Rainbow Connection. Teacher Guide

Transcription

1 Rainbow Connction Tachr Guid Karn Danils and Erika Mrschrod Cornll Cntr for Matrials Rsarch, Rsarch Exprinc for Tachrs July 2000 Modifid August 2001, KED INTRODUCTION W will invstigat th rlationship btwn color, wavlngth and nrgy for th visibl spctrum of light using light mitting diods (LEDs). Ths ar lctronic componnts which pass currnt in only on dirction. Whn currnt flows through an LED, th nrgy from that currnt is convrtd into light of a particular wavlngth associatd with th matrial insid th LED. Ths wavlngths ar usually printd on th packaging of th LED, and many diffrnt colors ar availabl. For a particular matrial, only crtain wavlngths ar possibl. Visibl light is just on part of th lctromagntic spctrum, and diffrnt colors ar distinguishd by thir diffrnt wavlngths (or, quivalntly, frquncis). Whn all wavlngths of visibl light ar shon togthr, th rsult is whit light. Th spctrum natur of this whit light can b rvald using a diffraction grating or prism, which bnds diffrnt wavlngths of light by diffrnt amounts. DEMO: Shin an ovrhad projctor or slid projctor through a diffraction grating or prism. Hav studnts not that th colors ar sprad out in a particular ordr, which thy will rcogniz from rainbows. Byond th rd is infrard radiation, and byond th blu is ultraviolt, nithr of which ar visibl to th nakd y. Elctromagntic Spctrum radio wavs microwavs infrard ultraviolt x rays gamma rays visibl low frquncy long wavlngth low nrgy high frquncy short wavlngth high nrgy Figur 1: Th lctromagntic spctrum. 1

2 All wavs, whthr light, sound, watr or stadium, travl at a spcific vlocity. If you mak on of ths typs of wavs with a particular frquncy, thy will always hav th sam wavlngth. DEMO: Hav a pair of studnts hold opposit nds of th rop on th surfac of a slippry floor whil th othrs gathr around. On studnt should hold thir nd stady with th othr wavs thir nd back and forth at first slowly (low frquncy), thn mor quickly (high frquncy). Hav studnts obsrv that a high-frquncy wav is shortr in wavlngth. It also taks mor nrgy to mak a highfrquncy wav, for a constant amplitud. W can think about a similar situation for a train, for xampl. If w wr standing bsid th track trying to figur out how fast it was going, w might count 15 train cars going by ach minut (60 sconds) this is a frquncy, Latr, whn th train stops, w could masur th lngth of th cars and find that thy ar 8 mtrs long (analogous to a wavlngth). From this, w can dtrmin th spd that th train had bn travling.! #"$&% "$'( W can also pictur a train travling along at a constant spd, but with a scond typ of car at th back nd of th train: ths ar only 6 mtrs long. Sinc th train spd is still constant, th frquncy with which w obsrv passing cars must incras whn w gt to th sction with th shortr cars, as it did with th rop wavs. ( ) "$$'( ** +, #"$ It is convnint to dscrib light in trms of its frquncy, wavlngth or nrgy. As with th train xampl, th unit for frquncy is Hrtz, abbrviatd Hz. On Hrtz is on cycl pr scond, 1/sc. Wavlngths ar oftn masurd in mtrs or fractions of mtrs: micromtrs (10-/. m, also calld microns), nanomtrs (10-/0 m), Ångstroms ( m), tc. All typs of light ar composd of th sam oscillations of lctric and magntic filds, but at longr or shortr wavlngths. Rgardlss of wavlngth, all light travls at a constant spd, 5 * 7 %6 m/s8, and th product of th wavlngth and th frquncy (in appropriat units) will always giv this valu. Thus, th highr th frquncy, th shortr th wavlngth, as with th rop wavs in th dmo and th train-car xampls. 5 :9; wav spd = wavlngth % [mtrs/sc] = [mtrs] % frquncy [Hrtz] (1) 2

