Chapter 37 The Quantum Revolution

Transcription

1 Chaptr 7 Th Quantum Rvolution Max Plank Th Nobl Priz in Physis 98 "in rognition o th srvis h rndrd to th advanmnt o Physis by his disovry o nrgy quanta" Albrt Einstin Th Nobl Priz in Physis 9 "or his srvis to Thortial Physis, and spially or his disovry o th law o th photoltri t" Th mystry o partils and wavs

2 Blakbody Radiation th lassial pitur Th lassial radiation ild: u ( T) 8 In a lassial statistial thory th avrag nrgy pr dgr o rdom is: k B T To th Rayligh-Jans law or a blak body mittr u ( T) 8 k B T Th ultraviolt atastroph

3 Extra: On th mod dnsity o th lassial radiation ild: Counting standing wavs Rayligh s mthod or sound wavs Allowd wavlngths on a string: l=l, l=l, l=l/,... Frqunis: =/l/l, /L, /L, /L,... Allowd rqunis ar spad by /L Sptral dnsity is thn (in dimnsion): Numbr o mods btwn and +D L/ In thr dimnsions analoguous mods: z y x k k k k Th numbr o mods btwn and +D is th volum in k-spa in units (/L) Hn: ) ( V L L k k N D D D D Spialtis (on otant o positiv k, polarizations) Radiation mod dnsity in a losd box o Lx Lx L 8 ) ( ) ( V N u m (Not, this is irrsptiv o th nrgy pr mod)

4 Extra: Law o quipartition or a lassial radiation ild Kinti nrgy pr dgr o rdom kin k B T For ah sinusoidal osillation (harmoni osillator) th potntial nrgy is qual to th kinti nrgy pot k B T Classial quipartition (or harmoni osillator) kin pot k B T Not, latr: quipartition or quantum stats o Bohr atom is dirnt!

5 Blakbody Radiation toward th Quantum Hypothsis Plank: nrgy o th osillating mods om in disrt portions nh Din gomtrial sris: Z( x) nx d x Z( x) x dx x d dx x nx Probability that ours in th nrgy distribution o th avity (Maxwll Boltzmann) / kt p( ) Man nrgy p p With: x n nx x x n p n d n d p h kt ktx Z( x) n d dx nh n nh / kt n n ktx nh / kt n n Z( x) ktx x ktx x d dx ln Z( x) ktx x n d ktx dx h h / kt nx nx ln( x )

6 Plank s Quantum Hypothsis; Blakbody Radiation ) ( 4 ) ( / kt h h T u T I 8 8 ) ( / kt h h T u Radiation dnsity Radiation intnsity ) ( ) ( / 5 kt h h T I T I l l l l Saling rom rquny to wavlngth?

7 Plank s Quantum Hypothsis; Blakbody Radiation Plank ound th valu o his onstant by itting blakbody urvs to th ormula giving Plank s proposal was that th nrgy o an osillation had to b an intgral multipl o h. This is alld th quantization o nrgy.

8 Drivation o Win s law Radiation intnsity (Plank) I l ( T) I l ( T) h l 5 h / lkt Din (dimnsionlss) I l ( T) kt h 4 Univrsal shap: 5 x x 5 x g( x) h lkt x x 5 dg x x Maximum: 5 0 dx x x 4 For x x/5 so xˆ l max T h xk ˆ

9 Plank s Quantum Hypothsis; lading to Win s law Blakbody radiation or thr dirnt tmpraturs Not that rquny inrass to th lt. Th rlationship btwn th tmpratur and pak wavlngth is givn by Win s law:

10 Plank s Quantum Hypothsis; lading to Stan-Boltzmann s law Radiation intnsity I ( T) u 4 ( T) h h / kt Total intnsity I( T) 0 h h d / kt Us again: h x lkt Thn I( T) h kt h 4 x 0 x dx Chk Mathmatia (or solv): 0 x x 4 dx 5 Stan- Boltzmann I( T) T k With: W/m K 5h Intrprt th Physis o this law!

