General!Physics!I!&!II!Lab!! - UML Physics Lecture...

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General!Physics!I!&!II!Lab!!!

Course!Description!!Lab!Report!Template!and!Sample!!

Grading!Rubrics!Pre>Lab!Quizzes!

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!Source:!Christopher!Johnson;[email protected]!!!

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Table&of&Contents&

&General&Physics&Course&Information& ………………………………………………………&3&

General&Physics&Lab&Writing&Guide&& ………………………………………………………&6&

Sample&Lab&Report&& ………………………………………………………………………..&12&

Labs:&

Atomic&Energy&Levels&

& Grading&Rubric& ……………………………………………………………………….&&23&

& PreHLab&Quiz&& ……………………………………………………………………….&&24&

Capacitors&and&RC&Decay&

& Grading&Rubric& ……………………………………………………………………….&&25&

& PreHLab&Quiz&& ……………………………………………………………………….&&27&

Circular&Motion&and&Centripetal&Force&

& Grading&Rubric& ……………………………………………………………………….&&28&

& PreHLab&Quiz&& ……………………………………………………………………….&&30&

Converging&Lenses&

& Grading&Rubric& ……………………………………………………………………….&&31&

& PreHLab&Quiz&& ……………………………………………………………………….&&33&

Electric&and&Potential&Fields&

& Grading&Rubric& ……………………………………………………………………….&&34&

& PreHLab&Quiz&& ……………………………………………………………………….&&36&

Impulse&and&Momentum&in&Collisions&

& Grading&Rubric& ……………………………………………………………………….&&37&

& PreHLab&Quiz&& ……………………………………………………………………….&&39&

Motion&in&FreeHFall&

& Grading&Rubric& ……………………………………………………………………….&&40&

Ohm’s&Law&

& Grading&Rubric& ……………………………………………………………………….&&42&

& PreHLab&Quiz&& ……………………………………………………………………….&&44&

Projectile&Motion&

& Grading&Rubric& ……………………………………………………………………….&&45&

& PreHLab&Quiz&& ……………………………………………………………………….&&47&

Properties&of&a&Vertical&SpringHMass&System&

& Grading&Rubric& ……………………………………………………………………….&&48&

& PreHLab&Quiz&& ……………………………………………………………………….&&50&

Transverse&Mechanical&Waves&and&Resonance&

& Grading&Rubric& ……………………………………………………………………….&&51&

& PreHLab&Quiz&& ……………………………………………………………………….&&52&

Wavelength&of&Light&

& Grading&Rubric& ……………………………………………………………………….&&53&

& PreHLab&Quiz&& ……………………………………………………………………….&&55&

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96.104'[fill,in,section],General,Physics,II,Lab!!

Course!Information!!

Lab,Meeting,Time:!This!lab!section!meets!every!other![fill!in!weekday]!(starting!!with![fill!in!date])!at![fill!in!time]!SHARP.!The!lab!session!runs!as!long!as!it!takes!to!finish!the!experiment!with!satisfactory!data.!

!Location:!The!room!in!which!we!meet!will!vary!from!week!to!week!depending!on!!

the!availability!of!rooms!and!laboratory!materials!(we!share!both!with!many!other!lab!sections).!The!room!in!which!we!are!meeting!will!be!posted!on!the!doors!to!the!lab!rooms.!Check!the!postings!each!time!you!come!into!lab!to!find!out!where!we!are!meting!that!day.!The!room!in!which!we!meet!will!not!necessarily!be!the!same!room!listed!on!iSiS.!

!Instructor:![fill!in!name]!!Instructor,Contact,Information:![fill!in!email]!!!Office/Office,Hours:,I!have!a!cubicle![fill!in!cubicle!number]!in!Olney!219!where!I!!

can!meet!you!by!appointment.!Contact!me!well!in!advance!to!ensure!that!there!is!time!for!us!to!meet!before!your!lab!report!is!due,!I!have!a!very!busy!schedule!as!a!graduate!student!so!it!is!difficult!to!make!time!at!the!last!minute.!

!Faculty,Supervisor/Lab,Coordinator:!Dr.!Mittler,[email protected]!!Restrictions:!Consumption!of!food!or!drinks!is!strictly!prohibited!in!the!laboratory.!!Attendance/Make,Up,Work:,There!are!only!six!laboratory!sessions!per!semester.!!

The!score!for!each!lab!report!contributes!equally!to!each!student’s!grade.!Attendance!is!required!for!five!lab!sessions,!but!attendance!at!all!six!is!encouraged.!Any!student!that!misses!more!than!one!lab!session!(excused!or!not)!will!automatically!fail!the!course!and!will!be!encouraged!to!withdraw.!Make!up!work!is!not!allowed!in!any!case!for!any!experiment.!If!the!student!is!aware!of!a!conflict!in!advance,!it!is!their!responsibility!to!arrange!attendance!at!another!one!of!the!instructor’s!lab!sessions.!Students!are!required!to!be!punctual;!failure!to!do!so!will!result!in!missed!preSlab!quizzes!and!other!important!information.!Performing!the!experiment!under!the!supervision!of!another!instructor!is!not!permitted!because!each!instructor!teaches!each!lab!slightly!differently!and!has!slightly!different!labSwriting!requirements.!!

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Academic,Conduct:!Each!student!is!required!to!write!their!own!original!lab!report.!!Students!are!encouraged!to!work!together!to!perform!the!experiment!and!analyze!data,!but!the!language!of!each!report!must!be!unique.!The!student!is!responsible!for!appropriate!academic!conduct.!Cheating!of!any!form!will!result!in!a!failing!grade!on!the!lab!report!and!possibly!in!the!course!as!well.!The!university’s!academic!integrity!policy!is!available!online.!Whether!or!not!a!student!is!guilty!of!academic!misconduct!is!left!to!the!discretion!of!the!instructor,!as!are!the!consequences.!Lab!reports!that!raise!suspicion!will!be!submitted!to!the!physics!department.!Don’t!cheat.!!

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Scoring!!

Pre'Lab,Quizzes:!There!will!be!a!preSlab!quiz!at!the!beginning!of!each!lab!session!to!!test!the!student’s!preparation!for!the!experiment.!The!student!is!responsible!for!reading!and!understanding!the!lab!manual!before!coming!to!the!lab!session.!It!is!advised!that!the!student!do!the!reading!well!in!advance!so!that!they!have!the!opportunity!to!contact!the!instructor!with!any!questions!before!meeting!to!perform!the!experiment.!The!preSlab!quizzes!will!be!scored!out!of!ten!points!and!will!contribute!ten!out!of!the!one!hundred!points!available!for!each!report.!Missing!a!preSlab!quiz!due!to!tardiness!will!result!in!a!score!of!zero!on!the!quiz.!

!Lab,Reports:!Each!lab!report!will!consist!of!four!sections:!the!cover!page/lab!!

manual!pages,!the!objective!statement,!the!results/analysis!section,!and!the!discussion/conclusions!section.!LabSwriting!requirements!are!discussed!in!detail!in!the!labSwriting!guide!handed!out!along!with!the!course!information.!!

Grading:!Each!lab!report!will!be!scored!out!of!100!possible!points.!Each!component!!(preSlab!quiz,!cover!page/lab!manual!pages,!objective!statement,!results/analysis,!and!discussion/conclusions)!will!account!for!a!certain!amount!of!the!100!possible!points.!Each!report!will!be!graded!according!to!a!rubric!that!instructor!will!use!a!checklist!to!determine!what!necessary!information!is!included!in!each!section!of!the!report.!The!rubric!for!each!experiment!will!be!handed!out!at!the!lab!session!during!which!the!students!are!performing!the!experiment,!so!there!is!no!excuse!for!omitting!any!content!from!any!section!of!the!lab!report.!At!each!lab!meeting,!each!student!will!receive!their!graded!lab!report!from!the!previous!experiment!with!comments.!The!comments!are!intended!to!help!the!student!improve!on!how!they!write!the!next!lab!report.!Students!who!do!not!take!the!comments!into!consideration!

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will!be!heavily!penalized!for!repeating!the!same!mistakes.!Often!times,!some!comments!are!made!very!frequently.!For!this!reason,!the!instructor!will!use!an!abbreviated!notation!for!some!comments.!There!will!be!a!frequent!comments!key!that!gives!the!definition!of!each!abbreviation!for!each!experiment.!Any!student!who!has!performed!an!experiment!and!hands!in!any!written!report!will!receive!a!minimum!score!of!40!points!on!the!report.!At!the!end!of!the!semester,!the!instructor!will!determine!each!student’s!final!grade!by!averaging!the!five!highest!lab!report!scores.!The!instructor!will!scale!the!grades!appropriately!based!on!the!merit!of!the!class’s!overall!performance.!Standard!letter!grades!will!be!associated!with!percent!scores.!

