# 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:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \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**

^{SJK 01:39, 22 December 2010 (EST)}

Using the Bragg condition

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 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

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \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**