3 It is usful to rmmbr that light is just anothr form of nrgy: chmical nrgy and lctrical nrgy ar som othr common typs. Thr ar many units for nrgy in us today: Jouls (1 J = 1 kg m8 /s8 ), caloris (1 cal = J), and lctron volts (1 V = 1.6 % J) ar a fw xampls. If w rcall that lctron volts ar a masur of th nrgy of an lctron (of charg < ) in a lctric potntial (of voltag = ); w s thrfor that nrgy can b dfind as charg % voltag. Sinc th units of charg ar Coulombs (C), 1 Volt = 1 Joul/Coulomb. W alrady discovrd how to rlat th wavlngth and frquncy of light, and on of th arlist advancs in quantum mchanics was th rlation Max Planck found btwn th nrgy of light and its frquncy. >?; (2) nrgy = Planck s constant % [Jouls] = sc] % frquncy [Hrtz] As th twntith cntury has progrssd, Planck s constant has found its way to th hart of our quantum mchanical dscription of th univrs: it signifis th finst scal to which w can prob. LIGHT EMITTING DIODES Light mitting diods ar common in many lctronic dvics bcaus thy consum vry littl lctricity. Th rason for this is that th procss which allows thm to rlas photons is a fundamntal on, and thr ar vry fw losss, as with th hat producd by standard incandscnt lightbulbs. A lightbulb is basically a thin pic of (tungstn) wir. Whn th currnt passs through th wir it ncountrs som rsistanc (from th atomic structur of th wir, th polycrystallin natur of th wir, othr dfcts in th wir, tc.). This rsistanc lads to hating, and th hatd wir givs off radiation of a wid rang of wavlngths known as blackbody radiation. Most of th nrgy consumd by th wir is givn off in hat, so lightbulbs ar vry infficint light sourcs. In contrast, all of th nrgy consumd by th LED gos into lctron xcitation, which lads to mission of a particular wavlngth. highr nrgy ("conduction") band hω } band gap = E Battry lowr nrgy ("valnc") band Figur 2: Schmatic of nrgy bands. Battry pumps lctrons up to highr-nrgy band, and thy fall back down to th lowr-nrgy band, mitting light. 3

4 > > Th crucial matrial insid an LED is a smiconductor, which has crtain lctronic proprtis. All lctrons (on any atom) hav a particular nrgy, so w say that thy rsid in a particular nrgy lvl. In a solid systm (a smiconductor, a mtal) thr ar many lvls with th sam nrgy, and many mor with similar nrgis, so th lvls ar groupd in bands. In a smiconductor, thr is an nrgy gap (whr thr ar no lvls) btwn th band with th highst-nrgy lctrons and th lowst-nrgy mpty band; this is th nrgy gap which is crossd by xcitd lctrons whn a currnt is passd through th LED. (S Figur 2.) Th battry provids nrgy to lift lctrons to th highst-nrgy lvl from th lowst-nrgy lvl. Whn th lctrons rlax back to thir initial nrgy, thy mit light of nrgy, th sam nrgy it took to lift thm. For ach lctron which falls across th band gap, a photon with this nrgy is rlasd. To mak LEDs of diffrnt colors, diffrnt smiconductors ar usd so that th gap btwn th lvls has a diffrnt nrgy. A mor dtaild xplanation can b found at Washington Univrsity: MtalBonding/MtalBonding.html LED LABORATORY EXERCISE SETUP Studnts will construct a simpl lctric circuit composd of a battry (nrgy sourc), an LED (sourc of singl-wavlngth light), and a rsistor (dissipats xcss powr). Figur 3 shows how this is to b don, using standard lctrical symbols. Not that th rsistor and th battry both hav dirction to thm: if on is rvrsd with rspct to th othr, th LED will not light up. Th battry will b lablld A and B, and th flat dg of th LED corrsponds to th flat lin shown in th circuit diagram. Th rsistor can fac ithr dirction within th circuit, and li on ithr sid of th LED. + Top Viw V Voltmtr LED + 3 (6) V Battry + Sid Viw (a) 33 (180) Ω Rsistor (b) + Schmatic Figur 3: (a) Circuit diagram for LEDs. Th rsistor can go on ithr sid of th LED. (b) Locating th cathod (C ) and anod (D ) on a LED, so that it can b proprly orintd within th circuit. 4