! !Deadlines:!Lab!reports!are!due!one!week!from!the!date!on!which!the!experiment!!

was!performed!at!the!start!of!the!alternate!lab!session.!Labs!that!are!turned!in!after!the!start!of!the!lab!session!([insert!time]!exactly)!will!be!considered!one!day!late.!Students!can!hand!late!lab!reports!into!the!late!box!outside!of!Olney!113.!Lab!reports!that!are!turned!in!on!the!next!day!will!be!considered!two!days!late,!the!next!day!will!be!three!days!late,!etc.!Five!points!per!day!will!be!taken!off!the!score!of!late!lab!reports.!Since!late!lab!reports!do!not!go!directly!into!the!hands!of!the!instructor,!it!is!not!guaranteed!that!the!instructor!will!receive!the!lab!report.!If!a!student!needs!to!go!print!a!lab!before!turning!it!in,!the!lab!report!is!not!exempt!to!the!deadline.!It!is!strongly!encouraged!to!turn!the!lab!report!in!on!time!and!for!this!reason!it!is!advised!that!the!student!print!and!staple!the!lab!report!well!in!advance!before!coming!to!lab.!Lateness!also!decreases!the!minimum!lab!report!score.!The!minimum!score!for!a!lab!report!that!is!on!time!is!40/100,!the!minimum!score!for!a!lab!that!is!one!day!late!is!30/100,!etc.!!!

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Lab$Writing+Guide++

First&and&foremost,&it&is&essential&for&each&student&to&realize&that&lab&writing&is&a&writing'exercise.&All&lab&reports&must&be&written&in&formal&English.&All&guidelines&that&apply&to&normal&formal&writing&still&apply&to&lab&writing&(indent&new&paragraphs,&use&proper&punctuation,&etc.).&EVERY+statement+that+appears+anywhere++in+the+lab+report+(other&than&the&cover&page&and&titles&and&axis&labels&on&graphs)&MUST+BE+A+COMPLETE+SENTENCE.+Use+of+sentence+fragments+and+incomplete+sentences+will+greatly+decrease+the+grade+on+the+lab+report.&All&lab&reports&must&be&word@processed,&double@spaced&in&either&Cambria&or&Times&New&Roman&size&12&font.&Do&not&attempt&to&make&your&lab&report&look&longer&by&increasing&the&margin&size,&the&font&size,&or&the&line@spacing.&The&goal&of&lab@writing&is&to&include&all&of&the&content&necessary&to&explain&your&goals&to&the&reader&and&to&explain&how&you&achieved&those&goals.&It&is&somewhat&of&an&art&to&be&as&complete&as&possible&while&also&being&as'concise'as'possible.&For&this&reason,&we&strictly&adhere&to&a&technical&writing&format.&The&requirements&for&writing&each&section&of&the&lab&report&are&outlined&below.&It&is&essential&that&you&include&every&section&in&the&order&listed.&Every&section&other&than&the&cover&page&and&lab&manual&pages&requires&a&bolded,&left@justified&heading.&Do&not&italicize,&underline,&or&enlarge&the&section&headings.&Do&not&punctuate&section&headings&(do&not&use&colons&or&anything&like&that).&Do&not&leave&section&headings&standing&on&their&own&at&the&bottom&of&a&page,&put&the&section&heading&on&a&new&page&so&that&the&beginning&of&the&new&section&appears&directly&below&it.&Use&the&sample&lab&report&that&the&instructor&handed&out&along&with&the&lab@writing&guide&and&course&information&as&a&formatting&reference.&Treat&the&sample&lab&report&only&as&a&formatting&reference,&do&not&use&it&to&influence&your&writing&style&or&content.&These&are&the&requirements&for&each&section:&&Cover+Page:&The&cover&page&lists&your&name,&the&course&and&section&number,&the&&

instructor’s&name,&the&title&of&the&experiment,&the&date&on&which&you&performed&the&experiment,&and&your&lab&partner’s&name.&The&cover&page&should&be&its&own&piece&of&paper&with&the&above&information&typed&on&its&own&line&in&the&order&listed&above&and&centered&(vertically&and&horizontally)&on&the&page.&Use&normal&size&12&font&for&every&piece&of&information&on&the&cover&page&(no&enlarged,&bolded,&italicized,&underlined,&or&otherwise&altered&text).&THE+COVER+PAGE+COUNTS+FOR+FREE+EASY+POINTS.+DO+NOT+LOSE+POINTS+ON+THE+COVER+PAGE!!!!&

+Lab+Manual+Pages:&You&are&required&to&hand&in&the&lab&manual&pages&that&pertain&&

to&the&experiment.&The&lab&manual&pages&can&be&photocopied&or&taken&directly&out&of&the&lab&manual&itself.&These&pages&will&suffice&as&the&introduction&and&procedure&sections;&it&is&not&necessary&to&write&an&original&introduction&or&procedure&section.&Include&all&lab&manual&pages&for&the&experiment&except&for&those&pertaining&to&the&results&and&analysis&section&(tables,&figures,&instructions&for&analysis,&etc.).&

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Include&the&lab&manual&pages&in&the&order&in&which&they&appear&in&the&lab&manual.&&&

Objective+Statement:&Do&not&copy&the&objective&statement&from&the&lab&manual.&You&&will&receive&a&score&of&zero&on&the&objective&statement&if&you&copy&the&objective&statement&from&the&lab&manual.&The&objective&statement&is&essential&to&the&lab&report.&It&tells&the&reader&what&your&goals&are,&and&the&rest&of&your&report&explains&how&you&achieved&your&goals.&The&objective&statement,&like&all&statements&in&your&lab&report,&must&be&a&complete&sentence.&It&should&be&written&in&the&past&tense&and&active'voice&and&it&should&use&first&person&pronouns.&Here&is&an&example&of&a&good&objective&statement&for&one&of&the&General&Physics&I&labs,&“We&conducted&the&motion&in&free@fall&experiment&in&order&to&examine&the&relationships&between&position,&velocity&and&acceleration,&as&well&as&to&determine&the&gravitational&constant,&g,&for&an&object&in&free@fall.”&Notice&how&it&is&a&complete&sentence,&not&a&sentence&fragment&like,&“To&determine&the&gravitational&constant,&g”.&Also,&it&uses&a&first&person&pronoun&in&the&past&tense&and&active&voice,&“We&conducted”.&DO&NOT&USE&THE&PASSIVE&VOICE.&DO&NOT&WRITE&“the&experiment&was&conducted”.&Remember,&YOU&CONDUCTED&the&experiment.&These&guidelines&apply&to&every&sentence&in&every&section&of&your&lab&report.&For&clarity:&EVERY&SENTENCE&IN&YOUR&LAB&REPORT&SHOULD&ALWAYS&BE&IN&THE&ACTIVE&VOICE,&IN&THE&PAST&TENSE,&AND&YOU&SHOULD&USE&FIRST&PERSON&PRONOUNS&AS&OFTEN&AS&POSSIBLE.&NEVER&USE&THE&PASSIVE&VOICE.&

&Results+and+Analysis:&The&results&and&analysis&section&is&the&meat&of&the&lab&report&&

and&carries&the&most&weight&in&terms&of&the&grade.&The&results&and&analysis&section&is&ONE+SECTION+that&includes&your&results&and&your&analysis.&&Like&all&other&sections,&the&results&section&requires&a&left&justified,&bolded&heading&without&punctuation.&The&results&and&analysis&section&explains&how&you&manipulated&your&data&in&order&to&achieve&your&objectives.&You&do&not&need&to&explain&how&you&obtained&your&raw&data;&the&procedure&section&from&the&lab&manual&pages&covers&that&information.&There&are&essentially&three&things&that&you&will&be&asked&to&do&in&the&results&section.&You&will&be&asked&to&explain&calculations,&to&display&tables,&and&to&display&figures.&It&is&essential&that&you&do&each&of&these&things&completely&and&properly.&&&When&you&are&asked&to&explain&a&calculation,&you&will&need&to&properly&include&an&equation&and&then&properly&display&a&sample&calculation.&When&you&include&an&equation,&it&should&be&centered&on&its&own&line,&separated&from&the&text,&with&its&number&in&parentheses&on&the&right&

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side&of&the&page.&The&number&should&be&in&between&one&open&and&one&closed&parenthesis,&no&other&punctuation.&It&is&extremely&important&that&you&number&equations&properly&in&the&order&in&which&they&appear&in&the&text.&After&you&have&assigned&a&number&to&an&equation&you&can&refer&to&that&equation&by&number&if&you&mention&it&later&in&the&report.&It&is&essential&that&you&master&this&lab&writing&technique.&You&are&required&to&number&all&equations&you&use&on&your&own;&you&should&disregard&the&equation&numbers&given&in&the&lab&manual.&Another&essential&lab&writing&technique&is&that&you&include&the&equation&fluidly&as&a&part&of&a&complete&sentence.&As&usual,&you&should&use&first&person&pronouns,&past&tense&and&active&voice;&if&it&is&necessary,&you&should&include&punctuation&with&your&equation.&As&part&of&the&sentence&that&includes&the&equation,&you&must&also&define'the'symbols&that&appear&in&the&equation.&You&must&do&this&completely&and&concisely;&define&a&symbol&once&and&stick&to&that&definition&for&the&rest&of&the&report.&It&is&very&important&that&each&symbol&represent&one&and&only&one&physical&quantity.&Do&not&over@define&symbols.&Once&you&have&defined&a&symbol&once,&you&do&not&need&to&re@define&it&if&it&appears&in&another&equation.&When&you&show&the&equation&on&its&own&line,&you&should&use&the&proper&symbols;&this&is&very&easy&to&do&with&the&equation&editor&in&Microsoft&word.&There&should&never&be&any&English&words&as&part&of&an&equation;&only&use&symbols&in&equations.&After&you&show&an&equation,&you&need&to&show&a&sample&calculation.&A&sample&calculation&is&an&example&of&how&you&used&your&data&in&that&equation.&Although&you&will&repeat&many&calculations,&you&only&need&to&formally&show&one'representative&sample&calculation&in&order&to&demonstrate&your&mastery&of&that&equation.&Like&the&equation&itself,&the&sample&calculation&should&read&fluidly&as&a&part&of&the&sentence&that&it&is&in.&In&this&sentence,&you&should&state&the&values&that&you&are&using&for&each&parameter;&this&is&analogous&to&how&you&define&the&symbols&in&the&sentence&that&includes&the&equation.&When&you&state&the&values,&you&must'include&the&units,&otherwise&the&value&is&meaningless.&You&should&also&include&the&units&in&the&sample&calculation&itself.&The&sample&calculation&should&also&appear&on&its&own&line.&Unlike&equations,&you&do&not&need&to&number&sample&calculations.&Here&is&an&example&of&how&to&properly&explain&a&calculation,&including&the&equation&and&the&sample&calculation:&

