u = A Z Chemistry 110 Fall 2010 Rayleigh-Jeans Law for Blackbody SI Units SI Units Secondary Units written in terms of Primary

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1 SI Uits Key Study Pits fr Petrucci et al., Secdary Uits writte i terms f Primary Capters 8 & 9 Nte: Fudametal cstats ad a peridic table will be prvided te midterm but equatis will t be give. Cemistry 0 Fall 00 SI Uits Cmm SI Prefixes Cemical Symbls Oe r Tw Letter Abbreviatis Carb: C Oxyge: O Nickel: Ni Gld: Au A Z ± Cemical Symbl Z Atmic N. p A Mass Number p + ± Carge p e Quatum Tery RayleigJeas Law fr Blackbdy 8πkT ρ( λ) 4 λ ρ ergy Desity k Bltzma' s Cstat T Abslute Temperature Yu d t ave t kw tis equati fr calculatis but yu suld kw tat te classical tery predicts a iverse relatisip betwee ergy Desity ad Wavelegt i.e. prprtial t λ 4 Ultravilet catastrpe eergy desity ges t ifiity as wavelegt gets smaller A failure f te classical tery Sme Imprtat quatis M Radiati c Plack's Cstat 6.66 x 0 c speed f u wave velcity ν frequecy λ wavelegt 34 ligt Js Ay wave u

2 Sme Imprtat quatis K K electr Ptelectric ffect electr m u u velcity f te electr m e mass f te electr Φ "wrk fucti" fr te metal e te eergy tresld fr remvig te e Φ ν Frequecy f te ligt tat is directed te metal surface ν ο Tresld frequecy fr te metal Ptelectric ffect Te pts f a ligt beam ave a caracteristic eergy determied by te frequecy f te ligt ( ). I te ptelectric effect, if a electr absrbs te eergy f e pt ad as mre eergy ta te wrk fucti ( 0 ), it is ejected frm te material. If te pt eergy is t lw, te electr is uable t escape te surface f te material. Icreasig te itesity f te ligt beam we > 0 icreases te umber f pts i te ligt beam, ad tus icreases te umber f electrs emitted witut icreasig te eergy tat eac electr pssesses. Te eergy f te emitted electrs des t deped te itesity f te icmig ligt, but ly te eergy f te idividual pts. lectrs ca absrb eergy frm pts we irradiated, but tey fllw a "all r tig" priciple. All f te eergy frm e pt must be absrbed ad used t liberate e electr frm atmic bidig, r te eergy is reemitted. If te pt eergy is absrbed, sme f te eergy liberates te electr frm te atm, ad te rest ctributes t te electr's kietic eergy as a free particle. Sme Imprtat quatis ergy f a Pt Radius ad ergy f t Br Orbit c r a were a 5.9 pm te Br Radius cr.79x0 8 J Sme Imprtat quatis ergy fr cage f discrete rbits frm i t f <0 fr emissi >0 fr absrpti cr i f pt e trasiti betwee rbits ergy fr pt emitted r absrbed fr discrete trasiti betwee rbits Nte tat tis eergy is simply te abslute value (i.e. psitive) f te eergy cage sw abve fr te trasiti betwee rbits c ergy cage fr trasiti betwee rbits ergy f a pt Study Tip: Rearrage te equati relatig wavelegt () ad te trasiti eergies () fr emissi ad absrpti t give te fllwig expressi ad use it t slve sme f te prblems: ( f x i ) were R.097 x 0 7 m R ( i f ) Te Rydberg cstat (R ) is actually te mst precisely kw pysical cstat f all. m e e 4 R (73) x 0 7 m c Sme Imprtat quatis Nte tat tese equatis apply t as well (Z) s tey are geeral Memrize tese equatis as tey are geeral fr, e +, Li + etc. (Nte te Z) Orbit ergy fr like species (ly e electr) Z cr Z Z Atmic Number Z cr i f 8.79x0 J a 5.9 pm a r Z ergy cage fr e jump betwee rbits frm i t f fr like species <0 fr emissi >0 fr absrpti r is radius f t rbit

