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

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 * style="background-color: #EEE"|[[Image:owwnotebook_icon.png|128px]] Electron Diffraction
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Electron Diffraction Lab
Purpose
 * Notes same as Paul Klimov
 * 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:

$$ d sin \theta = \lambda $$

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:

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

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

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

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

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

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. 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.

Week1
SECOND TRIAL

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.

Corrections
L=130.0±2mm Glass thickness=1.5mm radius of curvature=66.0mm Accepted seperation of carbon atoms=.123nm and .213nm $$ {delta}{L} = {R}({1-cos(arcsin({D}/{2R}))})$$

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
 * 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

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 Outer Diameter
 * Spacing from slope: .216nm (1.4% error from accepted value of .213nm)
 * Spacing from slope: .124nm (.81% error from accepted value of .123nm)

Summary
Lab Summary


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