&“We&determined&the&force&on&each&object&using&Newton’s&second&law,&&

F=ma,& & & & & & (1)&&

where&m&was&the&mass&of&the&ball&and&a&was&its&acceleration.&For&example,&when&the&&&0.5&kg&ball&was&accelerating&at&9.8&m/s,&we&calculated&a&force&of&&

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F=(0.5&kg)(9.8&m/s)=4.9&N.”&&

Notice&how&both&the&equation&and&the&sample&calculation&are&part&of&their&own&sentence.&Both&sentences&use&first&person&pronouns,&active&voice,&and&are&in&the&past&tense.&The&sentence&for&the&equation&clearly&defines&the&symbols&used&in&the&equation&and&the&sentence&for&the&sample&calculation&clearly&states&the&values&used&in&the&equation.&I&did&not&over@define&the&symbol&F&for&force&because&it&is&obvious&that&F'symbolizes&force&based&on&the&first&part&of&the&sentence,&“We&determined&the&forces”.&The&equation&F=ma'is&punctuated&because&it&is&a&fluid&part&of&the&sentence&and&will&be&read&as&such.&If&I&need&to&refer&to&this&equation&later&in&the&lab,&I&would&simply&refer&to&it&as&“equation&1”.&The&sample&calculation&is&also&punctuated&because&“a&force&of&4.9&Newtons”&is&part&of&the&sentence.&&Another&thing&you&will&be&asked&to&do&in&the&results&section&is&to&display&tables&properly.&Similarly&to&equations,&tables&should&be&numbered&in&the&order&in&which&they&appear&in&text.&If&the&lab&manual&gives&a&table&number&you&should&ignore⁢&define&tables&by&your&own&numbering&scheme&(sometimes&your&scheme&and&the&lab&manual’s&scheme&can&coincide).&Do&not&number&tables&with&parenthesis&like&you&do&for&equations.&When&you&include&a&table,&you&must&write&a&complete&sentence&that&refers&to&the&table&by&number.&Always&capitalize&the&word&“Table”&when&you&refer&to&a&table&by&number.&You&should&also&use&complete&sentences&to&caption&tables.&The&caption&should&appear&directly&below&the&table,&centered&on&the&page&and&single@spaced.&You&are&allowed&to&use&the&tables&you&fill&out&by&in&the&lab&manual,&but&it&is&required&that&they&appear&in&a&professional&manner.&If&you&plan&to&include&the&hand&written&tables,&you&are&encouraged&to&take&your&raw&data&during&the&procedure&on&your&own&paper&so&you&can&make&a&finalized,&neat&version&on&the&lab&manual&page.&You&are&also&encouraged&to&make&your&own&digital&tables&(in&excel&or&word).&&Regardless&of&the&format&you&choose,&your&tables&must&be&included&in&the&text&in&the&proper&order&where&you&refer&to&them.&You&should&keep&tables&and&their&captions&continuous;&if&a&caption&doesn’t&fit&on&the&page&under&the&table,&move&the&table&to&a&new&page&so&that&the&caption&has&space&to&follow&it&directly.&Always&include&units&in&parenthesis&in&the&first&row&to&indicate&that&they&apply&to&all&values&in&the&column.&Continuing&with&our&example&from&how&to&explain&calculations&properly,&let’s&suppose&we&wanted&to&tabulate&some&force&calculations.&You&would&want&to&say&something&like&this:&

&“After&we&calculated&the&forces&acting&on&all&three&balls,&we&organized&our&data&into&&Table&1.&

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Ball&#& m&(kg)& a&(m/s2)& F&(N)&1& 0.5& 9.8& 4.9&2& 0.75& 9.8& 7.35&3& 1.0& 9.8& 9.8&

&Table&1:&This&table&includes&all&of&our&force&calculations.”&

&Notice&how&every&statement&associated&with&the&table&is&a&complete&sentence&written&in&the&active&voice.&&&Another&thing&you&will&be&asked&to&do&in&the&results&section&is&to&include&figures&properly.&Figures&include&all&graphs&and/or&diagrams.&Figures&have&their&own&numbering&scheme,&separate&from&equations&and&tables.&All&figures,&both&diagrams&and&graphs,&are&included&in&the&same&numbering&scheme.&If&you&show&a&diagram&first,&that&diagram&will&be&Figure&1,&and&if&a&graph&were&to&follow&later,&that&graph&would&be&Figure&2&and&vice&versa.&You&should&include&figures&in&essentially&the&same&manner&as&you&include&tables.&Number&them&in&the&order&in&which&they&appear&in&text&and&refer&to&them&by&number&in&a&sentence&before&you&display&them.&Also&include&captions&in&complete&sentences&directly&after&figures&centered&on&the&page&and&single@spaced.&You&can&include&hand@drawn&figures,&but&again&make&sure&they&look&professional&and&appear&fluidly&in&text&in&the&proper&order&where&you&refer&to&them.&It&is&recommended&that&you&make&your&own&figures&using&a&computer&in&order&to&include&them&most&fluidly&in&your&text.&Keeping&with&our&example,&this&is&how&you&would&want&to&include&a&figure&properly:&

&“Then&we&plotted&our&force&calculations&in&Figure&1.&

&

&&

Figure&1:&Our&results&show&that&force&increases&linearly&with&mass.”&

0&2&4&6&8&10&12&

0& 0.2& 0.4& 0.6& 0.8& 1& 1.2&

Force+(N)+

Mass+(kg)+

Force+vs+Mass+

10

&Again,&every&statement&is&a&complete&sentence.&Notice&that&the&figure&has&a&title,&axes&labeled&with&units,&and&appropriately&scaled&axes.&All&graphs&require&all&of&these&components.&&The&important&parts&of&the&results&section&are&explaining&calculations,&displaying&tables,&and&displaying&figures.&Usually,&we&will&do&some&calculations,&then&organize&them&into&a&table,&then&plot&our&results&in&a&figure.&We&always&want&to&explain&our&manipulations&of&data&in&a&logical&order,&starting&with&what&we&obtained&from&the&experimental&procedure&and&building&up&from&there.&Sometimes,&you&may&create&a&figure&during&the&experiment&then&manipulate&your&data&from&there;&it&depends&on&the&experiment.&

&Discussion+and+Conclusions:+This&section&discusses&the&experimental&findings&of&&

the&experiment&and&addresses&any&relevant&conclusions.&Here,&the&question&“What&do&the&results&mean?”&should&be&answered.&Essentially,&what&has&the&student&learned&from&the&experiment?&These&questions&should&be&answered&scientifically,&keeping&the&objectives&of&the&experiment&in&mind.&Always&be&sure&to&directly&address&your&objectives&and&how&well&you&achieved&them.&This&section&should&also&address&experimental&error&(not'uncertainty).&Sources&of&experimental&error&are&systematic&flaws&in&the&data&acquisition&process&that&make&the&experiment&slightly&not&ideal.&The&student&should&state&the&sources&of&experimental&error&and&how'they&affected&the&results.&“Human&error”&is&not&a&source&of&experimental&error.&If&there&was&“human&error”&in&an&experiment,&the&student&will&be&required&to&redo&the&experiment&before&receiving&a&grade&on&the&lab&report.&This&is&not&a&paper&for&English&or&history&class&where&the&conclusion&is&simply&a&jumble&of&random&thoughts&thrown&into&the&paper&just&to&finish&it&late&at&night&the&day&before&it&is&due.&Conclusions&written&in&this&manner&will&score&very&low.&Do&not&shoot&for&quantity&here,&try&to&be&complete&while&being&as&concise&as&possible.&Neatly&written&or&typed&answers&to&the&questions&at&the&end&of&the&lab&manual&pages&should&be&included&after&the&conclusion.&

&&&&&&&&

11

Chris Johnson

Physics 300-201

Professor Michael Vineyard

Bragg Reflection: Using X-Ray Diffraction Spectra to Determine the Lattice Constants of NaCl and KBr Monocrystals

4/15/2011

Partners: Arkadiy Norkin, Ana Mikler and Hillary Bauer

12

Abstract We used a Bragg x-ray reflection apparatus to detect the angles at which x-rays

interfered constructively after they reflected off of NaCl and KBr crystals. From the

interference peaks on the Bragg diffraction spectra, we were able to extract the lattice

constant a0 for each crystal. We calculated a0 to be equal to 570 ± 30 pm and 660 ± 30

pm for NaCl and KBr respectively. The actual values of these lattice constants, a0 =

564.02 pm for NaCl and a0 = 659.8 pm for KBr, do fall within our range of uncertainty

from our measured values (Atomic and nuclear physics 2).

