How does the de-broglie wavelength of charged particle change when accelerating potential increases?

1 Answer
Feb 22, 2018

Well, the potential that accelerates the charged particle gives it a kinetic energy in #"eV"# for every charge unit it has. First,

#lambda = h/(mv)#

for mass-ive particles. We know that the kinetic energy is

#K = 1/2 mv^2#,

so

#v = sqrt(2K//m)#

This means for particles with mass,

#color(blue)(lambda) = h/(mcdot sqrt(2K//m))#

#= color(blue)(h/(sqrt(2mK)))#

We see that as #Kuarr#, #lambdadarr#.

So, as the accelerating potential increases, the kinetic energy of the particle increases, the de Broglie wavelength decreases, and the particle acts more classically.