Experimental Fact: E = nhf

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CHAPTR 3 The xperimetal Basis of Quatum PHYS-3301 Lecture 4 Sep. 6, 2018 3.1 Discovery of the X Ray ad the lectro 3.2 Determiatio of lectro Charge 3.3 Lie Spectra 3.4 Quatizatio 3.

9 Pair Productio ad Aihilatio (Aderso; 1932; 1936*) The Plack s Black-Body Radiatio Law: The ergy () i the electromagetic radiatio at a give frequecy (f) may take o values restricted to = hf

1 CHAPTR 3 The xperimetal Basis of Quatum PHYS-3301 Lecture 4 Sep. 6, Discovery of the X Ray ad the lectro 3.2 Determiatio of lectro Charge 3.3 Lie Spectra 3.4 Quatizatio 3.5 Blackbody Radiatio (Plak; 1900; 1918*) 3.6 Photoelectric ffect (istei; 1905; 1921*) 3.7 X-Ray Productio (Rötge;1895; 1901*) 3.8 Compto ffect (Compto; 1927; 1927*) 3.9 Pair Productio ad Aihilatio (Aderso; 1932; 1936*) The Plack s Black-Body Radiatio Law: The ergy () i the electromagetic radiatio at a give frequecy (f) may take o values restricted to = hf where: = a iteger h = a costat h ( Plack Costat ) -34» J s xperimetal Fact: = hf BUT Why should the eergy of a lectromagetic wave be Quatized? (= iteger) No xplaatio util 1905 Albert istei A wave is a Cotiuous Pheomeo

2 3.6: Photoelectric ffect lectromagetic Albert istei radiatio postulated iteracts the existece with electros of quata withi of light metals -- photos ad gives -- which, the electros whe icreased absorbedkietic by aeergy. electrolight ear ca the surface give electros of a material, eough could extra givekietic the eergy to electro allow eough them to eergy escape. to escape We call fromthe material. electros photoelectros. 3.6: Photoelectric ffect Albert istei postulated the existece of quata of light -- photos -- which, whe absorbed by a electro ear the surface of a material, could give the electro eough eergy to escape from the material. metal Pheomeo observed log time before istei, ad somethig very strage was observed: metal Pheomeo observed log time before istei, ad somethig very strage was observed: xperimetal Setup ve With Very strog light of low frequecy metal Cotradictig Classical Wave Physics NO electros

3 ve With Very-Very weak light itesity, but of high eough frequecy lectros Classical theory would predict that for extremely low light itesities, a log time would elapse before ay oe electro could obtai sufficiet eergy to escape. We observe, however, that the photoelectros are almost immediately. xperimetal Results 1) The kietic eergies of the photoelectros are idepedet of the light itesity.??? 2) The maximum kietic eergy of the photoelectros, for a give emittig material, depeds oly o the frequecy of the light.??? 3) The smaller the work fuctio φ of the emitter material, the smaller is the threshold frequecy of the light that ca eject photoelectros.??? 4) Whe the photoelectros are produced, however, their umber is proportioal to the itesity of light.??? 5) The photoelectros are emitted almost istatly followig illumiatio of the photocathode, idepedet of the itesity of the light.??? xperimetal Results istei s Theory istei suggested that the electromagetic radiatio field is quatized ito particles called photos. ach photo has the eergy quatum: where f is the frequecy of the light ad h is Plack s costat. The photo travels at the speed of light i a vacuum, ad its wavelegth is give by

4 Plack s Law ( = hf) Photoelectric ffect (Threshold frequecy) Albert istei proposed: The light is behavig as a collectio of particles called photos each of them havig eergy = hf ve With Very-Very weak light itesity, photo beam but of high eough frequecy = hf = hf lectros What happes is that 1 PHOTON ejects 1 LCTRON xample (1): Very itesive light beam, low frequecy light xample (2): SINGL PHOTON Very weak light beam of high frequecy photo beam = hf = hf SMALL (below the threshold) LARG ( is large) photo beam = hf = photo = hf LARG (above the threshold) NO lectros 1 electro There is o PHOTON capable of ejectig a LCTRON The PHOTON ejects 1 LCTRON

5 istei s Theory Coservatio of eergy yields: ergy Coservatio: where is the work fuctio of the metal xplicitly the eergy is photo = hf K max = hf "! The retardig potetials measured i the photoelectric effect are the opposig potetials eeded to stop the most eergetic electros.! Also kow at that time: Quatum Iterpretatio The kietic eergy of the electro does ot deped o the light itesity at all, but oly o the light frequecy ad the work fuctio of the material. istei i 1905 predicted that the stoppig potetial was liearly proportioal to the light frequecy, with a slope h, the same costat foud by Plack. To free a electro from the metal, oe has to pay a certai amout of eergy the Work Fuctio From this, istei cocluded that light is a particle with eergy:

! = 380m Repels electros U < 2Volts lectros are from plate 1 with a certai max. K.