3 Sme Imprtat quatis Nte tat tis equati applies t as well (Z) Z cr I Iizati ergy fr like species (cage f discrete rbits frm i t f fr like species e remved frm atm by iput f eergy A pt is absrbed t remve te electr ece >0 fr absrpti (tis is assumig te usual grud state f ) Tw New Ideas de Brglie quati predicts tat matter suld ave wavelike prperties p mu r pliear mmetum mmass uvelcity Plack s cstat λwavelegt de Brglie s quati mu Tw New Ideas Te Ucertaity Priciple Ucertaity I Psiti x p 4 Ucertaity I Mmetum Plack s Cstat Ucertaities are stadard deviatis Multielectr Atms Nucleus At r 0 Ψ is te prbability f fidig e at a sigle pit i space. By mappig Ψ at all pits i 3D space (r,θ,φ), we ca map te 3D electr prbability space fr eac rbital (r,θ,φ) Ψ Prbability at e pit ac electr will bey its w wavefucti Ψ ad explre a specific vlume i space caracteristic f te type f rbital te electr is i ac wave fucti Ψ as fur quatum umbers assciated wit it Ψ S it describes te rbital i wic a electr is fud ac electr is specified by a set f fur quatum umbers Tey determie were te electr is fud i a atm Kw te rules fr te quatum umbers Multielectr Atms P(r) te radial distributi fucti P(r) is te ttal itegrated prbability fr a sperical sell at distace r frm te ucleus r P(r) 4r Nte yu will t ave t d calculatis r plttig usig te radial distributi fucti Yu suld uderstad te ccept tat it is ttal prbability f fidig electr desity at a distace r frm te ucleus ad tat it ges t zer at te ucleus (r0) R ( r) Radial Wave Fucti ac type f rbital as Its w fuctial frm Nte P(r) 0 fr r 0 Multielectr Atms Orbital eergy depeds ad Z eff Zeff cr Orbital ergy fr a multielectr atm Z eff Z S Yu will t ave t calculate actual screeig ad Z eff but yu will ave t uderstad te peridic treds ad te screeig abilities f electrs I varius rbitals: Ier vs. valece s vs. p vs. d S screeig cstat

