User:Tyler Wynkoop/Tyler's Page/eDiffraction

Electron Diffraction
In 1929, Louis De Broglie won the Nobel prize for his research in the wave-particle duality of matter. He developed the famous De Broglie hypothesis in which he uses Einstein's λ=cν in analysis of matter. He developed the equation:

$$ \lambda = \frac{h}{p} $$

The Lab

In this lab we used a diffraction grating of graphite to produce visible results on a screen, via an electron beam. The crystal lattice of the graphite is known to have two characteristic spacings in which electrons are diffracted through. These two spacings produce two rings in the electron beam on the screen. By measuring the voltage propelling the electrons and the diameter of the rings, we can measure the wavelengths of the electrons.

Data

According to our data the d-spacing of the crystal lattice is d = .195E-9 ± 1E-12 nm and d = .114E-9 ± 0.4E-12 nm. The accepted values are d = 0.213*10^-9 nm and d = 0.213*10^-9 nm, resulting in an 8% and 7% error respectively. Dan was able to develop a graph of error, here.



Using the Bragg condition

$$ 2\cdot d\cdot sin \theta = 2 \cdot d \theta = n \lambda \,\!$$

Simplifying for small angles, and remembering that the angle of diffraction is 2θ, the relationship becomes

$$ \frac{R \cdot d}{L}=\lambda $$

where
 * R = .066 meters
 * L = .13 meters

This yields
 * λ = 9.900E-11±1.02E-13
 * λ = 5.788E-11±4.06E-13

Links
 * Data Record