2. qv ((=1.6x10-19 C) (2V) = 3.2 x 10-19 J = 2 ev) is the max.

The work fuctio of tugste surface is 5.4eV.

7eV. Fid Plack s costat from these data. c Ke = hf - W = h -W l Determie the max.

6 ! = 380m Repels electros U < 2Volts lectros are from plate 1 with a certai max. K. If oe have eough K to surmout the electrostatic P differece (qv), o electros will reach place 2. qv ((=1.6x10-19 C) (2V) = 3.2 x J = 2 ev) is the max. that ca be surmouted, so the max K must be 2 ev. " =?! f max mi =? =? Usig the equatio, Problems 1. The work fuctio of tugste surface is 5.4eV. Whe the surface is illumiated by light of wavelegth 175m, the maximum photoelectro eergy is 1.7eV. Fid Plack s costat from these data. c Ke = hf - W = h -W l Determie the max. wavelegth (l ) light that ca eject electros from this metal. The limit of ejectig electros occurs whe a icomig photo has oly eough eergy to free a electro from the metal, with oe left for K.

Problems 1. The work fuctio of tugste surface is 5.4eV. Whe the surface is illumiated by light of wavelegth 175m, the maximum photoelectro eergy is 1.7eV. Fid Plack s costat from these data.

The threshold wavelegth for emissio of electros from a give metal surface is 38

7 Problems 1. The work fuctio of tugste surface is 5.4eV. Whe the surface is illumiated by light of wavelegth 175m, the maximum photoelectro eergy is 1.7eV. Fid Plack s costat from these data. -7 ( Ke + W) l ( 1.7eV + 5.4eV) m -15 c h= = = ev s 8 Ke = hf - W = h -W c 3 10 m/ s l = ev s J / ev = J s 2. The threshold wavelegth for emissio of electros from a give metal surface is 380m. (a) what will be the max kietic eergy of electros whe lis chaged to 240m? (b) what is the maximum electro speed? 3.7: X-Ray Productio A eergetic electro passig through matter will radiate photos ad lose kietic eergy which is called bremsstrahlug, from the Germa word for brakig radiatio. Sice liear mometum must be coserved, the ucleus absorbs very little eergy, ad it is igored. The fial eergy of the electro is determied from the coservatio of eergy to be A electro that loses a large amout of eergy will produce a X-ray photo. (b) (a) c h W c c c æ 1 1 ö K = h - W = h - h = hcç - = 1.9eV è ø l = e 0 l1 l1 l0 l1 l0 2K 2 e 5 Ke = mv e /2 v= = m/ s me X-rays ca be produced by smashig high-speed electros ito a metal target. Whe they hit, these deceleratig charge produce much radiatio The Productio of X-Rays (Wilhelm Roetge 1901) (The reverse of the Photoelectric ffect) SURPRIS: xperimets idicate a cutoff wavelegth: Oops!!! Not etire spectrum!! Frequecy f, ergy =hf There is o classical explaatio for so sharp a termiatio of the spectrum CLASSICAL physics: Radiatio covers etire spectrum Photo = wave Bremsstrahlug Iverse process 1 photo -> 1 electro (?) 1 electro -> 1 photo (?)

8 SURPRIS: xperimets idicate a cutoff wavelegth: If the radiatio is quatized, the miimum allowed at f is hf (sigle photo). We ca t produce half a photo, so if multiple electros do t combie their s ito a sigle photo, o photo could be produced of > K of a sigle electros. Frequecy f INDD: Settig the K of a icomig electro = of oe photo Frequecy f INDD: 1 electro -> 1 photo Iverse Photoelectric ffect. Coservatio of eergy requires that the electro kietic eergy equal the maximum photo eergy where we eglect the work fuctio because it is ormally so small compared to the potetial eergy of the electro. This yields the Duae-Hut limit which was first foud experimetally. The photo wavelegth depeds oly o the acceleratig voltage ad is the same for all targets.

PHYS-3301 Lecture 5. CHAPTER 3 The Experimental Basis of Quantum. 3.8: Compton Effect. 3.8: Compton Effect. Sep. 11, 2018

PHYS-3301 Lecture 5. CHAPTER 3 The Experimental Basis of Quantum. 3.8: Compton Effect. 3.8: Compton Effect. Sep. 11, 2018 CHAPTER 3 The Experimetal Basis of Quatum PHYS-3301 Lecture 5 Sep. 11, 2018 3.1 Discovery of the X Ray ad the Electro 3.2 Determiatio of Electro Charge 3.3 Lie Spectra 3.4 Quatizatio 3.5 Blackbody Radiatio