Introduction Bragg reflection is a way of measuring the interatomic spacing of a monocrystal

by detecting and analyzing the interference pattern caused by the x-rays reflected off of

the lattice planes of the crystal. This concept is very similar to slit diffraction of visible

light, but in this case the uniform structure of the atoms in the crystals serves as the slit

and we detect the angles at which constructive interference occurs. William Lawrence

Bragg and William Henry Bragg first proposed Bragg reflection in 1913 when they found

that crystal solids produced defined patterns of reflected x-rays. The Braggs explained

this phenomenon by modeling the structures of these crystals as uniform parallel planes

of atoms arranges in a lattice. Bragg diffraction is ideal for measuring interatomic spacing

using x-rays because x-ray wavelengths are comparable to interatomic distances. The

Braggs’ idea confirmed the existence of real particles at the atomic level and also

provided a useful tool for measuring interatomic distances (Wikipedia). Figure 1

illustrates this concept.

13

Figure 1: Two x-rays reflecting off of successive lattice planes in a crystal will reflect and

cause constructive interference when they reflect off of the planes at the correct angles. Here, λ is the wavelength of the x-rays, d is the lattice plane spacing and θ is the incident

and reflected angle. The first and second planes correspond to n = 1 and n = 2 respectively. Image courtesy of “Bragg Law”.

The x-rays will interfere constructively when the Bragg condition is satisfied,

n λ = 2 d sin (θ ) (1)

Changing the angle can cause displacement of the wavelengths; destructive interference

occurs when the waves are out of phase by half of a wavelength. In a cubic crystal with

NaCl structure, the d-spacing corresponds to half of the lattice constant,

d = a0 / 2 (2)

This allows us to write Equation 1 in terms of a0,

n λ = a0 sin (θ ) (3)

In order to determine the lattice constant, a0, we must therefore determine the sines of the

angles that correspond to constructive interference caused by x-rays of a certain

wavelength reflecting off of the nth lattice plane. The slope of a graph of sin (θ ) vs. n λ

14

will give a value for a0. In our experiment, we used molybdenum x-rays of two

wavelengths λα = 71.08 pm and λβ = 63.09 pm at the Kα and Kβ lines respectively. This

causes the interference pattern to have two peaks (Kα and Kβ) for each diffraction order;

one is caused by interference of x-rays of each wavelength (Solid-state physics 1).

Procedure We used a Bragg diffraction apparatus called the Rontgenerat X-ray Apparatus to

adjust the incident and reflected angles of x-rays incident on crystal samples as shown in

Figure 2.

Figure 2: Our Bragg diffraction apparatus allowed us to sweep through a range of incident and reflected angles in order to find constructive interference.

In our apparatus, we had an x-ray machine to the left of the collimator (part a in

Figure 2). The x-ray source produced both Kα and Kβ x-rays that passed through the

axis of the counter tube are parallel to the incident x-ray beam .As the lattice planes are seldom precisely parallel to the sur-face of the crystal, the zero point of each crystal must becalibrated individually.

Setup

Setup in Bragg configuration:

Fig . 3 shows some important details of the experiment setup .To set up the experiment, proceed as follows (see also theInstruction Sheet for the x-ray apparatus):

– Mount the collimator in the collimator mount (a) (note theguide groove).

– Attach the goniometer to guide rods (d) so that the distances1 between the slit diaphragm of the collimator and thetarget arm is approx . 5 cm . Connect ribbon cable (c) forcontrolling the goniometer.

– Remove the protective cap of the end-window counter,place the end-window counter in sensor seat (e) andconnect the counter tube cable to the socket markedGM TUBE .

Apparatus

1 X-ray apparatus . . . . . . . . . . . . . . 554 811

1 End-window counterfor !, ", # and x-ray radiation . . . . . . . 559 01

1 LiF monocrystal for Bragg reflection . . . 554 77

additionally required:

1 P C with Windows 9 x/NT

Safety notes

The x-ray apparatus fulfills all regulations governing anx-ray apparatus and fully protected device for instructionaluse and is type approved for school use in Germany (NW807/97 Rö).

The built-in protection and screening measures reduce thelocal dose rate outside of the x-ray apparatus to less than1 $Sv/h, a value which is on the order of magnitude of thenatural background radiation.

Before putting the x-ray apparatus into operation in-spect it for damage and to make sure that the highvoltage is shut off when the sliding doors are opened(see Instruction Sheet for x-ray apparatus).Keep the x-ray apparatus secure from access by un-authorized persons.

Do not allow the anode of the x-ray tube Mo to overheat.

When switching on the x-ray apparatus, check to makesure that the ventilator in the tube chamber is turning .

The goniometer is positioned solely by electric steppermotors.

Do not block the target arm and sensor arm of thegoniometer and do not use force to move them .

Fig. 2 Schema tic diagram of diffrac tion of x-rays a t a mono-crystal and 2% coupling be tween counter-tube angle andsca ttering angle (glancing angle)1 collima tor, 2 monocrystal, 3 counter tube

Fig. 3 Experiment se tup in Bragg configura tion

P7.1.2.1 LEYBOLD Physics Leaflets

2

15

collimator to get a direct, uniform beam of x-rays heading toward the crystal sample. The

x-rays then reflected off of the sample held on the target stage (part f in Figure 2). After

reflecting off of the sample, the x-rays moved toward the Geiger-Müller counter tube

(part e in Figure 2) that detected the intensity of the x-rays. When we swept through

ranges of angles, the machine electronically pivoted the detector and the crystal with

respect to the incident x-ray beam in 2θ coupling in order to maintain equal incident and

reflected angles. The detector was connected to a computer program that plotted the

spectra of detected x-rays. Our machine had knobs on the side of it that controlled the

voltage, U, the current, I, the increments of θ by which the system rotated, Δθ, the time

step spent on detecting each angle, Δt and the range of angles over which the machine

would scan. For both of our runs we used U = 35.0 kV, I = 1.00 mA, Δθ = 0.1° and Δt =

5 s. For the NaCl crystal, we scanned over a range of 4° - 35°. For the KBr crystal, we

scanned over a range of 2.5° - 40°. Before each data acquisition, we set the machine back

to the zero point (where the lattice planes and the counter tube are parallel to the incident

x-ray beam) by pressing the reset button to calibrate it. After zeroing the apparatus and

programming our desired rotation parameters, we ran the experiment, started the data

acquisition and recorded the spectra searching for interference peaks. We then used a

peak-fitting program to analyze the peaks to find their centroids and σ values. We took

various safety measures including using lead-impregnated glass in the machine to block

radiation and using the appropriate voltage and current.

16

Results We produced spectra of the Kα and Kβ interference peaks caused by x-rays

reflecting off of NaCl and KBr crystals. Figures 3 and 4 show these plots of θ vs. the log

of the counting rate, R.

Figure 3: This shows the peaks produced by the interference of x-rays after reflecting off

of the lattice planes of the NaCl crystal.

0"

100"

200"

300"

400"

500"

600"

700"

0" 5" 10" 15" 20" 25" 30" 35" 40" 45"

Log$R$

θ!(°)$$

NaCl$Bragg$Spectrum$

17

Figure 4: This shows the peaks produced by the interference of x-rays after reflecting off of the lattice planes of the NaCl crystal.

After analyzing our data with a peak-fitting program, we found values for the

centroids of the peaks, θ and the σ value for each peak from which we extracted an

uncertainty in θ, Δθ. The uncertainty in Δθ is equal to 3σ because 99.8% of data points

lie within three standard deviations from the mean of a normal distribution. We then

calculated the sine of each angle and propagated the uncertainty in θ by taking the sign of

each Δθ. We then determined the diffraction order, n, for each set of peaks and the line

(Kα or Kβ) to which each peak corresponded. Each of these combinations was associated

with a certain wavelength (λα = 71.08 pm and λβ = 63.09 pm) that we multiplied by the

diffraction order to get values for n λ.

0"

50"

100"

150"

200"

250"

300"

350"

400"

450"

0" 5" 10" 15" 20" 25" 30" 35" 40"

Log$R$

θ!(°)$$

KBr$Bragg$Spectrum$

18

Crystal n Line θ (°) σ (°) Δθ (±°) sin (θ) Δ sin(θ) (±) λ (pm) nλ (pm) NaCl 1 Kβ 5.43 0.11 0.33 0.09 0.006 63.09 63.06 1 Kα 6.10 0.10 0.30 0.11 0.005 71.08 71.08 2 Kβ 10.93 0.10 0.30 0.19 0.005 63.09 126.1 2 Kα 12.38 0.10 0.30 0.214 0.005 71.08 142.2 3 Kα 18.76 0.07 0.21 0.322 0.004 71.08 213.2 KBr 1 Kβ 6.51 0.14 0.42 0.11 0.007 63.09 63.06 1 Kα 7.29 0.16 0.48 0.13 0.008 71.08 71.08 2 Kβ 12.95 0.21 0.63 0.224 0.01 63.09 126.1 2 Kα 14.67 0.15 0.45 0.253 0.003 71.08 142.1 3 Kα 22.17 0.29 0.57 0.377 0.009 71.08 213.2

Table 1: This shows the angles at which we found constructive interference along with the diffraction order, line, and n λ to which each corresponds for each crystal. All

uncertainties are shown.

After we accumulated this data, we made a plot of sin (θ ) vs. n λ for each

crystal’s data set. From there, we fit a linear regression line to each set of data points and

used the slope of each line to determine the lattice constant, a0 for each crystal. Figure 5

shows this plot.

