# Electron Diffraction Lab

## Summary

Using an electron gun and a high Voltage power source we accelerate are going to accelerate electrons through a diffraction grating to find out more about the wave representation of electrons. Louis de Broglie was first to hypothesize that electromagnetic waves could be interpreted as particles waves. Due to the interaction of the nickel grid and the electrons our electrons are diffracted into two rings which will glow on a luminescent part of the bulb. The wave-particle duality of electrons allows for the diffraction of electrons as if it is a wave. By finding the diffraction lattice distance using methods using the wave representation of electrons I can show that Louis De Broglie's theory of particle-wave duality for an electron is indeed true.

## Method

In this experiment we will find the separation of the lattice by comparing the ring size to various Voltages. The accelerating Voltage is directly related to the momentum of the electron which can be related to the wavelength by

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

as explain in the lab manual I relate the lattice seperation by to the accelerating voltage and the radius by

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

in order to find a relation between the radius we found and the accelerating voltage we must see how our radius is affected in the geometry of the bulb.

$D=2 L tan(\frac{arcsin(\frac{r}{k})}{2})$

## Results and Analysis

• Threw away data noted in our lab manual after the point where the center ring became nearly invisible.

the known values of the separation of the diffraction grating are dinner= .123 douter= .213

my values were

$d_i=.1167(.069) \$ nm

$d_o=.283(.017) \$ nm

SJK 03:15, 18 December 2008 (EST)
03:15, 18 December 2008 (EST)
You have a good use of the SEM to talk about consistency of your answer with the accepted value. However, I don't understand the systematic error leading to tiny value for standard deviation? It's very difficult to assess anything without any graphs or links to any kind of analysis.

My value for the inner radius works out to show that the assuming electrons to have a wave representation works out correctly. My value for the inner radius falls well within one standard deviation of the known value for the lattice separation. However my value for the outer radius come out to be close in percent difference ,but very far in standard deviations to the actual value. There was a large amount of systematic error that probably led to the tiny value for standard deviation. The outer radius showed less change in radius than inner radius and this led to many of the data points of the outer radius to be very similar.

### What I learned

This lab took a different approach to solving the problem than I had thought of before. Rather than starting with a theory to find a constant we used a constant to prove a theory. In order to show that particle wave duality is indeed an effective method of thinking about electrons we used a known constant (the lattice spacing) and used our knowledge of wave diffraction to show that electrons act in the same way.