(5-2) The interplanar spacing for the planes in the nickel crystal from which reflection intensity maxima were detected is 9.1 x 10-11m (this can be found by x-ray diffraction). Davisson & Germer applied a voltage of 54 V to accelerate the electrons and observed that - as predicted if the electron beam behaved as a wave – there were maxima and minima in the intensity of the reflected beam when the angle between the beam and the reflecting planes in the crystal was varied. The smallest angle which gave a maximum in intensity for the reflected beam was measured to be 65o relative to the reflecting planes in the crystal.
You can use these data to deduce the apparent wavelength of the electrons and then investigate whether it is consistent with the de Broglie equation. To do this you will need some numbers:
Electron charge: 1.602 x 10-19 C Electron mass: 9.109 x 10-31 kg
Planck constant: 6.626 x 10-34 Js
① Use Bragg’s law to find the measured electron wavelength.
② Calculate the energy that an electron picks up when it is accelerated by a voltage of 54 V (recall that voltage = energy / charge).
③ Once the electrons have been accelerated to this energy, there’s effectively no longer any force acting on them, so the energy they have picked up is just kinetic energy. Therefore you can calculate their velocity. Use the simple non-relativistic kinetic energy expression: provided the velocity you deduce is not approaching the speed of light, this will be fine for our purposes.
④ Hence use Louis’ equation to deduce what the wavelength associated with such a moving electron should be. Compare this with the value you deduced in ① and hence decide whether he was barking up the right tree.