A modified oscilloscope is used to perform an electron interference experiment.?

Question

A modified oscilloscope is used to perform an electron interference experiment. Electrons are incident on a pair of narrow slits 0.0602 µm apart. The bright bands in the interference pattern are separated by 0.424 mm on a screen 20.9 cm from the slits. Determine the potential difference through which the electrons were accelerated to give this pattern.

Answer 1

The fringe separation (s) is given by

s=Dλ/d, thus   λ=sd/D

where s=0.424 mm, D=20.9 cm and d=.0602 µm.  ÃŽÂ» is the electrons' DeBroglie wavelength given by

λ=h/p

where h=Planck's constant, p=the momentum of the electrons.

Their energy equals eV, where V is the voltage, thus

p^2/2m=eV

Thus

V=  (hD/ s d ) ^2 / (2 me).