User:Tyler Wynkoop/Notebook/Junior Lab/Electrondiff

Electron Diffraction
Overview

The concept of this lab is to measure the diameter of inner and outer rings displayed on a screen. These measurements can be then analyzed to determine the De Broglie wavelength of the electrons.

Theory

De Broglie proposed that matter shared the wave-particle duality of light. This experiment is designed to demonstrate and measure this concept. An electron beam is passed through an extremely thin graphite screen. The graphite has a hexagonal crystalline shape with two distinct distances of .123nm and .213nm. The electrons incident on this screen are diffracted through each of these spacings, producing the two concentric circles on the display screen.

Equipment
 * Voltage source
 * Digital calipers
 * Low voltage bias
 * Electron diffraction tube
 * Banana plug cables

Set Up

The set up for this lab was quite complicated. The image link below shows how the cables and devices are to be set up. Otherwise, a room with total darkness is required to see the rings and measure them accordingly. | Set Up Image

Procedure

Professor Gold's Lab Manual

As far as physical work was concerned, only the measurement of the rings was required. I found that using two hands, and steadying hands on the diffraction bulb allowed for better accuracy.

Data

NOTE: I measured the outer diameter of the rings

5kV 4.8kV 4.6kV 4.4kV 4.2kV 4.0kV 3.8kV adjusted magnet to realign beam 3.6kV 3.4kV 3.2kV 3.0kV adjusted magnet to realign beam 2.8kV The lines have have become too vague and indistinct. The exact location of the "Maximum" could be anywhere within in several millimeters.
 * Outer Ring: 38.70mm, 37.29mm, 39.31mm
 * Inner Ring: 22.21mm, 22.39mm, 21.84mm
 * Outer Ring: 38.70mm, 38.83mm, 38.45mm
 * Inner Ring: 22.94mm, 22.32mm, 22.49mm
 * Outer Ring: 39.4mm, 39.14mm, 39.76mm
 * Inner Ring: 23.55mm, 23.50mm, 23.39mm
 * Outer Ring: 40.51mm, 40.50mm, 40.15mm
 * Inner Ring: 24.25mm, 24.30mm, 23.59mm
 * Outer Ring: 41.79mm, 41.11mm, 41.36mm
 * Inner Ring: 24.76mm, 24.63mm, 24.54mm
 * Outer Ring: 43.41mm, 42.40mm, 42.29mm
 * Inner Ring: 25.55mm, 25.29mm, 25.92mm
 * Outer Ring: 45.08mm, 44.67mm, 45.13mm
 * Inner Ring: 27.12mm, 26.73mm, 26.75mm
 * Outer Ring: 46.14mm, 45.19mm, 45.38mm
 * Inner Ring: 28.09mm, 27.40mm, 27.54mm
 * Outer Ring: 47.83mm, 47.32mm, 47.14mm
 * Inner Ring: 28.78mm, 29.17mm, 29.04mm
 * Outer Ring: 48.71mm, 48.68mm, 47.88mm
 * Inner Ring: 29.17mm, 29.25mm, 29.07mm
 * Outer Ring: 49.75mm, 49.74mm, 49.53mm
 * Inner Ring: 29.91mm, 29.69mm, 30.42mm

Analysis

Here is the raw data. The individual points are plugged into the formula from Gold's manual, an corrected for the curvature of the glass.

$$d = \frac{4 \pi L h c}{D \sqrt{2 e V m c^2}}$$

Thanks

Dan Wilkinson for recording the data.

Alexandra S. Andrego and Anastasia A. for their excellent lab notebook.

Darell Bonn for the image of the device setup.