength of the electron is λ = `"h"/"mv" = "h"/sqrt(2"emV"`