User:Richard T. Meyers/Notebook/Phys307l/Electron Diffraction Lab

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Contents

Electron Diffraction

Low Voltage Correction Device
Low Voltage Correction Device

Procedure

High Voltage and Heater Supply
High Voltage and Heater Supply

Along with the Lab Manual the procedure for this experiment is primarily just adjusting the high voltage and measuring the associated diameters of the projected diffraction pattern. We used a micrometer to measure the diameters of the rings of the diffraction pattern. The wiring diagram for the set up is shown Here.

Data

The Diffraction Bulb
The Diffraction Bulb

Unfortunately I analyzed the data in EXCEL and I forgot how to export the spreadsheet to openwetware, however I did use a conversion site the results are below the raw data. The raw data is shown below:

View/Edit Spreadsheet
' ' ' ' ' ' ' ' Inner Ring Outer Ring ' ' ' ' ' ' ' '
Trial 1-3LINESTInterceptSlopeSlopey1tan(theta) 1D real 1y2tan(theta)2D real 2Linear Fit 1Linear Fit 2
50000.0141421362436.871193.3046325.90832754822.784203538.136027721230.7862812001.5935851.1000770420.09309547824.20482442.6268923360.14473227837.6303922222.9517182338.95106685
47500.01450952524.7837.931835.2118712.1822125623.2226109538.81026507InterceptIntercept1.1734012920.09617579125.005705592.7834770410.14907654738.7599022923.4038960439.68643108
45000.0149071225.4939.3323.6970627239.539935855.54577172510.644258921.2422593430.0989843425.735928442.9977161130.15483973540.2583311423.8932503240.48225437
42500.015339325.2541.3324.2127850340.33307758STDEVSTDEV1.2187575370.09803446325.488960483.3186010450.16312576442.4126986624.4251714541.34730294
40000.01581138825.8742.8824.7761304541.199460042.2727137863.6960513811.2799430240.1004893926.127241393.5794392850.16959266744.0940933125.0062115342.2922323
37500.01632993226.1643.4425.394910642.1510969d1d21.3090918290.10163888226.426109263.6763158980.17193925444.7042060325.6444275343.33014528
35000.01690308527.344.2326.0788572943.202954962.58861E-101.59175E-101.426959960.10616533627.602987373.8153815240.17525907945.567360526.3498569644.4773656
32500.0175411627.6946.526.840275544.37395831d1-SEd2-SE1.4684885110.10771677628.00636174.2307722240.1848623948.0642213327.1351912845.75453301
30000.01825741928.9747.0227.6949897245.688443852.5934E-101.59469E-101.6091250640.11281954429.333081514.3292622060.18707616848.6398035628.0167520447.18819082
27500.0190692523149.8428.6637540447.17832978d1+SEd2+SE1.8458886740.12094812931.446513564.8854059980.19917740451.7861249729.0159452148.81315095
25000.0232.651.2729.774420248.886449952.58384E-101.58881E-102.0444685740.12738800633.120881555.1818548870.20537879353.3984862130.1614973450.67613061
50000.01414213621.6938.4622.784203538.136027720.8971123910.08400276921.840719852.8635834090.15125485339.3262617722.9517182338.95106685
47500.01450952523.0939.0823.2226109538.810265071.0175948810.08950833223.272166442.9588356710.15380841439.9901876423.4038960439.68643108
45000.0149071223.5739.1723.6970627239.539935851.0606916040.09139959123.763893562.9728013080.15417957940.0866905123.8932503240.48225437
42500.015339324.139.8824.2127850340.333077581.1093419670.09349009624.307424973.0842118380.15711205340.8491337124.4251714541.34730294
40000.01581138824.2141.5424.7761304541.199460041.1195794170.09392427424.420311373.3533153310.16399955642.6398844525.0062115342.2922323
37500.01632993225.2743.3325.394910642.15109691.2207072050.098113625.509535963.6571754330.17147788244.584249425.6444275343.33014528
35000.01690308526.6244.9626.0788572943.202954961.3560219360.1034638426.900598473.9463973650.17833683146.36757626.3498569644.4773656
32500.0175411626.345.2226.840275544.373958311.3232847150.10219409126.570463763.9936462930.17943539646.6532030127.1351912845.75453301
30000.01825741927.7847.1727.6949897245.688443851.4781595120.10807501628.099504234.3579058190.1877157548.8060951228.0167520447.18819082
27500.01906925229.847.9128.6637540447.178329781.7038881420.1161375830.195770894.5007481750.19087763249.6281843129.0159452148.81315095
25000.0230.651.5229.774420248.886449951.7978972310.11934281631.029132245.2346941090.20646765453.6815900230.1614973450.67613061
50000.01414213621.4535.9922.784203538.136027720.8772361230.0830604921.595727322.500551380.14113786536.6958449722.9517182338.95106685
47500.01450952521.4437.7623.2226109538.810265070.8764128750.08302123821.585521762.7580392460.14837872638.578468723.4038960439.68643108
45000.0149071222.9639.0923.6970627239.539935851.0060802840.08899644323.139075132.9603856690.15384964840.0009085923.8932503240.48225437
42500.015339323.3239.6924.2127850340.333077581.0381311850.09041432323.507723863.0541822280.15632653640.6448994624.4251714541.34730294
40000.01581138823.940.7524.7761304541.199460041.0908519540.09270094624.102246023.2237355760.16071620441.7862130925.0062115342.2922323
37500.01632993224.241.2225.394910642.15109691.1186467470.09388479924.410047853.3004952170.16266835542.2937722525.6444275343.33014528