19

Figure 5: This is the linear plot of sin (θ ) vs. n λ for each crystal’s data set. The data points for NaCl are circular and the data points for KBr are diamond-shaped. Each data

point is shown with error bars. The KBr error bars are difficult to see because they are so small.

The equations of the regression lines for NaCl and KBr were n λ = 567.3 (sin (θ ))

- 1.05 pm and n λ = 658.04 (sin (θ )) + 1.40 pm respectively. Propagating our

uncertainties into the slopes by finding the maximum and minimum slopes within our

uncertsainties, we get a0 = 570 ± 30 pm for NaCl and a0 = 660 ± 30 pm for KBr. This

means we found the sum of ion radii to be d = 285 ± 15 pm for NaCl and d = 330 ± 15

pm for KBr.

Discussions and Conclusion We were able to observe x-ray interference with our Bragg diffraction machine to

determine the interatomic spacing in NaCl and KBr crystals. We calculated a0 to be equal

to 567.3 ± pm and 660 ± 30 pm for NaCl and KBr respectively. The actual values of

0"

50"

100"

150"

200"

250"

0" 0.05" 0.1" 0.15" 0.2" 0.25" 0.3" 0.35" 0.4" 0.45"Sin(θ$)$

Linear$Plot$of$Sin(θ$)$vs.$nλ$$

nλ""(pm)"

20

these lattice constants, a0 = 564.02 pm for NaCl and a0 = 659.8 pm for KBr, do fall

within our range of uncertainty from our measured values. This means we found the sum

of ion radii to be d = 285 ± 15 for NaCl and d = 330 ± 15 for KBr. The NaCl lattice

shows a significantly smaller lattice constant than the KBr lattice, as the radii of the ions

involved are smaller.

Although or data does appear to be accurate, there must be some error associated

with our measurements that makes it imperfect. For instance, the linear regression lines

of the plots of sin (θ ) vs. n λ for each crystal’s data set are supposed to pass through the

origin. Our equations, however, have n λ - intercepts just above and below the origin.

Because the slopes appear to be correct, this must means that each set of data has been

shifted by the sin (θ ) values (slightly high sin (θ ) values for NaCl and slightly low sin(θ)

values for KBr). These discrepancies in the θ values were caused by imperfections in the

crystal and imperfect calibration of the Bragg diffraction machine.

Also, our spectra only show five peaks even though they cover the n = 1 to n = 3

diffraction orders. The β peak is invisible at the n = 3 diffraction order for both crystals

because we did not acquire perfect spectra. This could also be attributed to imperfections

in our samples. We could improve our data by setting a higher time step, Δt so that the

detector could spend more time at each angle.

This technique for measuring interatomic distances can be very useful for

determine the composition of materials; it is often use to test the validity of diamonds

(Wikipedia). It is incredible that we can learn so much about the composition of crystals

by observing the behavior of x-rays reflected off of them.

21

Works Cited

“Atomic and nuclear physics”. Leybold Physics Leaflets. Germany. Copyright Leybold

Didactic GmbH. <http://www.ld-didactic.de/literatur/hb/e/p6/p6362_e.pdf> "Bragg law." Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia

Britannica, 2011. Web. 09 May. 2011.

<http://www.britannica.com/EBchecked/topic/76973/Bragg-law>

“Bragg’s Law”. Wikipedia, the Free Encyclopedia.

<http://en.wikipedia.org/wiki/Bragg's_law>.

“Solid-state physics”. Leybold Physics Leaflets. Germany. Copyright Leybold Didactic

GmbH.

22

Atomic'Energy'Levels'Lab'Grading'Rubric'!

Name:_____________________________________! ! ! ! Grade:__________/100!

!

!

Pre9Lab:__________/10!'Cover'Page/Lab'Manual'Pages:__________/5!Name_____!

Course!&!Section!#_____!

Instructor’s!Name_____!

Title!of!Experiment_____!

Date!Experiment!was!Performed_____!

Partner’s!Name_____!

Lab!manual!pages!present!and!in!order______!

'Objective'Statement:________/10!Completely!and!concisely!address!all!of!your!objectives______!

!

Write!a!complete!sentence(s)!in!the!past!tense!and!active!voice!that!uses!first!person!

pronouns.______!

'Results:___________/50!!

Use!the!appropriate!objects!(figures,!tables,!and!explanations!of!calculations)!to!

explain!how!you!accomplished!your!objectives!to!the!reader.!Include!them!in!a!

logical!order!and!with!proper!form!according!to!the!labRwriting!guide.__________!

!

Answer!the!questions!at!the!end!of!the!lab!manual!pages!for!this!experiment.!Do!not!

number!your!answers!or!mention!the!lab!manual.!Simply!explain!your!answers!as!

though!you!are!genuinely!interested!in!communicating!you!findings!to!the!

reader.__________!

!

!

Conclusion:__________/25!!

Address!your!objectives_________!

!

Explain!how!sources!of!experimental!error!affected!your!results_______!

!

!

23

Atomic'Energy'Levels'Pre3Lab'Quiz!!!

Name:______________________________! ! !!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Score:_______/10!!Section#:_____________!!!

1. Explain!the!significance!of!the!equation!!! = !!".!!!"!! !.!Be!sure!to!address!the!

sign,!the!units,!and!the!symbol!n.!!!!!!!!!!!!!!!!!!!!

2. What!are!the!objectives!of!today’s!experiment?!!!!!!!!

!!!!!

!!

24

Capacitors*and*RC*Delay*Lab*Grading*Rubric!!

!Name:_____________________________________! ! ! ! Grade:__________/100!!!Pre8Lab:__________/10!*Cover*Page/Lab*Manual*Pages:__________/5!Name_____!Course!&!Section!#_____!Instructor’s!Name_____!Title!of!Experiment_____!Date!Experiment!was!Performed_____!Partner’s!Name_____!Lab!manual!pages!present!and!in!order______!*Objective*Statement:________/10!Completely!and!concisely!address!all!of!your!objectives______!!Write!a!complete!sentence!in!the!past!tense!and!active!voice!that!uses!first!person!pronouns.______!**Results*and*Analysis:__________/50!Explain!how!you!calculated!the!internal!resistance!of!the!voltmeter!_________!!Explain!how!you!calculated!the!capacitance!of!the!larger!capacitor!________!!Explain!how!you!calculated!the!capacitance!of!the!smaller!capacitor!_________!!Explain!how!you!calculated!the!capacitance!of!the!capacitors!in!series!_________!!Explain!how!you!calculated!the!capacitance!of!the!capacitors!in!parallel!(you!could!cover!this!step!and!a!few!of!the!previous!steps!in!one!sentence!to!avoid!repetition)!________!!Explain!how!you!predicted!the!capacitance!of!the!capacitors!in!series!________!!Explain!how!you!determined!the!percent!difference!between!your!experimental!value!and!the!value!you!predicted!for!the!capacitors!in!series_______!!Explain!how!you!predicted!the!capacitance!of!the!capacitors!in!parallel!_________!!Explain!how!you!determined!the!percent!difference!between!your!experimental!value!and!the!value!you!predicted!for!the!capacitors!in!parallel_______!

25

!Include!a!table!including!the!results!of!all!the!calculations!you!just!explained!______!!Include!a!graph!of!the!voltage!across!the!capacitor!against!time!_______!!Explain!how!you!determined!the!capacitance!of!the!larger!resistor!from!your!graph!________!!Include!a!natural!log!plot!in!order!to!linearize!the!relationship!between!the!voltage!across!the!capacitor!and!time!_______!!Explain!how!you!determined!the!capacitance!from!your!plot!______!!!Discussion/Conclusions:__________/25!Comment!on!how!well!you!achieved!your!objective(s)._____!!!Do!your!results!verify!theoretical!predictions?!How!do!your!values!for!the!capacitance!compare?_______!!Explain!the!concept!at!the!end!of!section!xii!in!the!procedure!_______!!Identify!sources!of!experimental!error!and!explain!how!they!affected!your!results._____!!Answer!the!questions!at!the!end!of!the!lab!manual!pages.!Make!sure!to!show!your!work!_______!!Additional*Comments:*

26

Capacitance)and)RC)Decay)Pre0Lab)Quiz!!!

Name:______________________________! ! !!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Score:_______/10!!Section#:_____________!!!Circle!all!appropriate!answers,!there!may!be!more!than!one.!!!1.!You!can!determine!the!equivalent!capacitance!for!capacitors!in!series!using:!

!a. the!same!method!you!use!to!determine!the!equivalent!resistance!for!!!!!!!!!!!!!!!!!!!!!!!resistors!in!series.!!b. the!same!method!you!use!to!determine!the!equivalent!resistance!for!!!!

resistors!in!parallel.!!c. the!same!method!you!use!to!determine!the!equivalent!spring!constant!for!!!!!!!!!!springs!in!series.!d. the!same!method!you!use!to!determine!the!equivalent!spring!constant!for!!

springs!in!parallel.!e. the!same!method!you!use!to!determine!the!power!dissipated!through!a!!

grounded!resistor.!!2.!You!can!determine!the!equivalent!capacitance!for!capacitors!in!parallel!using:!

!a. the!same!method!you!use!to!determine!the!equivalent!resistance!for!!!!!!!!!!!!!!!!!!!!!!!resistors!in!series.!!b. the!same!method!you!use!to!determine!the!equivalent!resistance!for!!!!

resistors!in!parallel.!!c. the!same!method!you!use!to!determine!the!equivalent!spring!constant!for!!!!!!!!!!springs!in!series.!d. the!same!method!you!use!to!determine!the!equivalent!spring!constant!for!!

springs!in!parallel.!e. the!same!method!you!use!to!determine!the!power!dissipated!through!a!!

grounded!resistor.!!3.!When!capacitors!are!disconnected!from!their!voltage!supply,!they!discharge:!! !

a. linearly!b. periodically!c. sinusoidally!d. exponentially!

