Chapter 7 : Atomic Structure and Periodicity

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1 Chapter 7 : Atomic Structure ad Periodicity Newto's famous apple tree (actually, a descedet of it) located outside his quarters at Triity. E. Rutherford J. Dalto Newto! Are you correct?

2 Electromagetic Radiatio Electromagetic Radiatio: Radiat eergy that exhibits wavelegth-like behavior ad travels through space at the speed of light i a vacuum. Oe of the ways of eergy travel through space. (Ex: Light from the su, Microwave, X-ray, Radiat heat from a fireplace) Waves have 3 primary characteristics:. Wavelegth (l): distace betwee two peaks i a wave. (m). Frequecy (): umber of waves per secod that pass a give poit i space. (Hz, s - ) 3. Speed : speed of light (c) is.9979 x 0 8 m/s. c = l

3 Electromagetic Radiatio MW ove High eergy beams Su light Coal fire Radio & TV

Frustratio of physics major studets (ed of 9C) Matter (particle) x Eergy (light : wave) The Nature of Matter mass

Max Plack (858-947) Nobel Prize, 98 Blackbody radiatio (900, M.

characteristic of this radiatig system oly, ot depedet upo the type of radiatio which is icidet upo it.

4 Frustratio of physics major studets (ed of 9C) Matter (particle) x Eergy (light : wave) The Nature of Matter mass positio o mass o positio cotiuity Everythig is solved. No more job left to solve. Max Plack ( ) Nobel Prize, 98 Blackbody radiatio (900, M. Plack) refers to a object or system which absorbs all radiatio icidet upo it ad re-radiates eergy which is characteristic of this radiatig system oly, ot depedet upo the type of radiatio which is icidet upo it. Eergy ca be gaied or lost oly i whole-umber muliples of the quatity h. E h h = Plack s costat, 6.66 x 0 34 J s =,,3.. Trasfer of eergy (eergy) is quatized, ad ca oly occur i discrete uit of size h. Each of these small "packets" of eergy is called quatum.

5 The Nature of Matter Photoelectric Effect (905) : the pheomeo i which electros are emitted from the surface of a metal whe light strikes it. Characteristics of Photoelectric effect. For the emissio of e -, ic > o (threshold frequecy, o ). Itesity of the icidet light, # of the emitted e - 's 3. ic, Kietic eergy of a emitted e - IR Red light Blue light o emissio UV Metal low-speed e - high-speed e - Explaatio of Photoelectric effect Electromagetic radiatio is quatized (cosist of photos). The itesity of light is a measure of # of photos. Eergy of icidet light (E photo = h) Speed of emitted e - KE e Albert Eistei ( ) Nobel Prize, 9 (Photoelectric Effect) mv Eergy required to remove e - from metal's surface (work fuctio) hv hv o

The Nature of Matter Special Theory of Relativity (905) Eergy ad mass E = mc E m photo photo hv E c hv c E mc l h c c h lc Compto (Nobel prize 9) did measure the photo. (Oly i relativistic sese.

6 The Nature of Matter Special Theory of Relativity (905) Eergy ad mass E = mc E m photo photo hv E c hv c E mc l h c c h lc Compto (Nobel prize 9) did measure the photo. (Oly i relativistic sese. No rest mass.) Albert Eistei ( ) Nobel Prize, 9 (Photoelectric Effect) Summary of Plack ad Eistei's works Compto effect. Eergy is quatized.. Electromagetic radiatio has particle properties as well as previously kow wave properties. Dual ature of light: wave ad particle

7 The Nature of Matter Mass Wave? for light, m h l c for a particle with velocity v, m l h de Broglie's equatio (Nobel 99) l h m Ex) Wavelegths of a electrom travellig with.00 x 0 7 m/s ad a 0.0 kg ball with 35 m/s? l e h m J s 3 (9. 0 kg)( m / s) m l ball h m J s (0.0kg)(35m / s) m ~ Å

$The Nature of Matter Diffractio: the$ wavefrot from the path predicted by

8 The Nature of Matter Diffractio: the deviatio of a electromagetic wavefrot from the path predicted by geometric optics whe the wavefrot iteracts with, i.e., is restricted by, a physical object such as a opeig (aperture) or a edge. (Properties of wave) Youg's experimet X-ray diffractio patter

$P Thomso (Nobel 937) ad his so (97) electro diffractio patters of a thi foil Proved that electro has a wave-like properties ad$ de Broglie's equatio is correct.

9 The Nature of Matter Davisso (Nobel, 937) - Germer Experimet (97) G. P Thomso (Nobel 937) ad his so (97) electro diffractio patters of a thi foil Proved that electro has a wave-like properties ad de Broglie's equatio is correct. All matter exhibits both particluate ad wave properties Large pieces of matter (baseball): predomiatly particulate properties Pieces of matter with itermediate mass (electro): both particulate ad wave properties Vert small "bits of matter" (photo): predomiatly wave properties

10 The Atomic Hydroge Spectrum Lie spectrum Balmer lies (visible) (885) E 3.6eV( ), 3,4,5.. 4 Later.. Lyma lie (UV) (906) E 3.6eV( ),,3,4.. Pasche lie(ir) (908) E 3.6eV( ), 4,5,6.. 9 Combied together... E 3.6eV ( ), Eergy of hydroge (eergy of electro i hydroge) is quatized.

