Physics 2D Lecture Slides Lecture 12: Jan 28 th 2004

Transcription

1 Brian Wcht, th TA, is away this wk. I will substitut for his offic hours (in my offic 3314 Mayr Hall, discussion and PS sssion. Pl. giv all rgrad rqusts to m this wk (only) Quiz 3 Will Covr Sctions.1-.5 Physics D Lctur Slids Lctur 1: Jan 8 th 004 Vivk Sharma UCSD Physics

2 Einstin s Explanation of PhotoElctric Effct What Maxwll Saw of EM Wavs What Einstin Saw of EM Wavs Light as bullts of photons Enrgy concntratd in photons Enrgy xchangd instantly Enrgy of EM Wav E= hf Einstin s Explanation of Photolctric Effct Enrgy associatd with EM wavs in not uniformly distributd ovr wav-front, rathr is containd in packts of stuff PHOTON E= hf = hc/λ [ but is it th sam h as in Planck s th.?] Light shining on mtal mittr/cathod is a stram of photons of nrgy which dpnds on frquncy f Photons knock off lctron from mtal instantanously Transfr all nrgy to lctron Enrgy gts usd up to pay for Work Function Φ (Binding Enrgy) Rst of th nrgy shows up as KE of lctron KE = hf- Φ Cutoff Frquncy hf 0 = Φ (pops an lctron, KE = 0) Largr intnsity I mor photons incidnt Low frquncy light f not nrgtic nough to ovrcom work function of lctron in atom

3 Photo Elctric & Einstin (Nobl Priz 1915) Light shining on mtal cathod is mad of photons Enrgy E, dpnds on frquncy f, E = hf = h (c/λ) This QUANTUM of nrgy is usd to knock off lctron E = hf = ϕ + KE V = KE = hf ϕ s lctron I 3 = 3I 1 I = I 1 I 1 = intnsity -V S Photo Elctric & Einstin (Nobl Priz 1915) Light shining on mtal cathod is mad of photons Quantum of Enrgy E = hf = KE + ϕ KE = hf - ϕ Shining Light With Constant Intnsity f 1 > f >f 3 f 1 f f 3

4 Modrn Viw of Photolctric Effct Is h sam in Photolctric Effct as BB Radiation? Slop h = 6.66 x JS Einstin Nobl Priz! No mattr whr you travl in th galaxy and byond..no mattr what xprimnt You do h : Planck s constant is sam NOBEL PRIZE FOR PLANCK

5 Work Function (Binding Enrgy) In Mtals Photolctric Effct on An Iron Surfac: Light of Intnsity I = 1.0 µ W/cm incidnt on 1.0cm surfac of F Assum F rflcts 96% of light furthr only 3% of incidnt light is Violt rgion ( λ = 50nm) barly abov thrshold frquncy for Ph. El ffct (a) Intnsity availabl for Ph. El ffct I =3% 4% (1.0 µ W/c (b) how many photo-lctrons mittd pr scond? # of photolctron s Powr = = h f 3% 4% (1.0 W/cm hc µ λ m ) 9 9 (50 10 m)(1. 10 J / s) = 8 ( J is )(3.0 1 m s (c) Currnt in Ammtr : i = ( C)( ) (d) Work Function Φ = hf0 = ( V s)( s ) = = 4.5 V =.4 10 i ) 0 / ) 10 A

6 Photon & Rlativity: Wav or a Particl? Photon associatd with EM wavs, travl with spd =c For light (m =0) : Rlativity says E = (pc) + (mc ) E = pc But Planck tlls us : E = hf = h (c/λ) Put thm togthr : hc /λ = pc p = h/λ Momntum of th photon (light) is invrsly proportional to λ But w associat λ with wavs & p with particls.what is going on?? A nw paradigm of convrsation with th subatomic particls : Quantum Physics X Rays Brmsstrahlung : Th Braking Radiation EM radiation, producd by bombarding a mtal targt with nrgtic lctrons. Producd in gnral by ALL dclrating chargd particls X rays : vry short λ pm (10-1 m), larg frquncy f Vry pntrating bcaus vry nrgtic E = hf!! Usful for probing structur of sub-atomic Particls (and your tth)

