# User:Chad A McCoy/Notebook/Jr. Lab/2008/10/12

From OpenWetWare

< User:Chad A McCoy | Notebook | Jr. Lab | 2008 | 10

Electron Diffraction | Main project page Previous entry Next entry |

## Electron Diffraction Calculations/Analysis- Calculations and data analysis were carried out using the programs MatLab and Maple.
- The work done in Maple involves the conversion of the ring heights from those projected on the curved surface of the electron diffraction tube to ones that would be seen on a flat screen tangent to the center of the tube.
- The work done in MatLab consists of all numerical calculations to find the spacing between molecules in the graphite crystal lattice, along with finding the error relative to known values of the spacing.
- The calculations done in Maple can be accessed at File:Electron diffraction.mw. NOTE: the file is in the format of a maple worksheet and cannot be properly opened outside of Maple.
- The calculations done in MatLab can be accessed at File:ElectronDiffraction.doc.
^{SJK 02:09, 19 October 2008 (EDT)}
- From my calculations, the spacing in the crystal lattice of graphite calculates as
**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 d=.109nm, .203nm}**, whereas the accepted values are**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 d=.123nm, .213nm}** - That gave a percent error of 11.7% on the .123nm distance and 4.9% on the .213nm distance.
- Using the largest value within the calculated error of
**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 d=.003nm, .006nm}**the percent error calculated to be 8.9% and 2.0%. - A graph of D (the extrapolated ring diameter) against the square-root of the anode Voltage, showed an approximate linear relationship, which proves that De Broglie's hypothesis is correct as the linear relationship is seen between the momentum of the particle and its wavelength due to the uncertainty in it's position.
- Therefore, my final values for the lattice spacing are
**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 d=.109(3)nm and .213(6)nm}**
^{SJK 02:25, 19 October 2008 (EDT)}^{SJK 02:32, 19 October 2008 (EDT)} |