We begin our exploration of electrons by considering
the DeBroglie hypothesis, stating that there is a relationship between
the way light behaves (they way it moves in waves) and the way electrons
may behave. That is if electrons move the way light does then they
move in waves where their momentum (p) can be used to derive their wavelength
(l). So the following equations may apply:
This is very important because if one can determine the
wavelength of something then one can determine the energy level of an electron
when it is bonded to an atom.
If electrons behave in this wave nature we can diffract them, so we need a grating fine enough to diffract one of the smallest things known. If wavelengths are considered, the wavelength of an electron is about four fifths of a nanometer, this is way smaller than light. Rather than use a grating that was nearly visible to the naked eye (like we did with light) we used a crystal (spacing of 0.2 nanometers) as our grating. In the procedure we would accelerate an electron to a specific energy (anywhere between 2-5 KeV), the electrons would be accelerated (in a vacuum) towards a thin chicken wire mesh of polycrystalline graphite. This chicken wire mesh has different grove spacing (d1 = 0.213nm as well as d2 = 0.123). After hitting the photo crystal the electrons would be diffracted in circles. These circles are created because the photo crystal has many different orientations unlike our gratings used for light. Taking measurements of the circles at different voltages along with a known distance of 14cm (L) (from the screen to the graphite mesh) would give us the diffraction angles (q=D/2L) then the wavelengths (l=(0.2nm)D/2L) for the electrons.
