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

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:

{{#widget:Google Spreadsheet |key=0AlAK7TMhL37adFBlSzdqR3pjdGcwWExmVGJHRHBwRXc |width=775 |height=575 }}

'	'	'	'	'	'	'	'	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

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:

[math]\displaystyle{ y=R-\sqrt{R^2-\frac{D_{observed}^2}{4}}\,\! }[/math]

[math]\displaystyle{ tan(\theta)=\frac\frac{D_{observed}}{2}{L-y}\,\! }[/math]

[math]\displaystyle{ D_{corrected}=2Ltan(\theta)\,\! }[/math]

With the corrected diameters I was able to calculate the [math]\displaystyle{ d }[/math] using the following equations:

[math]\displaystyle{ d=\frac{2hLc}{{D}\sqrt{2eV_{accelerated}c^2}}=\frac{2hL}{{D}\sqrt{2eV_{accelerated}}}\,\! }[/math]

further this becomes:

[math]\displaystyle{ d=\frac\frac{2hL}{\sqrt{2me}}{slope}\,\! }[/math]

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:

[math]\displaystyle{ d1=2.59(5)*10^{-10}m=0.259(5)nm\,\! }[/math]

[math]\displaystyle{ d2=1.59(3)*10^{-10}m=0.159(3)nm\,\! }[/math]

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:

[math]\displaystyle{ %=\frac{0.259-0.213}{0.213}*100=21.59%\,\! }[/math]

[math]\displaystyle{ %=\frac{0.159-0.123}{0.123}*100=29.27%\,\! }[/math]

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.