7 X Ray Production Mchanism whn lctron passs nar a positivly chargd targt nuclus containd in targt matrial, its dflctd from its path bcaus of its lctrical attraction, xprincs acclration. Ruls of E&M say that any chargd particl will mit radiation whn acclratd. This EM radiation appars as photons. Sinc photo carris nrgy and momntum, th lctron must los sam amount. If all of lctron s nrgy is lost in just on singl collision thn hc hc V = hf max = or λmin = λ V min X Ray Spctrum in Molybdnum (Mo) Braking radiation prdictd by Maxwll s qn dclratd chargd particl will radiat continuously Spiks in th spctrum ar charactristic of th nuclar structur of targt matrial and varis btwn matrials Shown hr ar th α and β lins for Molybdnum (Mo) To masur th wavlngth, diffraction grating is too wid, nd smallr slits An atomic crystal lattic as diffraction grating (Bragg)

8 X rays ar EM wavs of low wavlngth, high frquncy (and nrgy) and dmonstrat charactristic faturs of a wav Intrfrnc Diffraction To prob into a structur you nd a light sourc with wavlngth much smallr than th faturs of th objct bing probd Good Rsolution λ<< X rays allows on prob at atomic siz (10-10 )m Compton Scattring : Quantum Pool! 19: Arthur Compton (USA) provs that X-rays (EM Wavs) hav particl lik proprtis (acts lik photons) Showd that classical thory faild to xplain th scattring ffct of X rays on to fr (not bound, barly bound lctrons) Exprimnt : shin X ray EM wavs on to a surfac with almost fr lctrons Watch th scattring of light off lctron : masur tim + wavlngth of scattrd X-ray

9 Compton Effct: what should Happn Classically? Plan wav [f,λ] incidnt on a surfac with loosly bound lctrons Æintraction of E fild of EM wav with lctron: F = E Elctron oscillats with f = fincidnt Evntually radiats sphrical wavs with fradiatd= fincidnt At all scattring angls, f & λ must b zro Tim dlay whil th lctron gts a tan : soaks in radiation Compton Scattring : Stup & Rsults λ = (λ ' λ ) (1 cos θ ) Scattrd λ ' largr than incidnt

10 Compton Scattring Obsrvations Compton Scattring : Summary of Obsrvations λ = (λ ' -λ ) (1 cos θ )! Not isotropy in distribution of scattrd radiation How dos on xplain this startling anisotropy?

11 Compton Effct : Quantum (Rlativistic) Pool Compton Scattring: Quantum Pictur Enrgy Consrvation: E+m c = E' + E Momntum Consrv: p = p'cos θ +p cosφ 0= p'sin θ -p sinφ Us ths to liminat lctron dflction angl (not masurd) p cos φ = p sin φ = p = p pp 'cosθ + p ' 4 p p'cosθ p 'sinθ Squar and add Eliminat p & E using E = pc + mc & E = ( E E') + m c

12 Compton Scattring: Th Quantum Pictur (( ') + mc ) = p pp θ p' E E 'cos + + ( mc ) E For light p= c Enrgy Consrvation: E+m c = E' + E Momntum Consrv: p = p'cos θ +p cosφ 0= p'sin θ -p sinφ Us ths to liminat lctron dflction angl (not masurd) E + E' EE' + ( E E ') mc EE + E E = E E = c ' ( ') mc E 'cos E-E' 1 h = (1 cos θ ) ( λ' λ) = ( )(1 cosθ) EE' mc mc θ EE' E' cosθ + c c c Ruls of Quantum Pool btwn Photon and Elctron h ( λ ' λ) = ( )(1 cos θ) mc

13 Chcking for h in Compton Scattring Plot scattrd photon data, calculat slop and masur h λ It s th sam valu for h again!! Compton wavlngth λ C =h/m c 1-cos ϑ h ( λ ' λ) = ( )(1 cos θ) mc Enrgy Quantization is a UNIVERSAL charactristic of nrgy transactions!