orbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the

Transcription

1 Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly undrstand and dscrib th atom. Wav-particl duality, Probabilistic formulation of quantum physics Chap. 28

2 Lctur 22-2 Elctron Enrgy Lvls in Solids Whn grat many (ordr of Avogadro s numbr) atoms com togthr to form a solid, th individual atom s nrgy lvls split up into dns groups of lvls for th combind solid, calld nrgy bands. Ths bands span ssntially continuous rang of nrgis.

3 Lctur 22-3 Enrgy Bands for Solids hols Dark rgions ar filld (i.., thr ar lctrons occupying thr). Elctrons can only mov to availabl (unoccupid) stats. Thr ar many unoccupid stats narby in a conductor but thr is non in an insulator. Small numbr of lctrons can mak a transition in smiconductors.

4 Lctur 22-4 Stimulatd Emission of Light Incidnt photon with hf = E stimulats mission of photon of th sam frquncy. So mor photons com out as hav gon in. Cascading ffct can occur! Emittd photon in phas with incidnt photon. Cohrnt amplification. lasr

5 Lctur 22-5 Lasr Light amplification by stimulatd mission of radiation Cohrnt, narrow, and intns Monochromatic (can b tunabl as in liquid dy lasrs) Can b continuous or pulsd Can b mad using solid, liquid, gas, or vn fr lctrons. Sustaind population invrsion is rquird.

6 Lctur 22-6 H-N Lasr (continuous) Exampls of Lasrs Littl populatd, thus population invrsion asy.

7 Lctur 22-7 Compton Scattring (Compton Effct) Whn X-ray striks mattr, EM radiation is found to scattr with longr wavlngth than in th incidnt ray. Classically, th incidnt ray should vibrat chargs in th targt with th targt rradiating with th sam frquncy/wavlngth as in th incidnt ray. In quantum physics, w viw this as th collision of a photon and an lctron instad. Som of th nrgy of th incidnt photon is transfrrd to th lctron. Thus th nrgy of th photon is rducd, or th frquncy dcrass.

8 Lctur 22-8 c Compton Scattring (continud) c Photon: In vacuum, always travls with spd c. Enrgy: hf = cp Momntum: p = hf/c = h/λ

9 Lctur 22-9 Compton Scattring with a fr lctron c c Enrgy consrvation: Momntum consrvation: E γ = K + E γ i i f hf = K + hf i hc hc = K + λ λ f f p γ = p + p γ i f h h = p cos φ + cos θ λ λ i f h 0 = sin θ p sin φ λ f f i h m c K + m c = ( m c ) + ( cp ) ( 1 cos ) λ λ = θ Compton Wavlngth 2.43 pm

10 Lctur Photolctric Effct vs Compton Scattring Photolctric ffct An incidnt photon knocks out an lctron. No photon coms out. Compton scattring (from an atom) An incidnt, high-nrgy photon scattrs off of an lctron, knocking it out of th atom as wll as itslf gtting scattrd into smallr frquncy. Th trm Compton scattring is also usd to dscrib mor gnral photonlctron scattring vnts as wll.

11 Lctur Physics 219 Qustion 1 April 12, 2012 Which of th following is a proprty of th photolctric ffct but not on of Compton scattring? A. Photon (EM radiation) is an incidnt particl. B. Photon of lowr frquncy coms out. C. Elctron gains nrgy and mrgs from atom(s). D. Photon of highr frquncy coms out. E. Photon is compltly absorbd.

12 Lctur Wav-Particl Duality 1 In quantum physics, th wav-natur and particl-natur of an objct ar closly linkd. Thy turn out to b two aspcts of th sam rality. Considr again th two-slit intrfrnc pattrn for light, whr th part of th wav passing through on slit intrfrs with th part of th wav passing through th othr slit, producing an intrfrnc pattrn of intnsity. Wav natur!

13 Lctur Wav-Particl Duality 2 From a particl-lik point of viw, th intnsity is proportional to th numbr of photons. So th fring pattrn can b viwd as a map of how many photons landd whr. (A photomultiplir can count thm.) Now what if w turn down th light intnsity nough so that on photon at a tim lavs th sourc? (a) Initially, photons sm to land at random placs. Not just at th placs xpctd for ballistic trajctoris but no apparnt intrfrnc pattrn. (b) Gradually, bands of prfrrd landing aras mrg. (c) Evntually, clar intrfrnc pattrn forms. Intrfrnc pattrn lik on from wavs! Somhow, ONE photon knows about BOTH slits and intrfrs with itslf!?

14 Lctur Wav-Particl Duality 3 Evn on photon vidntly diffracts i.., thy do not always travl ballistically. Evn on photon knows about both slits and intrfrs with itslf. It is impossibl to prdict whr a givn photon will land, but thr is vidntly a wll-dfind pattrn on avrag. Not only that, but also Thr is a wll-dfind probability for a photon to land at a plac. ( wav function ) 2 If w put a dtctor on ach slit to find out which slit a photon has gon through, thn no intrfrnc pattrn any mor!!

15 Lctur Wav-Particl Duality 4 If w plac dtctors on th slits, w can dtrmin which slit ach photon gos through. Thn, no mor intrfrnc. By masuring th location of th photon at th slits, w somhow mak th photon act mor lik a particl and lss lik a wav. Masurmnts affct what is bing masurd. In this cas, if w don t find out which slit th photon has gon through, thn it is as if it has gon through both slits and th part which has gon through on slit intrfrs with itslf which has gon through th othr slit, so to spak. As soon as you try to find out which slit it rally gos through, though, it rally dos go through on but not th othr, and thus no intrfrnc!! I am going to tll you what natur bhavs lik. Do not kp saying to yourslf, if you can possibly avoid it, but how can it b lik that? Nobody knows how it can b lik that. R. P. Fynman

16 Lctur D Brogli s Thory of Mattr Wavs If a photon can bhav as ithr a particl or a wav, what about an lctron, proton, atom, tc? Othr particls, such as lctrons, do hav a wav natur also. Th wavlngth λ of a particl dpnds on its momntum p, and is calld th d Brogli wavlngth: h λ = p hc A photon: E = hf =, E = cp λ h λ = p d Brogli proposd that th sam holds for any particl!

17 Lctur Exampls What is th wavlngth of an lctron that is moving at a spd of 4 m/s? λ h h = = p m v Js = = kg 4 m / s 4 m What is th wavlngth of a 0.25 kg rock that is moving at 4 m/s? λ h h = = p m v rock Js = = kg 4 m / s 34 m Much mallr than any known lngth!! No wav natur shows up.

18 Lctur Physics 219 Qustion 2 April 12, 2010 According to d Brogli s thory, vry particl bhavs also lik a wav with a wavlngth rlatd to its momntum. Now considr a basball thrown at a battr at 50 mils/hr. Th battr hits th ball and it travls to th outfild at 100 mils/hr. If th d Brogli wavlngth of th ball was λ just bfor bing hit by th battr, what is it just aftrward (whn it is travling with 100 mils/hr)? A λ B. 0.5 λ C. λ D. 1.5 λ E. 2 λ