# User:Garrett E. McMath/Notebook/Junior Lab/2008/10/13

Electron Diffraction Main project page
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## Electron Diffraction Lab

• Notes same as Paul Klimov

Purpose

• Study wave nature of electrons
• Study and verify the De Broglie hypothesis of $\lambda = \frac{h}{p}$
• Measure spacing of diffracting planes in graphite

## Formulas

In the early 1900s, deBroglie postulated that matter must have wavelike properties, just like light waves can have particle like nature. He postulated that matter waves have wavelength:

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

Not long after his proposition, experimental evidence for his postulate was provided, when electrons were observed to diffract. The relationship for light diffraction passing through a slit of width d, is:

dsinθ = λ

For small angles, this relationship simplifies to:

$\frac{dD}{2L}=\lambda$

where D is the spacing between the maxima on the screen, a distance L away.

$\lambda = \frac{h}{p} = \frac{h}{\sqrt{2mE_{k}}}=\frac{h}{\sqrt{2meV_{a}}} =\frac{2\pi\hbar}{\sqrt{2meV_{a}}}$

Setting the wavelength of the electron equal to the wavelength in diffraction, we get:

$\frac{Dd}{2L}=\frac{2\pi\hbar}{\sqrt{2meV_{a}}}$

$d=\frac{4\pi\hbar L}{D\sqrt{2meV_{a}}}$

$r=slope\cdot\frac{1}{\sqrt{V}}$

SJK 17:11, 1 November 2008 (EDT)
17:11, 1 November 2008 (EDT)
What is r? And I think you forgot a factor of 2 in your final answer

$slope=\frac{Lh}{\sqrt{2me}\cdot d}$

$d=\frac{Lh}{\sqrt{2me}\cdot slope}$

## Equipment

• Tel 2501 Universal stand
• Electron Diffractor 2555 (5Kv .3mA)
• Teltron Limited London England 813 KV Power Unit
• HP 6216B Power Supply
• Wavetek Meterman 85XT multimeter
• Shock proof Calipers number 6020

## Cautions

Given the tiny current, electrical shock is probably the least worries.SJK 02:54, 1 November 2008 (EDT)
02:54, 1 November 2008 (EDT)
It's microamp current when the electrons are traveling through the vacuum bulb...if you made a direct connection with your body, much more current could flow! Thus you should assess the maximum current of the power supply, not the maximum current draw of the device

Also, please take a look at My comments on Paul's notebook, since your notes are the same.
However, the diffraction device, and especially its contents look (and are) quite fragile. More specifically, it is in our best interest to keep the heater current below the .25mA rating to prevent damage to the graphite foil.

## Procedure

• We set up 2 power supplies in our circuit but only used one. The setup matched the schematic provided in Dr.Golds manual.
• The heater was turned on and we waited for several minutes to wait for the filament to heat up. The filament was glowing shortly after it was turned on.
• We have an ammeter set up in series to measure the current of the heater because we cannot let it exceed .25mA. Attaining a comparable current could result in the graphite foil being punctured.
• The diffraction maxima will be measured with the calipers. As suggested by Dr.Koch, we will be measuring the inner diameter of the outer ring and the outer diameter of the inner ring.

## Data

### Week1

V (V) outer diameter (mm) inner diameter (mm)
4900 38.62324±1.5 24.1555±1.5
4800 39.76624±1.5 24.38400±1.5
4700 40.3098±1.5 24.4792±1.5
4600 40.89400±1.5 24.58212±1.5
4500 41.66794±1.5 25.1206±1.5
4400 42.0015±1.5 25.89022±1.5
4300 42.38752±1.5 28.70200±1.5
4200 43.7388±1.5 28.88234±1.5
4100 43.36288±1.5 29.45384±1.5
4000 45.31106±1.5 29.7307±1.5
3900 45.62094±1.5 30.1498±1.7
3800 45.6438±1.7 30.23616±1.7
3700 47.7393±1.7 31.0515±1.7
3600 48.38700±1.7 31.87700±1.7
3400 50.01006±1.7 32.2072±1.7
3200 52.83454±1.7 32.4739±1.7
SECOND TRIAL

V (V) outer diameter (mm) inner diameter (mm)
4900 39.20236±1.5 21.84400±1.5
4800
4700
4600
4500 41.82618±1.5 25.1206±1.5

We started taking more data, but the measurements were so similar that we thought it would be pointless to continue. We will fit it before the next period and see if we have any major outliers. If this is the case, we will go back and make some adjustments.