35000.01690308524.8542.526.0788572943.202954961.1801004710.09645248925.077647263.5145016820.16800344943.6808968126.3498569644.4773656
32500.0175411624.9643.326.840275544.373958311.1906673390.0968873925.19072133.6519647460.17135209144.5515435927.1351912845.75453301
30000.01825741925.6943.9727.6949897245.688443851.2620206140.09977630625.941839513.7693019880.17416524145.2829627828.0167520447.18819082
27500.01906925226.345.8328.6637540447.178329781.3232847150.10219409126.570463764.1057129050.18201779147.3246255829.0159452148.81315095
25000.0228.6946.929.774420248.886449951.5777912910.11170186329.042484454.3064225380.18656482348.5068539230.1614973450.67613061
50000.01414213622.4438.3122.784203538.136027720.9606918860.08695024922.60706482.8407886770.15063792739.1658610322.9517182338.95106685
47500.01450952523.1140.0323.2226109538.810265071.019372310.08958709723.292645213.1080309180.15773259841.0104755923.4038960439.68643108
45000.0149071224.1740.9823.6970627239.539935851.1158511270.09376637924.379258643.2611770910.16167106142.0344759223.8932503240.48225437
42500.015339325.2741.2324.2127850340.333077581.2207072050.098113625.509535963.3021389920.16270992942.304581624.4251714541.34730294
40000.01581138825.5343.0524.7761304541.199460041.246198760.09914270425.777103033.6086995250.17030444344.2791551225.0062115342.2922323
37500.01632993225.8744.4825.394910642.15109691.2799430240.1004893926.127241393.859977470.17631200345.8411207225.6444275343.33014528
35000.01690308526.2445.7226.0788572943.202954961.3171923920.10195612226.508591664.0853781410.18155159247.2034138126.3498569644.4773656
32500.0175411626.8146.5926.840275544.373958311.3756549360.10421821827.096736614.2477289890.18524516348.163742527.1351912845.75453301
30000.01825741927.0747.427.6949897245.688443851.4027572180.1052510927.365283454.4020292540.18869731649.0613022128.0167520447.18819082
27500.01906925227.7848.4728.6637540447.178329781.4781595120.10807501628.099504234.6105483410.19327782150.2522334729.0159452148.81315095
25000.0228.7149.2829.774420248.886449951.5800188220.1117816729.063234294.771980270.19676107751.1578799530.1614973450.67613061
50000.01414213622.7338.3322.784203538.136027720.9858724970.08809112822.903693242.8438223530.15072016439.1872427522.9517182338.95106685
47500.01450952523.3138.9323.2226109538.810265071.0372339340.09037492323.497479872.9356378370.15319008239.829421223.4038960439.68643108
45000.0149071223.739.3923.6970627239.539935851.0725212260.09191213623.897155433.0070878990.15508739640.3227228623.8932503240.48225437
42500.015339324.139.9124.2127850340.333077581.1093419670.09349009624.307424973.088967780.15723613340.881394724.4251714541.34730294
40000.01581138824.8940.3924.7761304541.199460041.1839373690.09661062325.118761853.1655987930.15922336441.3980745825.0062115342.2922323
37500.01632993226.0641.4425.394910642.15109691.2990023260.10124241626.323028273.3367603770.16358337342.5316770425.6444275343.33014528
35000.01690308526.6342.8526.0788572943.202954961.3570516220.10350353626.910919283.5742891510.16946711144.0614489126.3498569644.4773656
32500.0175411627.3943.5226.840275544.373958311.4364888270.10652322627.696038853.6902704230.17227493144.7914821727.1351912845.75453301
30000.01825741928.0444.6427.6949897245.688443851.5062824770.10911039328.368702153.8886677010.17698647446.0164831728.0167520447.18819082
27500.01906925229.0945.1128.6637540447.178329781.6226516930.11329880429.457688993.9736187180.17897046546.5323207829.0159452148.81315095
25000.0229.8445.7829.774420248.886449951.7085262260.11629767430.237395254.0964629440.18180585347.2695218830.1614973450.67613061
50000.01414213622.7437.2522.784203538.136027720.9867467360.0881304822.913924932.6824718190.14628779138.0348257622.9517182338.95106685
47500.01450952523.338.1223.2226109538.810265071.036337080.09033552323.487236112.8120549470.14985696938.9628120623.4038960439.68643108
45000.0149071223.7638.9523.6970627239.539935851.0780037280.09214874423.958673382.9387252350.15327250639.8508515623.8932503240.48225437
42500.015339324.2340.0824.2127850340.333077581.1214459550.09400322724.440839083.1159924940.15793952641.0642767524.4251714541.34730294
40000.01581138824.640.5624.7761304541.199460041.1562647590.09546447924.820764423.1929812840.15992805641.5812945825.0062115342.2922323
37500.01632993225.0140.9125.394910642.15109691.1954864610.09708510725.242127863.2497571720.16138036141.9588939725.6444275343.33014528
35000.01690308525.6241.6326.0788572943.202954961.2550859140.09949907625.869759783.3682526590.16437426242.7373080926.3498569644.4773656
32500.0175411626.6743.1226.840275544.373958311.36117440.10366232726.952205013.6207855130.17059767444.3553951727.1351912845.75453301
30000.01825741927.2744.1427.6949897245.688443851.4237909520.10604605727.571974833.7993963050.17488030445.4688791728.0167520447.18819082
27500.01906925228.0344.7628.6637540447.178329781.5051957520.10907055828.358345083.9102617170.17749263646.1480853229.0159452148.81315095
25000.0228.9345.7729.774420248.886449951.6046292420.11265982529.29155454.094614330.18176347247.2585026330.1614973450.67613061

