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

## Contents

### Electron Diffraction

Low Voltage Correction Device

## Procedure

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

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:

 ' ' ' ' ' ' ' ' Inner Ring Outer Ring ' ' ' ' ' ' ' ' Trial 1-3 LINEST Intercept Slope Slope y1 tan(theta) 1 D real 1 y2 tan(theta)2 D real 2 Linear Fit 1 Linear Fit 2 5000 0.014142136 24 36.87 1193.304632 5.908327548 22.7842035 38.13602772 1230.786281 2001.593585 1.100077042 0.093095478 24.2048244 2.626892336 0.144732278 37.63039222 22.95171823 38.95106685 4750 0.014509525 24.78 37.93 1835.21187 12.18221256 23.22261095 38.81026507 Intercept Intercept 1.173401292 0.096175791 25.00570559 2.783477041 0.149076547 38.75990229 23.40389604 39.68643108 4500 0.01490712 25.49 39.33 23.69706272 39.53993585 5.545771725 10.64425892 1.242259343 0.09898434 25.73592844 2.997716113 0.154839735 40.25833114 23.89325032 40.48225437 4250 0.0153393 25.25 41.33 24.21278503 40.33307758 STDEV STDEV 1.218757537 0.098034463 25.48896048 3.318601045 0.163125764 42.41269866 24.42517145 41.34730294 4000 0.015811388 25.87 42.88 24.77613045 41.19946004 2.272713786 3.696051381 1.279943024 0.10048939 26.12724139 3.579439285 0.169592667 44.09409331 25.00621153 42.2922323 3750 0.016329932 26.16 43.44 25.3949106 42.1510969 d1 d2 1.309091829 0.101638882 26.42610926 3.676315898 0.171939254 44.70420603 25.64442753 43.33014528 3500 0.016903085 27.3 44.23 26.07885729 43.20295496 2.58861E-10 1.59175E-10 1.42695996 0.106165336 27.60298737 3.815381524 0.175259079 45.5673605 26.34985696 44.4773656 3250 0.01754116 27.69 46.5 26.8402755 44.37395831 d1-SE d2-SE 1.468488511 0.107716776 28.0063617 4.230772224 0.18486239 48.06422133 27.13519128 45.75453301 3000 0.018257419 28.97 47.02 27.69498972 45.68844385 2.5934E-10 1.59469E-10 1.609125064 0.112819544 29.33308151 4.329262206 0.187076168 48.63980356 28.01675204 47.18819082 2750 0.019069252 31 49.84 28.66375404 47.17832978 d1+SE d2+SE 1.845888674 0.120948129 31.44651356 4.885405998 0.199177404 51.78612497 29.01594521 48.81315095 2500 0.02 32.6 51.27 29.7744202 48.88644995 2.58384E-10 1.58881E-10 2.044468574 0.127388006 33.12088155 5.181854887 0.205378793 53.39848621 30.16149734 50.67613061 5000 0.014142136 21.69 38.46 22.7842035 38.13602772 0.897112391 0.084002769 21.84071985 2.863583409 0.151254853 39.32626177 22.95171823 38.95106685 4750 0.014509525 23.09 39.08 23.22261095 38.81026507 1.017594881 0.089508332 23.27216644 2.958835671 0.153808414 39.99018764 23.40389604 39.68643108 4500 0.01490712 23.57 39.17 23.69706272 39.53993585 1.060691604 0.091399591 23.76389356 2.972801308 0.154179579 40.08669051 23.89325032 40.48225437 4250 0.0153393 24.1 39.88 24.21278503 40.33307758 1.109341967 0.093490096 24.30742497 3.084211838 0.157112053 40.84913371 24.42517145 41.34730294 4000 0.015811388 24.21 41.54 24.77613045 41.19946004 1.119579417 0.093924274 24.42031137 3.353315331 0.163999556 42.63988445 25.00621153 42.2922323 3750 0.016329932 25.27 43.33 25.3949106 42.1510969 1.220707205 0.0981136 25.50953596 3.657175433 0.171477882 44.5842494 25.64442753 43.33014528 3500 0.016903085 26.62 44.96 26.07885729 43.20295496 1.356021936 0.10346384 26.90059847 3.946397365 0.178336831 46.367576 26.34985696 44.4773656 3250 0.01754116 26.3 45.22 26.8402755 44.37395831 1.323284715 0.102194091 26.57046376 3.993646293 0.179435396 46.65320301 27.13519128 45.75453301 3000 0.018257419 