!4.!True!or!False.!To!a!good!approximation,!the!voltmeter!in!today’s!experiment!!!!!!!behaves!as!an!ideal!voltmeter!so!we!can!ignore!its!resistance!completely.!

27

Circular(Motion(and(Centripetal(Force(Lab(Grading(Rubric!!

!Name:_____________________________________! ! ! ! Grade:__________/100!!!Pre7Lab:__________/10!(Cover(Page:__________/5!Name_____!Course!&!Section!#_____!Instructor’s!Name_____!Title!of!Experiment_____!Date!Experiment!was!Performed_____!Partner’s!Name!!Lab(Manual(Pages:__________/5!Present_____!In!Order_____!Objective!(write!your!own!objective!not!copied!from!the!lab!manual)_____!!Results(and(Analysis:__________/60!Explain!how!you!calculated!the!linear!forces._____!!Explain!how!you!found!the!periods.!Even!though!this!is!a!trivial!calculation,!show!the!equation!and!a!sample!calculation!properly!to!practice!good!lab!writing!techniques.!____!!Explain!how!you!found!the!angular!velocities.______!!Explain!how!you!calculated!the!centripetal!forces.______!!Explain!how!you!calculated!the!percent!differences._______!!State!that!you!repeated!all!of!these!calculations!while!varying!different!parameters!(state!which!parameters!you!varied)._____!!Show!a!table(s)!of!your!data.!Include!the!table!properly._____!!!Discussion/Conclusions:__________/20!How!well!did!you!achieve!your!objective?!This!should!one!or!maybe&two!concise!statements._____!!!What!sources!of!experimental!error!affected!your!results?_____!

28

!!Clearly!explain!how!the!experimental!error!affected!your!raw!data!and!propagate!that!flaw!to!your!end!result!(conceptually,!not!mathematically).______!!Answer!the!questions!at!the!end!of!the!lab!manual.!Show!all!work!clearly!and!write!answers!in!complete!sentences.!The!reader!should!be!able!to!tell!what!the!question!is!asking!by!reading!your!answer._____!!Additional(Comments:(

29

Centripetal*Force*Pre/Lab*Quiz!!

!Name:_________________________________!!Section!#:_____________!!1.!Show!that!Fr!=!mrω2!is!Newton’s!second!law!in!radial!form.!Hint:!start!with!the!usual!form!of!Newton’s!second!law!and!make!substitutions!for!a!then!simplify!the!expression.!!!!!!!!!!!!!!!!!!!2.!Clearly!explain!the!function!of!the!orange!disk!in!today’s!experiment.!

30

Converging)Lenses)Lab)Grading)Rubric)!Name:_____________________________________! ! ! ! Grade:__________/100!!!Pre4Lab:__________/10!)Cover)Page/Lab)Manual)Pages:__________/5!Name_____!Course!&!Section!#_____!Instructor’s!Name_____!Title!of!Experiment_____!Date!Experiment!was!Performed_____!Partner’s!Name_____!Lab!manual!pages!present!and!in!order______!)Objective)Statement:________/10!Completely!and!concisely!address!all!of!your!objectives______!!Write!a!complete!sentence!in!the!past!tense!and!active!voice!that!uses!first!person!pronouns.______!)Results:___________/35!!Cylindrical!Lens!Include!a!figure!for!each!lens!orientation_________!!State!the!focal!length!you!obtained!for!each!lens!orientation__________!!Include!a!figure(s)!that!indicate!aberration_______!!Spherical!Lens!!Explain!how!you!calculated!the!focal!length_________!!Explain!how!you!calculated!the!magnification!from!the!object!and!image!distances________!!Explain!how!you!calculated!the!magnification!from!the!object!and!image!heights__________!!Explain!how!you!calculated!the!percent!difference!between!the!magnifications_______!!Include!a!table!of!the!various!object!distances!and!their!corresponding!image!distances_________!!

31

State!your!average!focal!length!you!obtained!from!your!table_______!!Plot!1/do!vs!1/di__________!!Determine!the!focal!length!from!the!average!of!the!intercept!values!on!the!two!axes_______!!Compare!your!focal!lengths_________!!Answer!question!#4!at!the!end!of!the!lab!manual!pages__________!!!Conclusion:__________/30!!Address!your!objectives_________!!Explain!how!sources!of!experimental!error!affected!your!results!(why!do!we!have!percent!differences?)_______!!Answer!questions!1,!2,!3,!and!5!at!the!end!of!the!lab!manual!pages_________!

32

Converging)Lenses)Pre-Lab)Quiz!!

Name:______________________________! ! ! ! ! Score:_________/10!!!!Section!#:__________! ! ! ! ! ! ! ! ! ! !

!Draw!a!ray!diagram!for!an!object!located!do=10!cm!in!front!of!a!converging!lens!whose!focal!length!is!f=30!cm!!!!!!!!!!!!!!!!!Determine!the!image!distance,!di,!using!the!thin!lens!equation.!!!!!!!!!!!Determine!the!magnification!(remember!to!consider!the!+/G!sign).!

33

Electric(and(Potential(Fields(Lab(Grading(Rubric!!

!

Name:_____________________________________! ! ! ! Grade:__________/100!

!

!

Pre6Lab:__________/10!(Cover(Page/Lab(Manual(Pages:__________/5!Name_____!







(Objective(Statement:________/10!Completely!and!concisely!address!all!of!your!objectives______!

!

Write!a!complete!sentence!in!the!past!tense!and!active!voice!that!uses!first!person!

pronouns!(we).______!

((Results(and(Analysis:__________/40!!

Properly!include!a!figure!that!represents!your!map!of!the!potential!field._____!

!

Properly!include!a!figure!that!represents!your!map!of!the!electric!field.______!

!

!

Discussion/Conclusions:__________/35!!

Comment!on!how!well!you!achieved!your!objective(s)._____!

!

Answer!the!questions!at!the!end!of!the!Mapping!Potential!Fields!procedure!section!

(part!iv)!in!the!lab!manual.______!

!

!

Answer!the!questions!at!the!end!of!the!Mapping!Electric!Fields!procedure!sections!

(parts!v,!vi,!and!vii)!in!the!lab!manual._____!

!

!

Identify!sources!of!experimental!error______!

!

!

34

Explain!how!sources!of!experimental!error!affected!your!results._____!

!

!

Answer!the!questions!at!the!end!of!the!lab!manual!pages.!Show!work!clearly!and!

neatly._____!

!

Additional(Comments:(

35

Electric(and(Potential(Fields(Pre0Lab(Quiz!!!

Score:! ! /10!Name:_______________________________!!Section!#:!96.1047_________________!!Fill!in!your!name!and!section!number!or!you!will!lose!a!point!for!each.!!Question!1!a).!Draw!the!electric!field!lines!coming!out!of!the!conducting!sphere!in!the!picture.!Use!an!appropriate!number!of!field!lines!and!do!not!attempt!to!make!a!three7dimensional!drawing.!(2!pts.)!!b).!After!you!draw!the!field!lines,!draw!the!equipotential!lines.!Two!or!three!equipotential!lines!will!suffice.!(2!pts.)!!!!! ! ! ! ! ! ! ! ! ! ! !!!!!!!!Question!2!What!is!the!name!of!the!idealized,!non7physical!entity!that!we!use!to!determine!the!force!associated!with!an!electric!field!at!a!certain!point!in!space?!(2!pts.)!!!!!!Question!3!The!diagram!on!the!chalkboard!represents!a!uniform!electric!field!pointed!in!the!positive!x!direction.!Which!path!(A,!B,!or!C)!would!require!the!most!work!to!move!a!positive!test!charge!along?!Which!path!would!require!the!least!amount!of!work?!!!Most:__________(2!pts.)! ! ! Least:__________(2!pts.)!

!!

!

36

Impulse(and(Momentum(in(Collisions(Lab(Grading(Rubric!!

!

Name:_____________________________________! ! ! ! Grade:__________/100!

!

!









!


pronouns.______!

!

Results(and(Analysis:__________/60!Properly!display!a!figure(s)!that!pertains!to!one!of!your!types!collisions._____!

!

!

Explain!how!you!calculated!the!impulse.!_____!

!

!

Explain!how!you!obtained!the!impulse!without!doing!any!calculations.!You!should!

explain!this!conceptually!and!display!an!equation.!You!do!not!need!to!show!a!sample!

calculation,!but!you!must!state!what!the!impulse!is!based!on!the!figure!you!have!

shown._____!

!

!

Properly!explain!how!you!found!the!percent!difference!between!the!values!you!

obtained!for!the!impulse._____!

!

!

State!that!you!repeated!these!calculations!for!various!situations!and!state!what!

these!situations!were._____!

!

!

Include!all!of!your!calculations!in!a!table(s)!and!be!sure!to!show!a!figure!for!each!

type!of!collision._____!

37

(Discussion/Conclusions:__________/20!Directly!address!your!objective._____!

!

!

Compare!impulse!in!elastic!collisions!to!impulse!in!inelastic!collisions!based!on!your!

results_____!

!

!

What!sources!of!experimental!error!affected!your!results?_____!

!

!

