Incident Beam d d , (a) (b) Figure 2: (a) Bragg condition for constructive interference, (shown in reflection mode). (b) Crystal structure of...

Use the Bragg condition, (2d sin(θ) =nλ), the de Broglie relationship (λ=h/p), and conservation of energy for the accelerated electrons (assuming the electrons start from rest at the filament and move through a potential difference V) to show that the diameter D of each diffraction ring is related to the electron accelerating potential V by:

D= ((Lh)/d)*(2/(meV))1/2

Here, h= Planck's constant, m and e are the mass and charge of the electron, L is the distance from the graphite target to the observing screen, and d is the distance between nearest-neighbor scattering planes. Use the small angle approximation in the Bragg rule to derive the equation for D

IncidentBeamdd ,(a)(b)Figure 2: (a) Bragg condition for constructive interference, (shown in reflection mode). (b) Crystal structure of graphiteshowing two sets of scattering planes corresponding to di - 1.23 A and de - 2.13 A. Since the crystals are arranged at variousangles, their individual diffraction pattern combines around 360" to form rings.