Analysis

height 500
height 500

For the correction of the diameter I had to use the trigonometric functions stated in the manual and a bit of reading on the subject, thank you Kirsten. The relations are as follows:

y=R-\sqrt{R^2-\frac{D_{observed}^2}{4}}\,\!

tan(\theta)=\frac\frac{D_{observed}}{2}{L-y}\,\!

D_{corrected}=2Ltan(\theta)\,\!

With the corrected diameters I was able to calculate the d using the following equations:

d=\frac{2hLc}{{D}\sqrt{2eV_{accelerated}c^2}}=\frac{2hL}{{D}\sqrt{2eV_{accelerated}}}\,\!

further this becomes:

d=\frac\frac{2hL}{\sqrt{2me}}{slope}\,\!

Using the experimentally found slopes and h being Plank's constant, e being the elementary charge, m being the mass of an electron and L and R being defined in the manual as 13cm and 66mm respectively. we calculated d as follows:

d1=2.59(5)*10^{-10}m=0.259(5)nm\,\!

d2=1.59(3)*10^{-10}m=0.159(3)nm\,\!

Error

The error I calculated using STDEV in EXCEL is 2.272 and 3.696 for the inner and outer ring respectively. From there I put these into the above equations to get the reported diameters. To calculate the percent error see below:

%=\frac{0.259-0.213}{0.213}*100=21.59%\,\!

%=\frac{0.159-0.123}{0.123}*100=29.27%\,\!

For how unsteady we were at taking the data with the calipers I think to have 30% error is fair.

Thanks

1)To exce2wiki.net for the conversion of an excel doc to wiki code converter. It saved me for hours of menial data input.

2)To Kirstin from who I got the relations for the diameter correction.

3)To Nathan for being a great lab partner.

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