How!did!these!sources!affect!your!results?______!

!

!

!

Answer!the!questions!at!the!end!of!the!lab!manual._____!

!


38

Impulse(and(Momentum(in(Collisions(Pre3Lab(Quiz!!!

Name:________________________________!!Section!#!:______________!!!1.!Indicate!whether!the!collision!between!the!following!objects!is!elactic!(E)!or!inelastic!(I).!Consider!collisions!that!are!approximately!elastic!to!be!elastic:!!!_______Two!billiard!balls!traveling!toward!each!other!!_______A!javelin!collides!with!the!ground!and!sticks!into!it!!_______A!ball!of!clay!thrown!at!a!concrete!wall!hits!the!wall!and!falls!straight!down!to!!

the!ground!!_______A!lab!cart!on!a!track!collides!with!a!sprig!!_______A!lab!cart!on!a!track!collides!with!a!plastic!airbag!!!!!2.!A!force!is!applied!to!an!object!for!a!total!time!of!10!seconds.!During!the!first!3!seconds,!the!magnitude!of!the!force!is!6!N.!During!the!last!7!seconds,!the!force!is!5!N.!What!is!the!total!impulse!felt!by!the!object!during!the!ten!seconds?!!

39

Motion&in&Free*Fall&Lab&Grading&Rubric!!

!

Name:_____________________________________! ! ! ! Grade:__________/100!

!

&Cover&Page/Lab&Manual&Pages:__________/5!Name_____!







&Objective&Statement:________/10!Completely!and!concisely!address!all!of!your!objectives______!

!


pronouns.______!

!

Results&and&Analysis:__________/55!Display!tables!1!&!2_____!

!

!

!

Explain!how!you!found!the!velocities_____!

!

!

!

Explain!why!the!time!associated!with!each!velocity!is!at!the!midpoint!of!the!

corresponding!time!interval!for!position_____!

!

!

!

Display!velocity!vs.!time!plot_____!

!

!

!

Explain!how!you!found!vo!and!a#in!the!equation!v!=!vo!+!at#_____!!

!

!

!

Display!position!vs.!time!plot_____!!

!

40

!

!

Explain!how!you!found!v*,!the!instantaneous!velocites,!by!finding!the!slope!of!the!tangent!lines!and!compare!them!to!the!velocities!in!the!table_____!

!

!

!

!

Discussion/Conclusions:__________/30!Address!the!relationships!between!position,!velocity!and!acceleration_____!

!

!

!

Address!experimental!error!(why!was!your!value!for!a!not!exactly!equal!to!the!accepted!value!for!g?).!State!source(s)!of!error!and!explain!how!they!affected!your!results_____!

!

!

!

How!could!we!minimize!experimental!error?_____!

!

!

!

Answer!discussion!questions!clearly!and!neatly_____!

!

!

!

!

!

Additional&Comments:&

41

Ohm’s&Law&Lab&Grading&Rubric!!

!

Name:_____________________________________! ! ! ! Grade:__________/100!

!

Pre6Lab:__________/10!&Cover&Page/Lab&Manual&Pages:__________/5!Name_____!







&Objective&Statement:________/10!Completely!and!concisely!address!all!of!your!objectives______!

!

Write!a!complete!sentence!in!the!past!tense!and!active!voice!that!uses!first!person!

pronouns.______!

&Results&and&Analysis:__________/50!Properly!include!a!figure!that!graphs!the!current!vs.!the!voltage!for!the!10!Ω!resistor._____!

!

State!the!resistance!you!find!from!the!figure!and!calculate!the!percent!difference!

between!your!resistance!and!10!Ω._______!!

Calculate!the!maximum!power!from!your!graph.________!

!

Include!a!figure!that!graphs!the!current!vs.!voltage!for!the!100!Ω!resistors!in!series________!

!

Explain!how!you!calculated!the!theoretical!resistance!due!to!the!two!resistors!in!

series.________!

!

Explain!how!you!calculated!the!percent!difference!between!your!resistance!and!the!

theoretical!value._______!

!

Include!a!figure!for!the!current!vs.!voltage!for!the!two!100!Ω!resistors!in!parallel._______!

!

Explain!how!you!calculated!the!theoretical!resistance!due!to!the!two!100!Ω!resistors!in!parallel._______!

42

!

Explain!how!you!calculated!the!percent!difference!between!your!value!and!the!

theoretical.________!

!

Include!the!graph!of!the!current!vs.!voltage!for!the!light!bulb.!State!your!value!for!

the!resistance!from!the!“straight!line”!region._______!

!

Explain!how!you!calculated!the!maximum!resistance!value._______!

!

Explain!how!you!compared!this!value!to!the!light!bulb’s!resistance!rating._______!

!

Include!a!figure!for!the!voltage!and!current!vs.!time!for!the!diode.________!

!

Explain!how!you!calculated!the!ratio!of!voltage/current.______!

!

Explain!how!you!calculated!the!power!and!compared!it!to!the!diode’s!rating.______!

!

Include!a!table!of!your!current!calculations!for!various!resistances.______!

!

Include!a!figure,!plotting!of!the!information!in!the!table.______!

!

!

Discussion/Conclusions:__________/25!Comment!on!how!well!you!achieved!your!objective(s)._____!

!

!

Do!your!results!verify!theoretical!predictions?._______!

!

!


!

!

Skip!the!questions!at!the!end!of!the!lab!manual!pages!for!both!experiments._____!

!

Additional&Comments:&

43

Ohm’s&Law&Pre&Lab&Quiz!!

Name:_____________________________! ! ! ! ! Score:_______/10!!Section!#:_______________!!Each!circuit!shown!below!contains!two!5!Ω!resistors!connected!to!a!2!volt!power!supply.!In!circuit!A,!the!resistors!are!configured!in!a!series,!while!in!circuit!B,!they!are!configured!in!parallel.!!!!!!!!!!!!!!!!!!!a)!Determine!the!effective!resistance!(Req)!for!each!circuit.!!!!!!!!b)!Using!Ohm’s!law,!determine!the!magnitude!of!the!current!in!each!circuit.!!!!!!!!True!or!False:!The!slope!of!the!graph!of!i!vs.!V!is!equal!to!1/R,!or!1/Req!for!a!system!of!multiple!resistors.!!!

44

Projectile*Motion*Lab*Grading*Rubric!!

!

Name:_____________________________________! ! ! ! Grade:__________/100!

!

!

Pre5Lab:__________/10!*Cover*Page/Lab*Manual*Pages:__________/5!Name_____!







*Objective*Statement:________/10!Completely!and!concisely!address!all!of!your!objectives______!

!


pronouns.______!

!

Results*and*Analysis:__________/55!!

Explain!how!you!calculated!the!initial!velocity!for!each!of!the!three!possible!initial!

velocities._____!

!

Explain!how!you!calculated!theoretical!values!for!t,!R!and!ymax._____!!

Explain!how!you!calculated!the!Δt%,!Δx%,!and!Δymax%!values._____!!

Display!a!table!showing!all!of!these!values.!_____!

!

Explain!how!you!used!equation!3!from!the!lab!manual!to!calculate!theoretical!y!

position!values!for!each!corresponding!x!position!value._____!

!

Explain!how!you!calculated!the!percent!difference!between!the!theoretical!and!

actual!y!positions._____!

!

Display!a!table!of!the!data!from!part!2._____!

!

Explain!the!first!“if!time!permits”!part._____!

!

45

Explain!the!math!behind!whether!or!not!you!can!use!the!2Wclick!velocity!to!reach!the!

range!you!found!for!the!70°!launch!with!3Wclick!velocity!using.!Is!it!possible!to!take!the!sine!of!a!number!that!is!not!between!zero!and!one?!Show!manipulations!of!

equations!with!numbers!here._____!

!

!

!

!

!


Comment!on!how!well!you!achieved!your!objective(s)._____!

!

!

Identify!sources!of!experimental!error!(why!do!we!have!percent!differences!in!the!

first!two!parts!of!the!experiment?)_____!

!

!


!

!

Answer!the!question!at!the!end!of!the!lab!manual!pages.!Show!work!clearly!and!

neatly._____!

Additional*Comments:*

46

Projectile*Motion*Experiment*Pre1Lab*Quiz*!

!Name:__________________________!!Section!#:_____________!!The!diagram!shows!a!ball!that!has!been!launched!from!launch!point!L!with!initial!velocity!vo!at!an!angle!θ#relative!to!the!horizontal!flat!ground.!The!total!time!of!flight!of!the!ball!was!t.!During!this!time,!the!ball!covered!a!horizontal!distance!d.!The!ball!is!pictured!at!positions!A,!B!and!C.!Position!A!took!place!at!time!t/4,!position!B!took!place!at!time!t/2!and!position!C!took!place!at!time!3t/4.!The!ball!is!at!its!highest!point!at!position!B.!!!!! ! !!!! ! ! ! B# # # #! ! !!! ! ! ! ! ! !

! !!!!!!!!!!!!A! ! ! ! ! ! !!C!!!!!!!!!!GGGGGGGGG!!!!!!L##)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))#!!! !!!|GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGdGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG|!!On!the!diagram,!draw!vectors!with!magnitudes!labeled!next!to!them!for!the!following:!!

a) The!ball’s!net!initial!velocity!at!the!launch!point!(vo).!Also!show!the!angle!θ!b) The!xGcomponent!of!the!ball’s!initial!velocity!at!the!launch!point!(vox)!c) The!yGcomponent!of!the!ball’s!initial!velocity!at!the!launch!point!(voy)!d) The!xGcomponent!of!the!ball’s!velocity!at!positions!A,#B!and!C!(vxA,B,C)!e) The!acceleration!of!the!ball!at!positions!A,#B!and!C!(aA,B,C)!f) The!yGcomponent!of!the!ball’s!velocity!at!position!B!(vyB)!

