From Last Time. Origin of Malus law. Circular and elliptical polarization. Energy of light. The photoelectric effect. Exam 3 is Tuesday Nov.

Transcription

1 From Last Tim Enrgy and powr in an EM wav Exam 3 is Tusday Nov. 25 5:30-7 pm, 2103 Ch (hr) Studnts w / schduld acadmic conflict plas stay aftr class Tus. Nov. 18 to arrang altrnat tim. Covrs: all matrial sinc xam 2. Bring: Calculator On (doubl-sidd) 8 1/2 x 11 not sht Polarization of an EM wav: oscillation plan of E-fild Exam rviw: Thursday, Nov. 20, in class 1 2 Origin of Malus law Polarizr transmits componnt of E-fild paralll to transmission axis absorbs componnt of E-fild prpndicular to transmission axis Transmittd intnsity: I I 0 cos 2 θ I 0 intnsity of polarizd bam on analyzr (Malus law) Allowd componnt paralll to analyzr axis Circular and lliptical polarization Circularly polarizd light is a suprposition of two wavs with orthogonal linar polarizations, and 90 out of phas. Th lctric fild rotats in tim with constant magnitud. Polaroid shts 3 4 Enrgy of light Quantization also applis to othr physical systms 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 5 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. 6 1

2 Th xprimnt Analyzing th data Light jcts lctrons from cathod with rang of vlocitis Rvrs potntial: applis lctric forc opposing lctron motion Stopping potntial: voltag at which highst kintic nrgy (K max ) lctrons turnd back Elctrons absorb fixd nrgy E absorb from light K max K max E absorb E absorb Bound in solid Escapd from solid E o K max E absorb Highst KE lctron Enrgy K max 7 Lowst KE lctron Rang of lctron nrgis in solid 8 Unusual xprimntal rsults Einstin s xplanation Not all kinds of light work Rd light dos not jct lctrons Mor rd light dosn t ithr 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. No mattr how intns th rd light, no lctrons vr lav th mtal If photon dosn t hav nough nrgy, cannot knock lctron out. Intnsity ( # photons / sc) dosn t chang this. Until th light wavlngth passs a crtain thrshold, no lctrons ar jctd. Minimum frquncy (maximum wavlngth) rquird to jct lctron 9 10 Einstin s analysis Elctron absorbs nrgy of on photon E absorb E photon hf K max E absorb 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 Qustion Potassium has a work function of 2.3 V for photolctric mission. Which of th following wavlngths is th longst wavlngth for which photomission occurs? a. 400 nm b. 450 nm c. 500 nm d. 550 nm. 600 nm Kmax hf Φ hc/λ Φ Th maximum wavlngth is whn Kmax 0: λ hc/φ nm. Quantization and photons Quantum mchanically, brightnss can only b changd in stps, with nrgy diffrncs of hf. Possibl nrgis for grn light (λ500 nm) On quantum of nrgy: on photon Two quanta of nrgy two photons tc E4hf E3hf Think about light as a particl rathr than wav. E2hf Ehf Th particl prspctiv Light coms in particls calld photons. Enrgy of on photon is Ehf f frquncy of light Compton scattring Photon loss nrgy, transfrs it to lctron Photon loss momntum transfrs it to lctron Total nrgy and momntum consrvd 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 15 Bfor collision Aftr collision Photon nrgy Ehf Photon mass 0 Photon momntum pe/c 16 On quantum of grn light On quantum of nrgy for 500 nm light ( ) # ( 3#10 8 m /s) E hf hc #10 $34 J $ s 500 #10 $9 m 4 #10 $19 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 (λ635 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 ( 4 10 #14 J /s)( 0.001s) 4 10 #17 J ( 4 10 #17 J) ( 1V / #19 J) 250V ( 250V )( 1photon /2.5V ) 100photons 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 Light in som cass shows proprtis typical of wavs In othr cass shows proprtis w associat with particls. Conclusion: Light is not a wav, or a particl, but somthing w havn t thought about bfor. Rminds us in som ways 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