5. Quantum Nature of the Nano-world ( Fundamental of. Quantum mechanics)

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Esmond Gibbs
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5. Quatu Nature of the Nao-world Fudaetal of What is the defiitio of aoaterials?

with great reductios i particle size ii New by uropea Uio: O 8 October, the uropea Coissio adopted

particles, i a uboud state or as a aggregate or as a aggloerate ad where, for 5% or ore of the

1 5. Quatu Nature of the Nao-world Fudaetal of What is the defiitio of aoaterials?? Quatu echaics i Origial: quatu size effect where the electroic properties of solids are altered with great reductios i particle size ii New by uropea Uio: O 8 October, the uropea Coissio adopted the followig defiitio of a aoaterial: [] A atural, icidetal or aufactured aterial cotaiig particles, i a uboud state or as a aggregate or as a aggloerate ad where, for 5% or ore of the particles i the uber size distributio, oe or ore eteral diesios is i the size rage. Need to cosider the effect of Quatu Mechaics!!

$Wave: Diffractio, M wave Particle: Photoelectric effect,$

2 leetary Quatu Mechaics. Matter Wave by de Broglie. Schrodiger equatio 3. Partical i a bo 4. Hyrdoge atos Matter Wave Duality of ight: Wave or Particle Wave: Diffractio, M wave Particle: Photoelectric effect, Blackbody radiatio, Copto effect

3 What did Plak do??? Quatizatio of eergy OR Quata Classical: kt cotiuous Plack: hf discrete, =,,3,. The result is cosistet with eperietal observatio!!! Plack s law: hf discrete, =,,3, Duality of Matters:. Matter Wave by de Broglie For a photo, hf pc, c f 3

4 h p wave particle h particle wave p The particle ature of atterold quatu echaics Thoso s odel e V B d 4

Rutherford odel All the ass ad positio charge e were cocetrated i a iute ucleus of the ato of diaeter -4 ad

5 Rutherford s odel of the ato I the particle scatterig eperiet, a large agle of scatterig is observed, which ca ot be observed by Thoso s odel. Rutherford odel All the ass ad positio charge e were cocetrated i a iute ucleus of the ato of diaeter -4 ad electros ust circle the ucleus i soe way. Proble of stability plaet odel Acceleratig electros electroagetic radiatio lose eergy atos will collapse to uclear diesios??? Why are atos stable??? - Bohr s odel 5

6 Atoic spectra: R f i, R

7 Bohr s odel h h h vr, r v p Bohr s postulate e, ucleus Coulob force. h, agular oetu quatized 3 a electro ovig i such a orbit does t radiate M eave total eergy is coserved. 4 Atos ca eist oly i certai state, ad the frequecy f of a eitted photo is equal to hf. Fro the postulate: e F 4 r vr v r e, speed quatized 4 v e c 4 37 diesioless v c 7

8 8 Atoic radius c c v r quatized If,.53 a A c r Bohr s radius a r Total eergy of a atoic electro ovig i oe of the allowed orbits. V K, v K r e V c c c c e c r e v For groud state of hydroge,, c 6eV ev, Hydroge-like atoic eergy level c a a The frequecy of the M radiatio eitted whe the electro akes a trasitio: h c h f c f, R hc c y c c hc c R y Rydberg costat The Bohr s odel ca eplai the atoic spectra successfully!!

9 De Broglie s postulate of atter waves For a photo, hf pc, c f h p De Broglie: Matter wave p v h h p v Wave-like properties of particles Matter Wave Revisit Bohr s odel h h h vr, r v p Two slit iterferece eperiet 9

10 Oe photo at a tie reaches the detector. 3. Heiseberg s Ucertaity priciples: The ore precisely the positio is deteried, the less precisely the oetu is kow p h

11 4. Schrodiger equatio -D total=kkietic+vpotetial d V d d probability Tie idepedet Schrodiger quatio: p H V Hˆ ergy ergy Hˆ Hˆ d V d d Hˆ d h h Stadard deviatio ergy ergy igevalue ad eigefuctio Tie idepede Sch. q. Solutio of Schrodiger quatio:. Ifiite potetial well

12 otherwise for V d d, A si, Noralize A d si,... 3,,, 8 h for si si si si si d d p i d d d p i d d p p p, p cos cos si

13 Reark: Copariso with classical results: I Potetial step V V for for Case I V 3

14 Regio I : Ae Be ik ik I, k reflected icidet A A A, B B B Regio II: Ce II ik De No reflected wave ik, D k V tras C C C Boudary coditios: A B C I I II II probability uber : legth legth k A B kc uber uber distace Reflectio ad trasissio v Probability flu tie distace tie T R tra i ref i v v v v I I I II tra k i k ref i B B A A C Ck A Ak A B C k k k k C A, B A A B C k k k k k 4kk T k k T R, R, wave property k k R k k 4

15 Reark: Classical: o reflectio for V R= Quatu : R for V, wave property Case II V boud Regio I : Regio II: ik ik I Ae Be, k Ce II De II caot diverge C Boudary coditios: A B D I II I ik B ik II A ik, A B D V 5

16 B B B ik A ik ik A ik B B R, T A A peetratio depth V A A A II Tuelig barrier V V for for for a a I II III Case I V ik ik Regio I : I Ae Be, k V Regio II :, II Ce De ik ik Regio III: III Fe Ge, k B.C., ust be cotiuous at, a ad let k=k A B C D ika ikb D C a a ika Ce De Fe a a D e C e ikfe ika 6

17 FF V T AA 4 V sih a V 6 V e a V V a a e e a 6 for aple: Scaig Tuelig Microscopy STM Fro IBM.STM Gallery 7

18 3. Case 3. Particle i a bo 3-D if,, corrospod to oe state y z y z y z y z if y z y z Hydroge Ato: 8

19 e V r, 4 r e, r,, R r 4 r Three quatu uber, l, l, r, R r Y,, Y, l, l, l l, l Rr : radial wavefuctio, Y: spherical wavefuctio lectro eergy i the hydroge ato is quatized. is a quatu uber,,,3, a 4 e 8 h 4 e 3.6 ev.58 --> Borh radius 9

22 Oritabl agular oetu ad Space quatizatio

23 3

PHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018

PHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018 CHAPTER 4 Structure of the Atom PHYS-3301 Lecture 7 4.1 The Atomic Models of Thomso ad Rutherford 4.2 Rutherford Scatterig 4.3 The Classic Atomic Model 4.4 The Bohr Model of the Hydroge Atom 4.5 Successes