!Using!vox!=!dx/tx!where!dx!is!the!distance!traveled!in!the!xGdirection!and!tx!is!the!amount!of!time!it!took!to!get!there,!how!far!has!the!ball!traveled!horizontally!at!positions!A,#B!and!C?!!

47

Properties)of)a)Vertical)Spring2Mass)System)Lab)Grading)Rubric!!

!

Name:_____________________________________! ! ! ! Grade:__________/100!

!

!

Pre2Lab:__________/10!)Cover)Page/Lab)Manual)Pages:__________/5!Name_____!







)Objective)Statement:________/10!Completely!and!concisely!address!all!of!your!objectives______!

!


pronouns.______!

!

Results)and)Analysis:__________/60!!

Explain!how!you!determined!the!spring!constant!k!by!plotting!the!displacement!due!to!various!masses.!This!involves!displaying!a!figure!properly._____!

!

Explain!how!you!determined!the!periods!based!on!the!spring!constant!k.!______!!

Explain!how!you!found!the!periods!from!one!of!the!plots!of!the!mass’s!oscillation.!

This!involves!showing!a!figure!then!explaining!a!calculation.________!

!

Explain!how!you!found!the!percent!differences!between!the!periods._______!

!

Display!a!table!that!shows!all!calculations!that!went!into!determining!the!percent!

differences.________!

!

Display!a!set!of!more!detailed!(zoomedRin)!plots!(position,!velocity,!acceleration,!

force!vs.!time)!representing!the!mass’s!oscillation.!_______!

!

Explain!how!you!determined!the!kinetic!energy!at!some!point!in!time._______!

!

Explain!how!you!determined!the!potential!energy!at!the!same!point!in!time._____!

!

Explain!how!you!determined!the!total!energy!at!the!same!point!in!time.______!

48

!

Explain!how!you!determined!the!force!using!two!different!methods!(Hooke’s!Law!

and!Newton’s!Law)!at!the!same!point!in!time.______!

!

Explain!how!you!found!the!percent!difference!between!the!forces!you!

calculated._____!

!

Explain!that!you!did!these!calculations!for!various!masses!when!the!displacement!

was!at!a!maximum,!a!minimum,!and!somewhere!in!between.________!

!

Display!a!table!of!the!energy!and!force!calculations.________!

!

!

Discussion/Conclusions:__________/15!Directly!address!your!objectives.______!

!

What!did!you!determine!about!the!relationships!between!potential!energy,!kinetic!

energy,!total!energy!and!force!in!a!vertical!springRmass!system?!Make!a!few!concise,!

well!thoughtRout!statements.______!

!

Address!sources!of!experimental!error!that!limited!your!ability!to!achieve!your!

objectives.______!

!

Additional)Comments:)

49

Properties)of)Energy)in)a)Vertical)Spring4Mass)System)Pre4Lab)Quiz))

!Name:______________________________________!!Section!#:_________________!!1.!Write!down!Hooke’s!law!for!the!force!exerted!by!a!spring!on!a!mass!based!on!its!!!!!!!displacement!from!equilibrium.!!!!!!!2.!Indicate!whether!the!following!are!true!(T)!or!false!(F)!!_____When!a!mass!at!the!end!of!a!spring!is!oscillating!about!equilibrium,!the!total!energy!of!the!system!at!some!moment!in!time!is!always!equal!to!the!total!energy!of!the!system!at!some!other!moment!in!time.!!!_____!When!a!mass!at!the!end!of!a!spring!is!oscillating!about!equilibrium,!the!potential!energy!of!the!system!at!some!moment!in!time!is!always!equal!to!the!potential!energy!of!the!system!at!some!other!moment!in!time.!!!_____When!a!mass!at!the!end!of!a!spring!is!oscillating!about!equilibrium,!the!kinetic!energy!of!the!system!at!some!moment!in!time!is!always!equal!to!the!kinetic!energy!of!the!system!at!some!other!moment!in!time.!!!_____The!spring!force!is!at!a!maximum!value!when!the!displacement!from!equilibrium!is!at!a!minimum!value.!!!!3.!In!today’s!experiment,!what!does!the!position!sensor!measure?!(circle!an!option)!!

a) The!mass’s!displacement!from!equilibrium!b) The!mass’s!kinetic!energy!c) The!maximum!displacement!of!the!mass!d) The!distance!from!the!sensor!to!the!mass!

50

Transverse(Mechanical(Waves(and(Resonance(Lab(Grading(Rubric!!

!

Name:_____________________________________! ! ! ! Grade:__________/100!

!

!









!


pronouns.______!

!

Results(and(Analysis:__________/35!!

Thoroughly!explain!all!manipulations!of!data!that!you!did!in!order!to!accomplish!

your!objective(s).!Properly!include!the!necessary!equations,!sample!calculations,!

tables!and!figures!in!a!logically!structured!order!to!effectively!communicate!your!

explanation._________!

!

!


Directly!address!your!objective(s).______!

!

Comment!on!how!well!you!achieved!your!objective(s).!Were!you!limited!in!your!

ability!to!test!your!objective?_______!

!

Answer!question!1!at!the!end!of!the!lab!manual.!Ignore!the!other!questions._______!

!

!


51

Transverse(Mechanical(Waves(and(Resonance(Pre3Lab(Quiz!!!

Name:________________________________!!Section!#!:______________!!!1.!First!indicate!whether!each!of!the!following!types!of!waves!is!mechanical!(yes!or!no)!then!indicate!whether!it!is!transverse!(yes!or!no)!!!! ! ! ! Mechanical?!(Y/N)!!!!!!!!Transverse!(Y/N)!!A!sound!wave!! ! ! ______! ! ! ______!!A!radio!wave! ! ! ! ______! ! ! ______!!A!string!carrying!a!pulse! ! ______! ! ! ______!(like!in!today’s!experiment)!!!!2.!A!string!is!oscillating!with!resonance,!resulting!in!a!standing!wave!over!a!distance!L.!The!resonance!has!four!antinodes!and!five!antinodes.!Draw!the!standing!wave.!What!is!the!wavelength!of!the!wave?!!!!

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Wavelength*of*Light*Lab*Grading*Rubric*!Name:_____________________________________! ! ! ! Grade:__________/100!!!Pre7Lab:__________/10!*Cover*Page/Lab*Manual*Pages:__________/5!Name_____!Course!&!Section!#_____!Instructor’s!Name_____!Title!of!Experiment_____!Date!Experiment!was!Performed_____!Partner’s!Name_____!Lab!manual!pages!present!and!in!order______!*Objective*Statement:________/10!Completely!and!concisely!address!all!of!your!objectives______!!Write!a!complete!sentence!in!the!past!tense!and!active!voice!that!uses!first!person!pronouns.______!*Results:___________/50!Include!a!table!with!the!information!you!recorded!in!parts!i!and!ii!of!the!procedure_______!!Explain!how!you!calculated!the!grating!constant,!d,!and!state!the!number!of!slits!per!unit!length_______!!Compare!your!answer!to!the!diffraction!grating’s!rating________!!Answer!the!first!part!of!question!1!at!the!end!of!the!lab!manual!pages________!!Answer!question!2!at!the!end!of!the!lab!manual!pages_________!!Include!a!table!of!the!measurements!you!made!for!the!y!values!and!their!corresponding!angles!in!part!iv!of!the!procedure_________!!Explain!how!you!calculated!the!difference!of!the!wavelengths!of!the!two!yellow!lines!for!n=2!and!n=3.__________!!Compare!your!values!to!the!known!value!of!21!Å!and!show!them!in!a!small!table!or!state!them!concisely!(part!v!of!the!procedure)_______!!

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Explain!how!you!calculated!the!wavelength!for!each!spectral!line.!Also!explain!how!you!calculated!the!percent!difference!between!your!values!and!the!values!given!in!appendix!A!of!this!experiment!in!the!lab!manual____________!!Include!a!table!with!your!values,!the!accepted!values,!and!the!percent!differences_______!!!!!Conclusion:__________/25!Address!your!objectives_________!!Explain!how!sources!of!experimental!error!affected!your!results_______!!Answer!the!questions!at!the!end!of!part!v!in!the!procedure!section________!!

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Wavelength*of*Light*Pre1Lab*Quiz!!!

Name:______________________________! ! !!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Score:_______/10!!Section#:_____________!!!

1. What!is!the!wavelength!of!white!light?!!a) 400?700!nm!b) 1,000?10,000!nm!c) 400?700!m!d) 400?700!km!e) The!wavelength!of!white!light!is!randomly!polarized!

!!!!

2. True!or!False:!Passing!monochromatic!light!through!a!diffraction!grating!will!result!in!discrete!bands!of!light.!

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3. How!fine!of!a!diffraction!grating!(what!d!would!you!need)!to!see!a!band!from!a!7,000!nm!light!source!at!an!angle!of!30°?!Remember!the!condition!for!constructive!interference!is!dsinθ=nλ.!!

!!!!!!!!!!!!!!!!!

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General!Physics!I!&!II!Lab!! - UML Physics Lecture...

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Transcript of General!Physics!I!&!II!Lab!! - UML Physics Lecture...