Blackbody Radiation. All bodies at a temperature T emit and absorb thermal electromagnetic radiation. How is blackbody radiation absorbed and emitted?

Transcription

1 All bodis at a tmpratur T mit ad absorb thrmal lctromagtic radiatio Blackbody radiatio I thrmal quilibrium, th powr mittd quals th powr absorbd How is blackbody radiatio absorbd ad mittd? 1

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3 A blackbody is a prfct absorbr of radiatio A simpl blackbody is giv by a hol i a wall of som closur Both absorptio ad ca occur Th radiatio proprtis of th cavity ar idpdt of th closur matrial 3

4 Th y axis is powr pr ara pr wavlgth 4

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6 Wi s displacmt law λmaxt Wavlgth dcrass as T icrass 3 Stfa-Boltzma law mk R( T ) εσt σ W / ( 2 4 m K ) Total powr / ara radiatd icrass as T 4 6

7 Attmpts to calculat th spctral distributio of blackbody radiatio from first pricipls faild Th bst dscriptio was giv by th Rayligh-Jas formula 2πckT λ ( λ, T ) 4 I This dscribd th distributio at log wavlgths but icrasd without limit as λ Ultraviolt catastroph 7

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9 Plack was abl to calculat th corrct distributio by assumig rgy was quatizd (h was dsprat) Microscopic (atomic) oscillators ca oly hav crtai discrt rgis E hf h Js Th oscillators ca oly absorb or mit rgy i multipls of ΔE hf 9

10 Plack s radiatio law agrd with data I ( ) λ 2 2πc h 5 λ 1, T hc / λkt 1 It lads dirctly to Wi s displacmt law ad th Stfa-Boltzma law It agrs with Rayligh-Jas formula for larg wavlgths S drivatios for both i Thorto ad Rx 1

11 W may driv th radiatio law latr i th cours but for ow cosidr Th lctromagtic rgy isid th (mtallic) cavity must xist i th form of stadig wavs with ods at th surfacs Classically, th quipartitio thorm givs th avrag rgy of a stadig wav ε kt Not th sam valu is prdictd for all stadig wavs idpdt of thir frqucy Th amout of radiatio comig out of th cavity is th th umbr of diffrt wav mods X th rgy pr mod 11

12 Lt Ehv, th th avrag rgy is ε whr ad 1 kt εp( ε ) P( ε ) ε kt hf kt is hf kt 1 kt hf kt hf kt kt th Boltzma distributio P( ε ) 12

13 Kitic Thory of Gass Basd o atomic thory of mattr Rsults iclud Spd of a molcul i a gas v rms (<v 2 >) 1/2 (3kT/m) 1/2 Equipartio thorm Itral rgy U f/2 NkT f/2 RT Hat capacity C V (du/dt) V f/2 R Maxwll spd distributio 13

14 14 To valuat this w us stadard tricks from statistical mchaics l d d d d d d

15 15 Ad ot ( ) X X X X K K

16 Puttig ths togthr w hav ε ε hf ε d kt l d hf 1 d d l 1 ( ) hf 1 1 hf kt hf hf ( 1 ) hf 1 hc λ d l d 1 ( )( 1 1 ) 1 hc λkt 2 16

17 To fiish th calculatio w d hav to multiply th avrag rgy of a wav of frqucy f x th umbr of wavs with frqucy f This would giv us th Plack distributio I ( λ T ) 2πc 1, 5 hc / λkt λ 2 h 1 17

18 You ca how Plack avoidd th ultraviolt catastroph Bcaus th rgy is proportioal to th frqucy Th avrag rgy is kt wh th possibl rgis ar small compard to kt Th avrag rgy is xtrmly small wh th possibl rgis ar larg compard to kt (bcaus P(ε) is xtrmly small) 18

19 Plack s papr is grally cosidrd to b th birthplac of quatum mchaics Rvisioist history? Plack did ot pay too much atttio to rgy quatizatio Nithr did ayo ls Thr is cotrovrsy of whthr h v itdd th rgy of a oscillator to b hf 19

20 Photolctric Effct Light icidt o a mtal will jct lctros Asid, othr mas of doig this ar with tmpratur, lctric filds, ad particl bombardmt 2

21 Photolctric Effct Exprimts showd Kitic rgy of th photolctros ar idpdt of th light itsity Th maximum kitic rgy of th photolctros dpds o th light frqucy Th smallr th work fuctio φ th smallr th thrshold frqucy to produc photolctros Th umbr of photolctros is proportioal to light itsity 21

22 Photolctric Effct 22

23 Photolctric Effct 23

24 Photolctric Effct Explaid by Eisti i o of his aus mirabilis paprs I his papr h assumd Elctromagtic fild was quatizd Light quata wr localizd i spac (lik particls) photos Ergy E hf I th photolctric procss, th rgy quata (photos) ar compltly absorbd 24

25 Photolctric Effct Thus photos ptrat th surfac of th mtal ad ar absorbd by lctros Th lctros ovrcom attractiv forcs that ormally hold thm i th matrial ad scap Cosrvatio of rgy givs hf 1/2mv 2 max + φ Ad cosqutly h prdictd 1/2mv 2 max V hf φ Not h/ ca b masurd from th slop 25

26 Photolctric Effct This was strag sic it ivolvd Plack s costat h This was a difficult xprimt to carry out It took almost a dcad to vrify Millika was th pricipl xprimtr (who trid to prov Eisti s thory wrog) Th d rsult was proof that light rgy is quatizd ad Ehf 26

27 Photolctric Effct 27