11 Photon Thory o Light and th Photoltri Et Einstin suggstd that, givn th suss o Plank s thory, light must b mittd in small nrgy pakts: Ths tiny pakts, or partils, ar alld photons.. Einstin mad a stp urthr than th assumptions o Plank who doubtd th rality o th quanta

12 Photon Thory o Light and th Photoltri Et Th photoltri t: i light striks a mtal, ltrons ar mittd. Masurmnt o kinti nrgy o ltrons: Stopping potntial Kmax V 0 Masurmnts at varying

13 Photon Thory o Light and th Photoltri Et Th partil thory assums that an ltron absorbs a singl photon. Plotting th kinti nrgy vs. rquny: h K W W 0 is matrial proprty In som ass svral kinti nrgis masurd: Last bound ltrons orrspond to th work untion: W 0 Minimum amount o nrgy rquird to rlas ltron h K max W 0 Quantum lvls This shows lar agrmnt with th photon thory, and not with wav thory: K No ltrons mittd or < 0 h W 0

14 Photon Thory o Light and th Photoltri Et I light is a wav, thory prdits:. Numbr o ltrons and thir nrgy should inras with intnsity.. Frquny would not mattr. I light is partils, thory prdits: Inrasing intnsity inrass numbr o ltrons but not nrgy. Abov a minimum nrgy rquird to brak atomi bond, kinti nrgy will inras linarly with rquny. Thr is a uto rquny blow whih no ltrons will b mittd, rgardlss o intnsity. Conlusion: light onsists o partils with nrgy E=h : photons

15 Enrgy, Mass, and Momntum o a Photon Clarly, a photon must travl at th spd o light. Looking at th rlativisti quation or momntum, it is lar that this an only happn i its rst mass is zro. p / mv/ v E p m 4 W alrady know that th nrgy is h; w an put this in th rlativisti nrgy-momntum rlation and ind th momntum: A photon must hav dirtdnss (and momntum) as ollows rom th Compton t

16 Compton Et Compton xprimnts (9) sattrd X-rays rom dirnt matrials hav slightly longr wavlngth than th inidnt ons th wavlngth dpnds on th sattring angl: Arthur Compton Th Nobl Priz in Physis 97 "or his disovry o th t namd atr him"

17 Compton Et This is anothr t that is orrtly prditd by th photon modl and not by th wav modl. Bor ollision photon ltron E h E m h l p h l Atr ollision photon E' ltron E tot h l' m h p' l' E p kin m v m

18 Compton Et Consrvation o nrgy h l h l' m Consrvation o momntum Along x: h h os mv os l l' Along y: h 0 sin mv sin l' Thr quations with unknowns, liminat v and Compton sattring: l' l h m os

19 Compton Et Dl m h os l os C Not that l C ~ nm So th ts is not so wll visibl with visibl light Compton prormd his xprimnt with x-rays

20 Photon Intrations; Pair Prodution Photons passing through mattr an undrgo th ollowing intrations:. Photoltri t: photon is ompltly absorbd, ltron is jtd.. Photon may b totally absorbd by ltron, but not hav nough nrgy to jt it; th ltron movs into an xitd stat.. Th photon an sattr rom an atom and los som nrgy. 4. Th photon an produ an ltron positron pair. Minimum nrgy: E h l m

21 Wav Natur o Mattr Just as light somtims bhavs lik a partil, mattr somtims bhavs lik a wav. Th wavlngth o a partil o mattr is. D Brogli wavlngth o mattr Louis D Brogli Th Nobl Priz in Physis 90 "or his disovry o th wav natur o ltrons"

22 Wav-Partil Duality; th Prinipl o Complmntarity W hav phnomna suh as diration and intrrn that show that light is a wav, and phnomna suh as th photoltri t and th Compton t that show that it is a partil. Whih is it? This qustion has no answr; w must apt th dual wav partil natur o light. Th prinipl o omplmntarity stats that both th wav and partil aspts o light ar undamntal to its natur.

23 Partils as Wavs; Wavs as Partils Youngs Intrrn xprimnt

24 Partils as Wavs "or thir xprimntal disovry o th diration o ltrons by rystals" Gorg P Thomson Clinton J Davisson 96 Claus Jönsson o Tübingn Ral two-slit xprimnt with ltrons Dubbd: th most amous xprimnts Wav partil duality o C 60 moluls Markus Arndt, Ola Nairz, Julian Vos-Andra, Claudia Kllr, Grbrand van dr Zouw and Anton Zilingr Natur 40, (4 Otobr 999) Rihard Fynman on th Doubl Slit Paradox: Partil or Wav? Whr is th limit? Dohrn??

25 Eltron Mirosops Eltrons wavs usd or imaging Wavlngths o about nm. Transmission ltron mirosop th ltrons ar ousd by magnti oils Sanning ltron mirosop th ltron bam is sannd bak and orth aross th objt to b imagd.