Early 1900 s Max Planck derives the blackbody intensity spectrum assuming each atom to be an oscillator emitting and absorbing photons discretely.

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1 Peludes to Quatum Mechaics ~ Blackbody Radiatio A blackbody absobs all icidet adiatio without eflectio o scatteig. The adiatio emitted fom a blackbody adiato by vitue of its tempeatue shows a chaacteistic spectum peaked i accodace with Wie's Law. P T *.90 3 m K Theoies poposed by Wie ad Raleigh/Jeas i the late 800's ad at the stat of 900 wee based o the idea of classically oscillatig electic chages withi the blackbody ad did ot coectly pedict the spectum. Ealy 900 s Max Plack deives the blackbody itesity spectum assumig each atom to be a oscillato emittig ad absobig photos discetely. h E hf Plack's Quatum Hypothesis x0 J s cuve fittig paamete fom blackbody expeimets fudametal costat of atue. Plack's Costat.

2 The spectal emittace I() give by Plack's Radiatio Law is: I( ) 5 e hc hc kt Fom this Wie's Law is foud by maximizig I () with espect to ad the blackbody Stefa-Boltzma Law fo total itesity I is foud by itegatig ove all : I P A 0 I( ) d T 4 Photoelectic Effect 905 Albet Eistei uses a paticle desciptio of light, photos, with discete eegies E hf to descibe the photoelectic effect.

3 Iceasig souce itesity iceases the # of photoelectos, but ot thei eegy a paticle itepetatio fo light may be moe appopiate: The expeimet: A eegetic beam of light falls o a metal sample ude a vacuum ad ea a adjustable electic field oieted to stop electos libeated off the sample. ) e - ejected fom the sample leave a et + chage cuet i the coected cicuity. ) The applied E field may be adjusted to coute the light dive effect which the allows fo a measue fo K max of the photoelectos K max = ev stop cicuit has o cuet The Results: K max is ot a fuctio of the light itesity. Lage E/B field i the light wave does ot poduce photoelectos that ae moe eegetic. K max is depedet o the light fequecy I moe photos with the same eegy f moe eegetic photos ad theefoe moe eegetic PE Photoelectic Equatio: hf K max Photo eegy = Photoelecto eegy + Mateial Wok Fuctio

4 Theefoe, whe K max 0 we have hf 0 O f 0 / h cutoff fequecy I.e., if f / h the o photoelectos ae emitted. Futhe, hf 0 such that by evaluatig the cutoff fequecy fo ay paticula sample vaious wok fuctios ae detemied. I tems of photo fequecy ad the sample wok fuctio, the stoppig potetial is: V stop e K max hf e mx b Which V stop vs. f is liea with slope h/e ad x-itecept f 0 = h Boh Atom By 94, two impotat discoveies wee givig statig diectio as to the atue of atomic stuctue:. The spectum of eegy levels fo Hydoge had bee ivestigated i the visible potio of the electomagetic spectum ad the ocotiuous atue of atomic eegy levels veified expeimetally.. The Thomso atom had bee eplaced with a uclea atom followig Ruthefod's scatteig expeimets i 9.

5 I 93 - Niels Boh obital-like costuct fo a atom equies L quatized which i tu pedictio fo H atom eegy level also quatized ad i good ageemet with expeimet. Boh theoy woks well fo hydoge ad oe-electo ios such as He + ad Li +, but the theoy is less pedictive whe multielecto atoms ae ivolved whee quatum effects equie a moe detailed aalysis. The electic foce o the H atom electo is: F k e m v Asset agula mometum quatized as: L mv v m ke m m ke m

6 mke Boh _ Obits E.g. = mke Boh _ Radius A This is the Boh Radius a o the obital adius of a goud state H atom electo. Boh eegy levels: E K U mv ke Usig L mv E ke ke E ke mke E mk e 4 3.6eV Eegy levels quatized ad good ageemet with the H atom spectum. Fially, asset the stability of the atom i ay of the statioay states.

7 It is the Boh adius that maximizes the pobability desity fo the goud state electo, but this does ot imply a 'obit'. E( ) 3.6eV Eegy levels i Hydoge ae: E( ) 3. 6eV 3.6 ev photo eeded to ioize H atom Betwee adjacet eegy levels, E E( ) E( ) E 3.6eV ( ) 3.6eV ( ) E Lim E 0 As 3 Givig cotiuous levels of classical theoy Coespodece Piciple.