4 Key Study Pits. Frce f Culmbic attracti is directly prprtial t te electrstatic carges (q ad q ) ad iversely prprtial t te square f te separati betwee te carges (r ).. Defiiti f istpe. 3. Defiiti f atmic umber. 4. Defiiti f mass umber. 5. Geeral frmula fr a elemet r i. 6. Orders f decreasig eergy, frequecy ad wavelegt fr te differet types f electrmagetic radiati. 7. Itesity f a wave is directly prprtial t te square f te amplitude. 8. S.I. uit f frequecy (z, s ). 9. Meaig f S.I. prefixes: pic, femt, a, etc. Key Study Pits () 0. Rage f visible electrmagetic radiati i ameters: apprx. 400 (blue)800 (red) m.. Ipase cstructive iterferece wave amplitude augmeted.. Outfpase iterferece wave amplitude cacelled. 3. Typical wave prperties f visible ligt: diffracti ad refracti. 4. c relatisip. 4. Plack s quatum tery relatisip:. 5. Classical wave tery cat accut fr atmic lie spectra, blackbdy radiati (ultravilet catastrpe) ad ptelectric effect. Key Study Pits (3) 6. Blackbdy radiati absrbs ad emits all radiati regardless f. Ctiuus spectrum, depedet temperature. Best example ligt emitted frm a t metal. 7. RayleigJeas tery predicted tat te eergy desity fr a blackbdy wuld be ifiite at lw ad tat it was iversely prprtial t 4 ad directly prprtial t abslute temperature T. 8. istei, ptelectric effect:: K e ½ m e u ( 0 ), were 0 is te tresld frequecy ad 0 (wrk fucti). 9., eergy assciated wit a pt (G.N. Lewis). 0. Br tery: electr eergy i statiary states is cstat Key Study Pits (4). Br assumed tat te rbital agular mmetum is quatized: /.. Br s radius equati: r a 0, were a 0 Br radius (5.9 pm). 3. Br s eergy equati: (cr )/.79 x`0 8 J/. 4. (grud state). 5., 3, 4,. (excited states). 6. ergy differece betwee rbits i Br s tery: fial iitial cr (/ i / f ).79 x0 8 cr (/ i / f ) J c/ 7. missi: electr i excited state drps dw t a lwer eergy state. Key Study Pits (5) 8. Absrpti: electr is a lwer eergy state is excited t a iger eergy e. 9. Twpt trasiti: If te eergy fr a sigle pt trasiti is, te te ttal eergy fr a twpt trasiti must equal. 30. Fr Lyma lie spectra i UV: f 3. Fr Balmer lie spectra i visible: f 3. Fr Pasce lie spectra i IR: f Iizati eergy is bewee ad ifiity states. 34. Br mdel applies t all like (e electr) systems, e.g., e +, Li +, Be 3+, B 4+, C 5+. etc. Remember Z is ivlved. Key Study Pits (6) 8. de Brglie: /mc fr a pt ad /mu fr matter (electr, eutr, etc.) were u velcity f te matter. 9. Wave prperties f matter cfirmed electr diffracti wrk f DavissGermer ad Tms. (U.K.). 30. eiseberg ucertaity priciple: x. p /. 3. At te atmic level, te act f measuremet cages te system. 3. Wavefucti squared ( ) electr prbability 33. Quatum umbers (, l, m l ad m s ) 34. s, p, d, f rbitals (l 0,,, 3, respectively). 35. m s +/ r /. 36. SterGerlac experimet wit Ag atms. 37. Degeerate rbitals f te same eergy..

5 Key Study Pits (7) 38. Fr ad like species, te rbitals fr a give value are degeerate. 39. N tw electrs ave exactly te same fur quatum umbers. 40. Nde zer prbability f fidig a electr. 4. Oe s rbital, tree p rbitals, five d rbitals ad seve f rbitals. 4. Fr a s rbital (sperically symmetrical), te ttal itegrated prbability at a distace r frm te ucleus depeds r, i.e., P(r) 4r.R (r). We r 0, P(r) Screeig stregt f electrs i differet rbitals i multielectr atms: s > p > d. 44. is directly prprtial t Z eff / ad s < p < d fr te same value f i multielectr atms Key Study Pits (8) 45. Aubau prcess fr electr cfiguratis. 46. Fur rules: () miimum eergy cfigurati; () Pauli exclusi priciple; (3) ud s rule; ad (4) ce rbitals f same eergy are filled sigly, additial electrs ca be added wit ppsite sig. 47. Kw te class exceptis t te Aufbau prcess: Cr, Cu. 48. Kw te sapes ad labelig f te s, p ad d rbitals 49. Disticti betwee metals ad metals. 50. Metals ted t lse electrs, wile metals ted t gai electrs. 5. Te elemets i Grups,, 3, 4, 5, 6 ad 7 wit s x p y valece electrs wat t acieve te earest ble gas electric cfigurati i rder t be mre stable. Key Study Pits (9) 5. Sme trasiti metals lse electrs t acieve ble gas electric cfiguratis. May trasiti metals d t. 53. xtra stability f alffilled d sells (3d, 4d, 5d) 54. w t calculate atmic ad iic radii. 55. Cmparis f atmic ad iic sizes. 56. Iselectric species ad cmparis f teir atmic ad iic radii Peridic ad grup treds i atmic ad iic radii. 58. Peridic ad grup treds i iizati eergy.