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In the Davisson-Germer experiment, electrons with a known initial energy bombarded a surface and the reflection of these electrons from the surface is detected. The surface acts like a diffraction grating with the atoms in the crystal making up the grating.⁴  Restart.

In the animation, you can change the accelerating voltage, V, or the initial energy of the impacting electrons. The kinetic energy of the electrons is equal to the energy given the electron in the acceleration region. In the animation, the detector moves to the point of maximum signal intensity, the first order diffraction pattern (n = 1) (the angle of the detector is given in degrees).

1. For the range of allowed accelerating voltages (10 - 100 V), can the electron kinetic energy be considered non-relativistic?
2. How does the angle of maximum signal depend on the electron energy?  Develop a relationship between electron kinetic energy and sin(θ).
3. If the distance between atoms of the material is 0.215 nm (as in nickel), what is the relationship between electron kinetic energy and wavelength?
4. What then is the relationship of electron momentum to wavelength?  You should find that p = h/λ , which is the de Broglie wavelength.

⁴As reminder, for light incident on a diffraction grating, the location of a bright spot for a given wavelength, λ, is given by d sin(θ) = n λ, where d is the spacing between the slits in the grating, n is an integer (the order of the maxima), and θ is the angle of the diffracted light from the original path. For commonly-used modern physics experiments that use high energy electrons (keV electrons instead of less than 100-eV electrons) impacting on a material (like graphite), the diffraction pattern is due to interference from electron waves scattered from multiple layers of the material. In that case, the electron beam does not impact the surface at a normal angle and the location of a bright spot is given by the Bragg relationship: 2d sin(θ/2) = n λ.