Maxwell s unification: From Last Time. Energy of light. Modern Physics. Unusual experimental results. The photoelectric effect

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1 From Last Tim Enrgy and powr in an EM wav Maxwll s unification: 1873 Intimat connction btwn lctricity and magntism Exprimntally vrifid by Hlmholtz and othrs, 1888 Polarization of an EM wav: oscillation plan of E-fild Thr is nothing nw to b discovrd in physics now. All that rmains is mor and mor prcis masurmnt, Lord Klvin, 1900 "Havir-than-air flying machins ar impossibl." (1895) 1 2 Modrn Physics Dramatic changs in physics at turn of cntury. Rlativity: Compltly diffrnt ida of tim and spac. Quantum Mchanics: Compltly diffrnt ida of mattr and light. Enrgy of light In th classical pictur of light (EM wav), w chang th brightnss by changing th powr (nrgy/sc). This is th amplitud of th lctric and magntic filds. Classically, ths can b changd by arbitrarily small amounts Brightnss, powr, unrlatd to frquncy, wavlngth Traditional concptions of mattr and light usful, but not fundamntal 3 4 Th photolctric ffct A mtal is a buckt holding lctrons Elctrons nd som nrgy in ordr to jump out of th buckt. Light can supply this nrgy. Enrgy transfrrd from th light to th lctrons. Elctron uss som of th nrgy to brak out of buckt. Rmaindr appars as nrgy of motion (kintic nrgy). A mtal is a buckt of lctrons. 5 Unusual xprimntal rsults Not all kinds of light work Rd light dos not jct lctrons Mor rd light dosn t ithr No mattr how intns th rd light, no lctrons vr lav th mtal Until th light frquncy passs a crtain thrshold, no lctrons ar jctd. 6 1

2 Th xprimnt Th Data Complication: Whn light jcts lctrons, thy hav rang of vlocitis Analyz: Apply variabl E-fild that opposs lctron motion Stopping potntial: voltag at which highst kintic nrgy (K max ) lctrons turnd back Stopping potntial dpnds on light frquncy Highr frquncy light jcts lctron with mor nrgy Stopping potntial gos to zro at som critical frquncy For light blow that frquncy, no lctrons ar jctd. 7 8 Analyzing th data Einstin s xplanation Elctrons absorb fixd nrgy E absorb from light K max Escapd from solid K max Einstin said that light is mad up of photons, individual particls, ach with nrgy hf. On photon collids with on lctron - knocks it out of mtal. Bound in solid E o E absorb Highst KE lctron Enrgy If photon dosn t hav nough nrgy, cannot knock lctron out. Intnsity ( # photons / sc) dosn t chang this. SOLID Lowst KE lctron Rang of lctron nrgis in solid 9 Minimum frquncy rquird to jct lctron 10 Einstin s analysis Elctron absorbs nrgy of on photon E absorb E photon hf h ( f f o) Slop of lin h/ Minimim frquncy hf o E o Work function hf Wavlngth dpndnc Short wavlngth: lctrons jctd Hi-nrgy photons Long wavlngth: NO lctrons jctd Thrshold dpnds on matrial Lo-nrgy photons

3 Quantization and photons Quantum mchanically, brightnss can only b changd in stps, with nrgy diffrncs of hf. Possibl nrgis for grn light (500 nm) On quantum of nrgy: on photon Two quanta of nrgy two photons tc Think about light as a particl rathr than wav. E4hf E3hf E2hf Ehf Th particl prspctiv Light coms in particls calld photons. Enrgy of on photon is Ehf f frquncy of light Photon is a particl, but movs at spd of light! This is possibl bcaus it has zro mass. Zro mass, but it dos hav momntum: Photon momntum pe/c Compton scattring Photons can transfr nrgy to bam of lctrons. Dtrmind by consrvation of momntum, nrgy. Compton awardd 1927 Nobl priz for showing that this occurs just as two balls colliding. Photon nrgy Ehf Photon mass 0 Arthur Compton, Photon momntum pe/c Jan 13, Compton scattring Photon loss nrgy, transfrs it to lctron Photon loss momntum transfrs it to lctron Total nrgy and momntum consrvd Bfor collision Aftr collision 16 On quantum of grn light On quantum of nrgy for 500 nm light ( ) ( m /s) E hf hc J s m J Quit a small nrgy! Quantum mchanics uss nw convninc unit for nrgy: 1 lctron-volt 1 V charg on lctron x (1 volt) (1.602x10-19 C)x(1 volt) 1 V 1.602x10-19 J In ths units, E(1 photon grn) (4x10-19 J)x(1 V / 1.602x10-19 J) 2.5 V Simpl rlations Translation btwn wavlngth and nrgy has simpl form in lctron-volts and nano-mtrs Grn light xampl: E hc constant [in V nm] wavlngth [in nm] 1240 V nm 2.5 V 500 nm

4 Photon nrgy What is th nrgy of a photon of rd light (635 nm)? A. 0.5 V B. 1.0 V C. 2.0 V D. 3.0 V E hc 1240 V nm 1.95 V 635 nm How many photons can you s? In a tst of y snsitivity, xprimntrs usd 1 milliscond (0.001 s) flashs of grn light. Th lowst powr light that could b sn was 4x10-14 Watt. How many grn (500 nm, 2.5 V) photons is this? A. 10 photons B. 100 photons C. 1,000 photons D. 10,000 photons ( J /s)( 0.001s) J ( J) ( 1V / J) 250V ( 250V )( 1photon /2.5V ) 100 photons Photon proprtis of light Qustion Photon of frquncy f has nrgy hf Rd light mad of ONLY rd photons Th intnsity of th bam can b incrasd by incrasing th numbr of photons/scond. Photons/scond nrgy/scond powr A rd and grn lasr both produc light at a powr lvl of 2.5mW. Which on producs mor photons/scond? A. Rd B. Grn C. Sam # photons scond Powr Enrgy/photon Powr hf Rd light has lss nrgy pr photon so nds mor photons! Nobl Trivia But light is a wav For which work did Einstin rciv th Nobl Priz? A. Spcial Rlativity: Emc 2 B. Gnral Rlativity: gravity bnds Light C. Photolctric Effct & Photons

5 Nithr wav nor particl In som cass light shows proprtis typical of wavs Intrfrnc, diffraction In othr cass, shows proprtis associatd with particls. Photolctric ffct, Compton scattring Conclusion: Light not a wav, or a particl, but somthing w havn t thought about bfor. Rminds us of wavs. In som ways of particls. Particl-wav duality Light has a dual natur Can show particl-lik proprtis (collisions, tc) Can show wavlik proprtis (intrfrnc). It is nithr particl nor wav, but som nw objct. Can dscrib it using particl languag or wav languag whichvr is most usful Photon intrfrnc? Singl-photon intrfrnc Do an intrfrnc xprimnt again. But turn down th intnsity until only ONE photon at a tim is btwn slits and scrn Only on photon prsnt hr? Is thr still intrfrnc? 1/30 sc xposur 1 sc xposur 100 sc xposur