5 D > 9 > 9 > > = 5 ' ' Color Wavlngth Voltag Frquncy (Hz) Enrgy (J) Planck constant )?E (nm) (volts) <= (F)@HG ) *I* L L infrard %6 1KJ %M -2140, N%O -/PQJ rd orang yllow grn blu Figur 4: Sampl data for a st of six LEDs. Wavlngth valus takn from manufacturr s information, voltags masurd, and rmaining columns calculatd. Whn th circuit is constructd corrctly, th LED will light up. If it dos not, try rvrsing th dirction of th LED with rspct to th battry, consulting Figur 3b for corrct orintation. Each group will nd a collction of 4 to 6 diffrnt colord LEDs, ach soldrd to a rsistor appropriat for th battry voltag, and a battry stup to provid powr. Th soldring can b don bforhand, or includd as part of th lab activitis. Th battry should b ithr 3 or 6 V, most asily providd by a pair of AA battris in a battry holdr or a 6V lantrn battry. For th 3V battry, a 33 R rsistor should b usd, whil a 180 R rsistor is appropriat for us in a 6V. It is possibl for ach group to gt only a fw LEDs at a tim, and swap with anothr group whn thy ar don, so that th total numbr of LED stups is rducd. Bcaus blu LEDs will nd to us approximatly 3 V in ordr to light up, thy will work bst with 6 V stups. TAKING MEASUREMENTS For ach color LED, attach th lads to th battry so that th light turns on. Masur th voltag drop (nrgy usd) across th LED using th multimtr, as shown in Figur 3. Rcord th voltag and th wavlngth (from tag, packaging, or catalog) for ach LED in th collction. If you and/or th studnts ar unfamiliar with th us of multimtrs, th following tips will hlp. Sinc w ar masuring voltag and not currnt, car must b takn that th lads of th multimtr ar attachd to th appropriat trminals on th multimtr (gnrally markd C and or COM and VR ). Thr may also b a dial which must b st to V to masur voltag, and somtims a corrct rang must b chosn as wll. ANALYSIS Studnts should graph wavlngth (or frquncy) vs. voltag (or nrgy) to s th rlationship. From this point, svral lvls of sophistication ar possibl. Whil wavlngth is th valu givn on th packag of th LED, th frquncy ( ) is th mor physically intrsting quantity, sinc it is rlatd to th nrgy ( ) of th light by Planck s constant (? ). Thrfor, studnts can dtrmin a valu for Planck s constant by convrting voltag to nrgy ( <,=, whr < is th charg on an lctron) and wavlngth to frquncy ( 5 :9 ) in whatvr units thy ar comfortabl with. Th slop of an nrgy vs. frquncy graph will giv a valu for Planck s constant for a lin which gos through th origin. 5

6 < U X 8 Enrgy (10-19 J) h = J s 0 S 0 T 2 4 Frquncy (10 14 Hz) V 6 W 8 Figur 5: Sampl graph for a st of LEDs: frquncy vs. nrgy, with bst fit lin through origin plottd and xprimntal valu for? (slop) shown. If doing th convrsions and fitting is not dsirabl, a simpl graph of voltag vs. wavlngth will still show a trnd which can b discussd qualitativly, and vn usd for xtrapolation and intrpolation. A sampl studnt handout suitabl for us in grads 6 8 is availabl which uss mostly qualitativ rasoning.?e 5 * 7 %6 m/s8 spd of light Y %O Coulomb lctronic charg, %6 -/PQJ s Planck s constant To dtrmin Planck s constant? in th most common units of FZ@;G, unit convrsion will b a ncssary part of th lab. Wavlngth will b givn in Å (Ångstroms, mtrs) or nm (nanomtrs, 10-/0 mtrs), so this convrsion is fairly simpl. Frquncy is dtrmind from Equation 1, with th rsulting units in Hz (sc-21 ). Rmmbr, this is motivatd by th rop dmonstration. For th nrgy part of th calculation, it is usful to considr what happns within th circuit. Concptually, lctrons lav th battry with som voltag (3V or 6V, dpnding on th stup). This voltag is th nrgy pr unit charg on th lctron, and th lctrons will hav lost it all by th tim thy gt around to th othr nd of th battry. Th LED will tak whatvr nrgy it nds (to produc light, anothr form of nrgy) and th rst will b usd up in th rsistor (which hats up ovr tim as a rsult). So, to dtrmin th nrgy of th light, w just nd to multiply I,Y th voltag (1 volt = 1 Joul/Coulomb) by th charg on th lctron ( % Coulomb) to gt th nrgy of th light producd by ach lctron, in Jouls. What is a Joul? It would tak 1 Joul of nrgy to lift a 1 kg wight by 10 cm. If w want to work outsid th mtric systm, anothr xampl would b to lift a 5 lb bag of flour by 1.7 6

