28. Quantum Physics Black-Body Radiation and Plank s Theory

Transcription

1 8. Quanum Pysics 8-1. Black-Body Radiaion and Plank s Teory T Termal radiaion : Te radiaion deends on e emeraure and roeries of objecs Color of a Tungsen filamen Black Red Classic Poin of View Yellow Wie Te ermal radiaion was considered o be simly due o acceleraed carged aricles near e surface. No rig! Black-body Radiaion All e lig is absorbed. Bu e radiaion deends on e emeraure of e inside wall.

2 λmat m K Wien s Dislacemen law Classical eory Inensiy Eerimenal Ulraviole caasroe Waveleng

3 Plank --- Elain e black-body radiaion wi wo assumions relaed o e oscillaing carges. 1. Te radiaion energy is Quanized. E n nf. Te rasonaors emi energy, e so-called oon. E f Plank succeeded in reroducing e black-body radiaion curve. Bu no body including Plank imself did no acce e quanum conce. -- Considered e assumions unrealisic.

4 8-. Te Pooelecric Effec Pooelecric effec 광전효과 Te firs discovery by Herz in V s : Soing oenial indeenden of e radiaion inensiy Elecrons aving a kineic energy K K ma e V s Caracerisics in e ooelecric effec i Cuoff frequency, f c No ooelecrons f < f c ii K ma is indeenden of e lig inensiy. iii Kma f iv Pooelecric effec occurs insananeously ~ sec.

5 Einsein 1905 Eend e quanum conce of Plank s Energy of e elecromagneic waves Poons Eac oon can give is energy o a single elecron. K ma f φ f c φ Work funcion Minimum energy bound in e meal ~ 3-6eV i Cuoff frequency ii iii φ f c f K ma K ma f φ iv Te aricle eory of lig K ma Cuoff wave leng λ c f c φ / c c c φ f c f

6 8-3. Te Comon effec Einsein E f f c E c Energy Momenum Holly Comon and Peer Debye in 193 carried an eerimen o rove Einsein s oin-like aricle conce. Te ooelecric effec -ray scaering: Te oal momenum of e oon-elecron air mus be conserved. a Classical Model E f E c Doler effecs

7 b Quanum Model λ λ 0 1 cosθ m c e <<, 0 Comon Sif λc nm m c e Comon Waveleng Comon s Eerimen λ nm

8 Eamle 8.4 λ nm θ 45 λ λc 1 cosθ λc 1 1/ nm λ nm E / E Poons and Elecromagneic Waves ig as a dual naure, Wave & Poon. ow frequency : ong waveleng More wave like Hig frequency : Sor waveleng More aricle like

9 8-5. Te Wave Proeries of Paricles Paricle also as a dual naure!! In 193, ouis Vicor de Broglie P. D. disseraion osulaed an elecron also as a dual naure. Peras all forms of maer ave wave as well as aricle roeries. Poon: E f E λ c λ Te waveleng of oon can be defined by e momenum. Elecron: de Broglie wave frequency of maer λ mv f E mv : de Broglie wavelegn Quanizaion of Angular Momenum in e Bor model de Broglie ; a dual naure of Maer Bor s eory : Semiclassical eory r λ A sanding wave form nλ πr n 1,,3, λ n mev m v e πr, me vr n n π

10 Angular momenum me vr n Quanizaion of angular momenum Sanding wave : Discree frequency If nλ πr, no sanding wave no closed circular orbi. De Broglie 193: All maers ave a dual naure. Ten an elecron mus eibi diffracion and inerference effecs. Davisson-Germer Eerimen 197: Measure e waveleng of elecrons. Crysalized NiO arge Diffracion aerns due o elecron beam. Eended work on many single-crysalline arges Conclude λ G. P. Tomson 198 Elecron diffracion aern from elecrons assing roug a gold foil Helium aom, Hydrogen aom, Neuron also sow e diffracion aern. Te maer wave is an Universal Naure

11 8-6. Te Double-Sli Eerimen Dsinθ λ Minimum λ λ sin θ θ D D Te number of elecrons deeced a a cerain so is roorional o e inensiy of wo inerfering maer waves.

12 How do we undersand e wave-caracer of elecrons? Poon Elecromagneic Wave I E : Wave funcion E r, B r Inerference effecs I * 1 + I cosφ Wic sli does e elecron ass roug? Sli 1 or Sli

13 8-7. Te Uncerainy Princile 197 Werner Heisenberg Heisenberg Uncerainy Princile A measuremen of osiion is made wi recision, and a measuremen of momenum is made wi recision. I is fundamenally imossible o make simulaneous measuremens of a aricle s osiion and momenum wi infinie accuracy. Similarly E ife-ime of a aricle λ λ Posiion of elecron λ

14 8-8. An Inerreaion of Quanum Mecanics de Broglie ; maer wave Ma Bor ; Elain aomic discree energy level Scrödinger ; Wave equaion A aricle is described wi a wave funcion, y, z,. Te robabiliy densiy P d d P d d 1 d Eecaion value e average osiion λ k π λ If k is deermined, en π Asin λ ik Ae 0 Asin k

15 A raveling elecron wave-ocke + +

16 8-9. A Paricle in a Bo In classical eory In Quanum Mecanics Asin k k nπ k nπ nπ Asin from Scrödinger Equaion Boundary Condiions n 1,,3, Analogous o e sanding wave de Broglie wave

17 nλ λ E n 1 λ / n n n m 8m mv n n 1,,3, Te energy of e aricle is quanized. Energy Quanizaion!! E n 8m n Eamle. i 1g of a ball, 1 m m 10-3 kg, J s E n n J If v 10 m/s, 1 E k mv 0. 05J n ~ ii an elecron 1 nm 10-9 m m kg 18 E n 6 10 n J 0.4n ev 1eV J 31 Very large value E E E eV 1.6eV 3.6eV

18 8-10. Te Scrödinger Equaion Asin k k π Asin d Acos d d d d d 1 E k mv m E k m d d Asin k m k d m d Ek A aricle in a oenial U E k d d E U m E U π λ λ

19 Scrödinger equaion is originaed from a wave equaion. k i Ae, Asin k, ω ω λ π k k λ,, k, ω π ω f E,,,, i i E ω U m U E E k + +,,, U m i + General form,, r U m r i r r + Time-deenden Scödinger equaion Time-indeenden E is fied r U m r E r r + Kineic energy Poenial energy Toal energy

20 A simle form of e one-dimensional Scödinger equaion E + U m d d m me k ik C1e + C E e ik k e ic 1 Asin k 0 E k π m 0 C + C Asin k me n Asin C ik 1 C 1 e i ik k nπ nπ 8m nπ n 0 sin k Boundary condiion a 0 Boundary condiion a

21 How o define A P 1 cos 1 sin A d n A d n A d π π 0 1/ A π n sin 1

22 8-11. Tunneling roug a Barrier T κ e Transmiance if T <<1 were mu E κ 0 d d+ D T + R 1 If an elecron is in a suc oenial well, wa is e robabiliy a e elecron is in eac region? In region I E In region II d, 1 Asin k m d 1 1 d E, + U m d d d In region III d d m κ U E κ Be κ m 3 E 3 k 3 3 ik C1e + C e ik mu E

23 Boundary Condiions 1 d d d + 3 d Normalized Condiion d + d D d d + d d + d 1 3 d Deermine e coefficien A, B, C 1, and C