27.78 47.17 27.69498972 45.68844385 1.478159512 0.108075016 28.09950423 4.357905819 0.18771575 48.80609512 28.01675204 47.18819082 2750 0.019069252 29.8 47.91 28.66375404 47.17832978 1.703888142 0.11613758 30.19577089 4.500748175 0.190877632 49.62818431 29.01594521 48.81315095 2500 0.02 30.6 51.52 29.7744202 48.88644995 1.797897231 0.119342816 31.02913224 5.234694109 0.206467654 53.68159002 30.16149734 50.67613061 5000 0.014142136 21.45 35.99 22.7842035 38.13602772 0.877236123 0.08306049 21.59572732 2.50055138 0.141137865 36.69584497 22.95171823 38.95106685 4750 0.014509525 21.44 37.76 23.22261095 38.81026507 0.876412875 0.083021238 21.58552176 2.758039246 0.148378726 38.5784687 23.40389604 39.68643108 4500 0.01490712 22.96 39.09 23.69706272 39.53993585 1.006080284 0.088996443 23.13907513 2.960385669 0.153849648 40.00090859 23.89325032 40.48225437 4250 0.0153393 23.32 39.69 24.21278503 40.33307758 1.038131185 0.090414323 23.50772386 3.054182228 0.156326536 40.64489946 24.42517145 41.34730294 4000 0.015811388 23.9 40.75 24.77613045 41.19946004 1.090851954 0.092700946 24.10224602 3.223735576 0.160716204 41.78621309 25.00621153 42.2922323 3750 0.016329932 24.2 41.22 25.3949106 42.1510969 1.118646747 0.093884799 24.41004785 3.300495217 0.162668355 42.29377225 25.64442753 43.33014528 3500 0.016903085 24.85 42.5 26.07885729 43.20295496 1.180100471 0.096452489 25.07764726 3.514501682 0.168003449 43.68089681 26.34985696 44.4773656 3250 0.01754116 24.96 43.3 26.8402755 44.37395831 1.190667339 0.09688739 25.1907213 3.651964746 0.171352091 44.55154359 27.13519128 45.75453301 3000 0.018257419 25.69 43.97 27.69498972 45.68844385 1.262020614 0.099776306 25.94183951 3.769301988 0.174165241 45.28296278 28.01675204 47.18819082 2750 0.019069252 26.3 45.83 28.66375404 47.17832978 1.323284715 0.102194091 26.57046376 4.105712905 0.182017791 47.32462558 29.01594521 48.81315095 2500 0.02 28.69 46.9 29.7744202 48.88644995 1.577791291 0.111701863 29.04248445 4.306422538 0.186564823 48.50685392 30.16149734 50.67613061 5000 0.014142136 22.44 38.31 22.7842035 38.13602772 0.960691886 0.086950249 22.6070648 2.840788677 0.150637927 39.16586103 22.95171823 38.95106685 4750 0.014509525 23.11 40.03 23.22261095 38.81026507 1.01937231 0.089587097 23.29264521 3.108030918 0.157732598 41.01047559 23.40389604 39.68643108 4500 0.01490712 24.17 40.98 23.69706272 39.53993585 1.115851127 0.093766379 24.37925864 3.261177091 0.161671061 42.03447592 23.89325032 40.48225437 4250 0.0153393 25.27 41.23 24.21278503 40.33307758 1.220707205 0.0981136 25.50953596 3.302138992 0.162709929 42.3045816 24.42517145 41.34730294 4000 0.015811388 25.53 43.05 24.77613045 41.19946004 1.24619876 0.099142704 25.77710303 3.608699525 0.170304443 44.27915512 25.00621153 42.2922323 3750 0.016329932 25.87 44.48 25.3949106 42.1510969 1.279943024 0.10048939 26.12724139 3.85997747 0.176312003 45.84112072 25.64442753 43.33014528 3500 0.016903085 26.24 45.72 26.07885729 43.20295496 1.317192392 0.101956122 26.50859166 4.085378141 0.181551592 47.20341381 26.34985696 44.4773656 3250 0.01754116 26.81 46.59 26.8402755 44.37395831 1.375654936 0.104218218 27.09673661 4.247728989 0.185245163 48.1637425 27.13519128 45.75453301 3000 0.018257419 27.07 47.4 27.69498972 45.68844385 1.402757218 0.10525109 27.36528345 4.402029254 0.188697316 49.06130221 28.01675204 47.18819082 2750 0.019069252 27.78 48.47 28.66375404 47.17832978 1.478159512 0.108075016 28.09950423 4.610548341 0.193277821 