Question

Double-slit experiment for electrons. Electrons in a beam are directed towards two slits. The electrons each have speed of 2000 m/s. The slits spaced 0.6 mm apart.

a. What is the De Broglie wavelength of these electrons? b. What is the width of the central maximum if the screen is 0.5 m away from the slits?

Answer 1

a.The de Broglie equation is an equation used to describe the wave properties of matter, specifically, the wave nature of the electron:​

λ = h/(m*v)

where λ is wavelength, h is Planck's constant, m is the mass of a particle, moving at a velocity v.

λ = (6.626* 10^-34) / (9.1* 10^-31 * 2000)

λ = 364 nm

The wavelength of beam of electron is 364 nanometer.

b. Formula for the width of the central maximum is:

y = 2*λ*D/d

y = 2*364 * 10^-9 * 0.5/0.6 * 10^-3

y = 0.606 mm