### Week2

After looking at our data from the first week, we decided that it would be a good idea to retake measurements some measurements. An important distinction is that this time we will be measuring the inner diameter of the inner ring, not the outer diameter as we did the first time. We also used a new caliper:

Electronic Digital Caliper: Carrera Percision.

V (V) outer diameter (mm) inner diameter (mm)
4900 36.99±2.5 N/A
4800 37.11±2.5 20.35±2.5
4700 37.31±2.5 21.74±2.5
4600 37.63±2.5 22.04±2.5
4500 38.02±2.5 22.50±2.5
4400 38.28±2.5 22.86±2.5
4300 38.64±2.5 22.24±2.5
4200 39.06±2.5 22.97±2.5
4100 39.45±2.5 23.03±2.5
4000 39.86±2.5 23.23±2.5
3900 40.15±1.7 23.55±1.7
3800 40.55±1.7 23.74±1.7
3700 40.92±1.7 24.17±1.7
3600 41.19±1.7 24.41±1.7
3400 41.87±1.7 24.78±1.7
3200 42.23±1.7 25.04±1.7

## Corrections

SJK 17:36, 1 November 2008 (EDT)
17:36, 1 November 2008 (EDT)
None of this is in your excel sheet, and thus I have no idea what you're doing with this information. More generally, it's not clear from your notebook or excel sheet how you converted slopes to lattice spacing. (the formula I see shows a factor of 2 error)
L=130.0±2mm
Glass thickness=1.5mm
Accepted seperation of carbon atoms=.123nm and .213nm
deltaL = R(1 − cos(arcsin(D / 2R)))


## Sources of Error

• Line clarity: As the voltage went down so did the clarity of the lines making it very difficult to get accurate readings
• Voltage reading: We did not have a multimeter on the voltage so our reading of the voltages were taken off the archaic meter that was grossly inaccurate at best
• Power Supply possibly dying: According to Dr. Koch other groups had smelled something coming from the power supply and we heard popping noises and saw voltage shifts while using the power supply. This may correspond to a dying power supply that would make sense as it may be the first one ever made SJK 16:18, 1 November 2008 (EDT)
16:18, 1 November 2008 (EDT)
ha ha, good one. Also, good job on recording this information.
• The Corrections As long as the corrections are inputed into the data these should not be an issue though after looking at the effect it is almost negilible and therefore will probably be left out of the final data.

## Data Analysis

• Analysis performed in Excel
SJK 17:16, 1 November 2008 (EDT)
17:16, 1 November 2008 (EDT)

I See what you did: you mixed up the "Y" and "X" columns in your linest function. You used the slope from the graphs, but the uncertainty from the LINEST...thus, your uncertainties are incorrect.
Inner Diameter

• y=mx+b: m=1.32 with an uncertainty of .062 and b=.0023 with an uncertainty of .0014 (R^2=.895)
• y=mx: m=1.47 with an uncertainty of .004 (R^2=.883)
Outer Diameter

• y=mx+b: m=1.71 with an uncertainty of .019 and b=.0126 with an uncertainty of .00076 (R^2=.984)
• y=mx: m=2.51 with an uncertainty of .0021 (R^2=.765)
Calculated Spacing of Carbon


Inner Diameter

• Spacing from slope: .216nm (1.4% error from accepted value of .213nm)

Outer Diameter

• Spacing from slope: .124nm (.81% error from accepted value of .123nm)