7 inchs. You could also calculat th total numbr of Jouls bing rlasd pr scond by th LEDs by masuring th currnt with th multimtr, th valu for which will b givn in Coulombs/sc (Amprs). MYSTERY LED Th tachr should prpar an LED (or nough for ach group to hav thir own) wrappd in black lctrical tap or nclosd in a film canistr, but with th lads xposd for tsting. Studnts can us thir multimtrs to dtrmin th voltag drop across th rsistor, and intrpolat/xtrapolat from thir graph to dtrmin a wavlngth and prdict a color. Whn all prdictions ar in, th color can b rvald. If an infrard LED is usd for this sction, it can lad to a discussion about othr parts of th lctromagntic spctrum. Whil th light is not visibl to th nakd y, it still bhavs in th sam way as with th othr LEDs. On nic fatur of digital camras is that thy ar snsitiv to nar infrard light, allowing studnts to indirctly s th light mittd from th LEDs if you hav on availabl. REFERENCES Patrick J. O Connor and Lah R. O Connor. Masuring Planck s constant using a light mitting diod. Th Physics Tachr. 12: 423 (1974). F. Hrrmann and D. Schätzl. Qustion #53. Masuring Planck s constant by mans of an LED. Amrican Journal of Physics. 64: 1448 (1996). L. Nivs, G. Spaviri, B. Frnandz, and R. A. Guvara. Masuring th Planck Constant with LEDs. Th Physics Tachr. 35: 108 (1997). Rogr Morhous. Answr to Qustion #53. Masuring Planck s constant by mans of and LED. Amrican Journal of Physics. 66: 12 (1998). MATERIALS [ R [ R R [ [ FOR EACH LAB GROUP a slction of diffrnt colord LEDs taggd with thir wavlngth and with a 33 rsistor soldrd to ach. pair of AA battris ( 1.5V ach ) in a battry pack (it is possibl to substitu a 6V lantrn battry with scrw-on trminals if th 33 rsistor is rplacd with on of 180 ) mystry LED (infrard for xtrapolation or orang for intrpolation), tapd ovr or hiddn in film canistr with lads poking out multimtr [ graph papr, rulr, calculator [ lab instruction sht 7

8 FOR CLASS DEMOS [ 10 to 15 ft. flxibl rop with cntr markd with pn [ columatd whit light sourc (ovrhad or slid projctor) [ diffraction grating or prism [ lctromagntic spctrum chart [ ovrhad and colord pns for drawing graphs [ digital camra for viw infrard LED PREPARING THE ELECTRONICS Whn soldring th LEDs to th rsistors, tak car not to allow th LED to bcom too hot. This can b avoidd by holding th lg bing soldrd with a pair of mtal plirs or an aligator clip to act as a hat sink. Th rsistors can b soldrd on ithr sid, but bing consistnt with th circuit diagram hlps insur that th LEDs ar placd into th circuit facing th corrct dirction. If battry holdrs ar bing usd, it hlps to soldr alligator clips to th trminals on th holdrs. This mans that studnts can quickly and scurly clip th LED stups into th circuit. If 6V lantrn battris ar bing usd, thy hav scrw-down trminals which ar most asily usd if flxibl wir lads ar soldrd to th nds of th LED stups. SOURCES FOR MATERIALS Radio Shack gnrally carris rd, yllow, and grn LEDs, and othr colors may b spcially ordrd. Hosflt Elctronics ( carris mor xotic LEDs for rasonabl prics. Whrvr th LEDs ar purchasd, b sur that th wavlngth (in nm or Å) is printd in th catalog or on th packaging, sinc this information is ndd for th quantitativ parts of th laboratory xrcis. EXTENSIONS Connctions to many branchs of scinc and math ar possibl. Blow ar gnral discussion qustions, as wll as suggstd activitis prtaining to various subjcts. Rfrncs ar providd for obtaining mor information. ASTRONOMY TAKING THE TEMPERATURE OF A STAR Whil stars gnrally look whitish, a mor carful xamination rvals that som of thm ar rdish whil othrs ar bluish. This is du to thir diffring surfac tmpraturs. Stars on th main 8