8 Tasitios betwee H-atom electoic eegy levels ca take place subject to selectio ules with the absoptio o emissio of photos with discete eegy whe this eegy is idetical to the eegy level diffeece E. Tasitios to the = level 3.6 E Lyma Seies UV photos. Tasitios to the = level E Balme Seies visible photos. Tasitios to the = 3 level E Pasche Seies IR photos. Tasitios to the = 4 level E Backett Seies IR photos.

9 Tasitios to the = 5 level E Pfud Seies IR photos. Lases {Light amplificatio by the stimulated emissio of adiatio} He-Ne Lases: 0:80 mix of He to Ne. 0) Cuet aises He atoms to a meta-stable state at E (lifetime befoe spotaeously decayig is ~.00 s vs. the omal 0 s decay time fo excited electos)

10 ) E is appoximately equal to a Ne excited state E 5 i.e., as E He atoms collide with Ne goud state atoms these goud state atoms ae the excited ito a E 5 eegy level which is above the ' E ' Ne level. ) The esult is that thee ae ow moe Ne excited electos i the E 5 level tha i the E goud level. 3) This populatio ivesio is what is equied to yield lasig. 4) As Neo E 5S E 3P spotaeous emissios take place these photos futhe stimulate tasitios ad Lase (QM effect) 5) Mios at each ed of the lase tube ehace the stimulated emissio by eflectig the photos back ito the lase cavity theeby iceasig the amout of stimulatio time. 6) Lases have scietific, idustial ad medical applicatio. 7) Lase light has the followig popeties a) Moochomatic ( pat pe millio) b) Coheet (Icadescet bulb has a coheece legth ~ m) c) Highly diectioal (agula divegece ot limited by filamet) d) Shaply focused (geate itesity P/A 0E7 W/m^)

11 Photo Eegy / Mometum Fom Relativity, E p c 4 m c m = 0 E pc fo massless paticles O p hf / c fo the photo: Ad p h / Light wave with paticle-like iteactios. 93 Compto Scatteig: The expeimet: Measue the shift i icidet x-ay photo wavelegths as they scatte off electos i a cabo taget. h mc ( Cos( )) Compto Shift Classically, a oscillatig taget eadiates at implyig = 0.

12 The model: y Photo Afte collisio hf Icidet Photo at hf x Electo afte collisio Cosevig Eegy: hf mc hf ' p c m c 4 Cosevig mometum: h P Pe mv p e p p ' p e p e ( p p ') ( p p ') p p p ' p p ' Cos( )

13 Solvig fo p i the eegy elatio ad equatig gives ' ( Cos( )) c Whee is the paticle Compto wavelegth h c mc m is the mass of paticle the x ay is scatteed fom ad is the photo scatteig agle. Wave Paticle Duality: Coside the double slit itefeece expeimet: ) Classically: Huyges wavelets at each slit popagate outwad fom each slit ad itefee costuctively/destuctively at the scee depedig o path legth diffeeces. A itefeece patte obtais. ) Quatum Mechaically: If oly oe photo passes though the appaatus at ay give momet, the do we expect a itefeece patte? A: Yes 3) Sice the Heisebeg ucetaity piciple x*p > h/4 allows us to kow with limited pecisio the locatio of this fiite mometum photo, e.g., which slit it passed though, uless we detect it at the slit i which case thee is o expeimet, the this oe photo has fiite pobability fo goig though both slit ad slit. 4) Itepet photo as a 'pobability wave' eteig the appaatus.

14 5) What? Yes, at the scee thee is a highe pobability of detectig the sigle photo ea maxima sice Pob I => Pob E. Why does this help? By assigig a pobability wave to the sigle photo that may subsequetly be used to detemie the pobability of fidig the photo withi a egio of space, we ca pedict the expeimetal esult: a itefeece patte which classical physics does ot aticipate. Photo is a paticle chaacteized with a wavefuctio, ad positio pobabilities ae foud via the squae of this waves amplitude. Poblem: Need a equatio descibig the wavefuctio evolutio. Stuck with itepetatio: Sigle photo wavefuctio moves fom souce to scee though both slits ad itefees yieldig a itefeece patte. Bottom Lie: If you wat to kow which slit the photo wet though, you will have to detect it at the slit, collapse the wavefuctio, ad will ot have a itefeece patte sice this is a diffeet expeimet. Light is a wave ad a paticle ad its paticle desciptio is i tems of a pobability wave. Quatum mechaics is ecessay fo the aalysis. Complemetaity Both paticle ad wave desciptios ae ecessay fo the complete desciptio of physical pheomea.