50.25223347 29.01594521 48.81315095 2500 0.02 28.71 49.28 29.7744202 48.88644995 1.580018822 0.11178167 29.06323429 4.77198027 0.196761077 51.15787995 30.16149734 50.67613061 5000 0.014142136 22.73 38.33 22.7842035 38.13602772 0.985872497 0.088091128 22.90369324 2.843822353 0.150720164 39.18724275 22.95171823 38.95106685 4750 0.014509525 23.31 38.93 23.22261095 38.81026507 1.037233934 0.090374923 23.49747987 2.935637837 0.153190082 39.8294212 23.40389604 39.68643108 4500 0.01490712 23.7 39.39 23.69706272 39.53993585 1.072521226 0.091912136 23.89715543 3.007087899 0.155087396 40.32272286 23.89325032 40.48225437 4250 0.0153393 24.1 39.91 24.21278503 40.33307758 1.109341967 0.093490096 24.30742497 3.08896778 0.157236133 40.8813947 24.42517145 41.34730294 4000 0.015811388 24.89 40.39 24.77613045 41.19946004 1.183937369 0.096610623 25.11876185 3.165598793 0.159223364 41.39807458 25.00621153 42.2922323 3750 0.016329932 26.06 41.44 25.3949106 42.1510969 1.299002326 0.101242416 26.32302827 3.336760377 0.163583373 42.53167704 25.64442753 43.33014528 3500 0.016903085 26.63 42.85 26.07885729 43.20295496 1.357051622 0.103503536 26.91091928 3.574289151 0.169467111 44.06144891 26.34985696 44.4773656 3250 0.01754116 27.39 43.52 26.8402755 44.37395831 1.436488827 0.106523226 27.69603885 3.690270423 0.172274931 44.79148217 27.13519128 45.75453301 3000 0.018257419 28.04 44.64 27.69498972 45.68844385 1.506282477 0.109110393 28.36870215 3.888667701 0.176986474 46.01648317 28.01675204 47.18819082 2750 0.019069252 29.09 45.11 28.66375404 47.17832978 1.622651693 0.113298804 29.45768899 3.973618718 0.178970465 46.53232078 29.01594521 48.81315095 2500 0.02 29.84 45.78 29.7744202 48.88644995 1.708526226 0.116297674 30.23739525 4.096462944 0.181805853 47.26952188 30.16149734 50.67613061 5000 0.014142136 22.74 37.25 22.7842035 38.13602772 0.986746736 0.08813048 22.91392493 2.682471819 0.146287791 38.03482576 22.95171823 38.95106685 4750 0.014509525 23.3 38.12 23.22261095 38.81026507 1.03633708 0.090335523 23.48723611 2.812054947 0.149856969 38.96281206 23.40389604 39.68643108 4500 0.01490712 23.76 38.95 23.69706272 39.53993585 1.078003728 0.092148744 23.95867338 2.938725235 0.153272506 39.85085156 23.89325032 40.48225437 4250 0.0153393 24.23 40.08 24.21278503 40.33307758 1.121445955 0.094003227 24.44083908 3.115992494 0.157939526 41.06427675 24.42517145 41.34730294 4000 0.015811388 24.6 40.56 24.77613045 41.19946004 1.156264759 0.095464479 24.82076442 3.192981284 0.159928056 41.58129458 25.00621153 42.2922323 3750 0.016329932 25.01 40.91 25.3949106 42.1510969 1.195486461 0.097085107 25.24212786 3.249757172 0.161380361 41.95889397 25.64442753 43.33014528 3500 0.016903085 25.62 41.63 26.07885729 43.20295496 1.255085914 0.099499076 25.86975978 3.368252659 0.164374262 42.73730809 26.34985696 44.4773656 3250 0.01754116 26.67 43.12 26.8402755 44.37395831 1.3611744 0.103662327 26.95220501 3.620785513 0.170597674 44.35539517 27.13519128 45.75453301 3000 0.018257419 27.27 44.14 27.69498972 45.68844385 1.423790952 0.106046057 27.57197483 3.799396305 0.174880304 45.46887917 28.01675204 47.18819082 2750 0.019069252 28.03 44.76 28.66375404 47.17832978 1.505195752 0.109070558 28.35834508 3.910261717 0.177492636 46.14808532 29.01594521 48.81315095 2500 0.02 28.93 45.77 29.7744202 48.88644995 1.604629242 0.112659825 29.2915545 4.09461433 0.181763472 47.25850263 30.16149734 50.67613061

## Analysis

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.