9 squnc rang from hot, blu stars (high mass) to coolr, rd stars (lowr mass). Astronomrs plot ths valus on a Hrtzsprung-Russll (HR) diagram. On asy-to-spot xampl of a rd star is Btlgus in th constllation Orion. Ths concpts ar rlatd to thos of blackbody radiation, listd undr Physics blow. Scinc Musum of Virginia: How Hot is that Star? Univrsity of Colorado, Bouldr: Physics EXPLORING THE UNIVERSE IN DIFFERENT WAVELENGTHS Until rcntly, astronomrs could only xplor th night sky using thir ys and tlscops, limiting thir vision to th visibl spctrum. Nw tchnologis allow thm to xplor using all parts of th lctromagntic spctrum, frquntly by placing tlscops abov th arth s atmosphr, in orbit. Hubbl Spac Tlscop Spac Infrard Tlscop Facility Chandra X-ray Obsrvatory Compton Gamma Ray Obsrvatory Exploratorium: Spctra from Spac from spac/ Cntr for Scinc Education: Light Tour of diffrnt wavlngths of light tour.html BIOLOGY CHLOROPHYLL, PHOTOSYNTHESIS, AND THE SUN Photosynthsis, th convrsion of radiant nrgy from sunlight to chmical nrgy in plants, works on th sam principl as th LEDs: a particular matrial (th chlorphyll molcul in this cas) can absorb a crtain amount of nrgy of on kind and mit that nrgy in anothr form. Th LED 9

10 taks in a particular amount of nrgy from an lctric currnt and mits light of a particular nrgy (wavlngth). Th chlorophyll taks in a particular wavlngth from sunlight and convrts that to chmical nrgy. Th sunlight xcits an lctron in th chlorophyll, and thn th xcitd lctron can b transfrrd to othr molculs to stimulat particular ractions. Evntually, th plant can us this nrgy to convrt CO 8 and H 8 O to th sugar for food. Studnts can obsrv th lctron transfr procss (oxidation/rduction) indirctly by adding a suitabl dy to chloroplasts from plants. As th chlorophyll absorbs light, lctrons ar xcitd. Th dy acts as an accptor for th lctron from th chlorophyll; th dy is rducd and th chlorophyll is oxidizd. DCPIP is a good dy for this, bcaus it is blu in its oxidizd stat and colorlss whn it is rducd. Thus, studnts can obsrv th color chang in th dy, which indicats that th first stp in photosynthsis is occuring. This xprimnt taks a fair bit of prparation, as it involvs harvsting th chloroplasts oftn from spinach (using a blndr and som chmicals for xtraction). A dscription of this lab is givn in: Dan, R. L. Th Amrican Biology Tachr, 58, (1996) RODS AND CONES IN THE EYE W can s bcaus of clls calld rods and cons. Whn light hits th y, it travls through th pupil to th rtina, whr th cons and rods ar locatd. In ths clls, th light causs a chmical raction which translats th light into a mssag for your brain. Th rod clls contain rhodopsin and th con clls contain rtinal. Th rtinal molculs absorb light of particular frquncis (rd, grn, or blu) and thn rlas corrsponding amounts of nrgy which is convrtd to an lctrical signal in th brain. So in a sns, thy work in th opposit dirction from th LEDs. Bcaus con clls ar snsitiv to only thr colors, ths ar th primary colors of light, which ar not th sam as th primary colors of pigmnts. Th Tch Musum of Innovation in San Jos vnts/onlin/color/vision/ Th Howard Hughs Mdical Institut Rd, grn, and blu color-mixing applt hwang/imag/rgbcolor.html CHEMISTRY FIREWORKS! (FLAME TESTS) Flam tsts ar usd to idntify ions in a salt (sodium in tabl salt, potassiun in potassium iodid, tc). Th flam color indicats th nrgy givn off by an xcitd lctron as it rturns to its ground stat. (Th hat from th flam xcits th lctron initially.) Th studnts can rlat th color of 10

11 th flam to th atomic structur, i.. why would it tak mor (lss) nrgy to xcit an lctron in on atom or anothr? Thr ar many ways to do a flam tst; th asist is to just put a mound of salt on a dish, add mthanol, and light! (Mthanol is a poison; do not ingst.) Som salts to try: NaCl (yllow), KCl (violt), BaCl 8 (grn-yllow), SrCl 8 (rd). Thr ar many rfrncs availabl in th Journal of Chmical Education. ABSORPTION SPECTRA OF CONJUGATED DYES A dy can b thought of as a box of a crtain siz in which an lctron can mov. Th siz of th box dtrmins th nrgy of th highst-nrgy lctrons (th ons that ar moving): th smallr th box, th highr th nrgy. W can think of this as taking a givn wav and squzing it into a smallr or biggr box: th wav in th smallr box has a highr frquncy and hnc a highr nrgy. Th lctrons ar bhaving lik wavs as thy mov around th box. Th color of th dy is th combination of wavlngths in whit light not absorbd by th dy, so th color sn is th conjugat of th color of light absorbd by th dy. Studnts can rlat th siz of a dy molcul to its color and th color it is absorbing. (Molcular structur can b obtaind from th chmical supplir.) Th standard rfrnc for this xprimnt is Shomakr, D. P., C. W. Garland, and J. W. Niblr, Exprimnts in Physical Chmistry. Nw York: McGraw-Hill (1996). Anothr vrsion on th wb, from th Univrsity of Nbraska-Lincoln: MATH GRAPHING In prparing th graph of nrgy vs. frquncy, studnts should b abl to rcogniz th \ form, whr ` in th modl w ar using. Som good qustions to rais includ: ^]E_ DN` [ Finding a bst fit lin (by y using graph papr, with a graphing calculator, or on a computr) to rlat frquncy to nrgy. [ Discussing what units th slop of th quation has. [ Thinking about why th intrcpt of th lin might or might not b at th origin. [ Talking about xprimntal rror, scattr of points, and th comparison of a group s data point to th plot for th ntir class. [ Whr xtrapolations/intrpolations ar valid. 11

12 TRIGONOMETRY Th wavs of light tak on sinusoidal forms, providing many connctions to frquncy, priod, wavlngth, and vn phas. Applt showing lctric and magntic componnts of light as sinusoids hwang/mwav/mwav.html PHYSICS Many connctions ar possibl: voltag ruls in circuits, lctromagntic spctrum, blackbody radiation, nrgy lvls, spctral lins, color mixing, diffraction, wav-particl duality, photolctric ffct, smiconductors, tc. In fact, much of twntith-cntury physics as bn involvd with th concpts raisd hr! For a collg-sophomor lvl physics txtbooks which covrs most of th physics topics mntiond abov, rfr to: R. A. Srway, C. J. Moss, C. A. Moyr. Modrn Physics. Saundrs Collg Publishing (1998). Rd, grn, and blu color-mixing applt hwang/imag/rgbcolor.html Applt showing lctric and magntic componnts of light hwang/mwav/mwav.html Univrsity of Colorado, Bouldr: Physics On possibl xtnsion of th lab xrcis for oldr studnts would b to hav thm rsarch and prsnt som of th biology, chmistry, and astronomy connctions basd on thir knowldg of physics. TECHNOLOGY Studnts can brainstorm ways in which LED tchonolgy is found in vryday dvics: computr indicator lights, on/off on stros, som nw flashlights, tc. Efficincy of dvics can b discussd via th diffrnc btwn LEDs and incandscnt lightbulbs. If th studnts assmbl th circuits thmslvs, soldring skills and th intrprtation of schmatic diagrams ar involvd. David Macaulay s Th Way Things Work or Th Nw Way Things Work Contains information on many dvics which mak us of ths concpts, in a fun and pictoral format. LED Musum 12