11 9 Paradox of Rutherford's Atom e - r total eergy E PE KE e 4 r o m p p E - as r 0 m e e ot to fall Why the radiate?

12 The Bohr Model Bohr s Theory.Atoms have well-defied electro orbits..they do t radiate. 3.Circular orbits: oly specific orbits with specific agular mometa, l = (h/ ), are allowed {quatizatio postulate, =,,3..} 4.Trasitios: electros go from oe orbit to other => emissio or absorptio of light (Nobel, 9) Do your ow math! It's actually very easy! Ze /4 o r = m e v /r l = (h/ ) = m e vr Z : uclear charge umber E = PE + KE igore this = -Ze /4 o r + / m p v p + / m e v e r

13 For oe electro atom: r E ao ( Z.78 0 ) ( =,,3...) 8 Z J ( ) E E E3 E 0 Z 3.6eV ( ) The Bohr Model (a o = 0.59 Å, Bohr radius, =, Z=) 0 Groud State: The lowest possible eergy state for a atom E E.78 0 (.78 0 E 8 8 J ( Z J ) Z ( ) ( ) { J ( Z ) (3.6eV) Z Rydberg costat (R H ) ) } ( ) For H lie spectrum 8 E.78 0 J ( ) 3.6eV ( ) ( ) Perfect!!!

The Bohr Model Ex) Wavelegth of the emissio lie for the trasitio of a hydroge electro from = 3 to = level? 0 E.78 0 3.05 0 9 J 8 J( ).78 0 8 J ( 4 c E hv h l 34 8 hc ( 6.66 0 J s)(.

14 The Bohr Model Ex) Wavelegth of the emissio lie for the trasitio of a hydroge electro from = 3 to = level? 0 E J 8 J( ) J ( 4 c E hv h l 34 8 hc ( J s)( m / s) 7 l m 656.7m 9 E J Ex) Eergy required to remove the electro from a hydroge atom i its groud state? E J ( Let's go! For H lie spectrum ) ) 9 8 J ( ).78 0 J (work fuctio) 8 E.78 0 J ( ) 3.6eV ( ) ( ) Perfect!!! Balmer Lyma Pasche

15 The Quatum Mechaical Model of the Atom Wait a miute.. Not well explai multi-electro atoms. Several more lies (i H spectrum) i magetic field stadig waves for a electro value of fuctio de Broglie said all movig particles have wave properties. l = h/mv stadig waves positio What does it mea? de Broglie ad Schrödiger (Nobel, 933) suggested that the electo has the properties of stadig wave boud to the ucleus. value of fuctio positio ot allowed

16 The Quatum Mechaical Model of the Atom Wait a miute.. Not well explai multi-electro atoms. Several more lies (i H spectrum) i magetic field Violate Heigeberg's ucertaity priciple. (Nobel, 93) : The positio ad mometum of a particle caot be simultaeously measured with arbitrarily high precisio. x ( m ) E t ( h ) I H spectrum, eergy is so precise => p 0 => x We caot describe orbits of e - 's but orbitals (regios describig the probable locatio of e - 's) Probability => Birth of Quatum Mechaics Priciples of Quatum Mechaics. Wave - particle duality of matter. The state of the matter (particle) ca be described by a wave fuctio (Y). 3. Y dt: the probabilty of fidig the matter i a regio dt. Not possible to describe e - as a sigle particle. Must cosider wave properties of e -

[ Y( x, y [ Y( x, y, z, z )] )] N N the ratio of the probabilities of fidig the electro at positios ad Y : probability distributio

17 The Quatum Mechaical Model of the Atom The Physical Meaig of a Wave Fuctio (Y) The square of the fuctio idicates the probability of fidig a electro ear a partiular poit i space. [ Y( x, y [ Y( x, y, z, z )] )] N N the ratio of the probabilities of fidig the electro at positios ad Y : probability distributio electro desity map (electro desity, electro probability) Radial probability distributio is the probability distributio i each spherical shell. Y of H s orbital (wave fuctio) most probable distace (for H s orbital => 0.59 Å, Bohr radius)

18 Quatum Numbers Schrödiger Equatio -D 3-D (shpherical coordiate) 3-D (cartesia coordiate) Ze /4 o r

19 Quatum Numbers Solutios of Schrödiger Equatio (for hydrogeic atoms) Y,l,ml = R,l (r)q l,ml (q,f)

20 Quatum Numbers Solutios of Schrödiger Equatio (for hydrogeic atoms) Y,l,ml = R,l (r)q l,ml (q,f) Pricipal quatum umber (QN) ( =,, 3,...) - related to size ad eergy of the orbital. Agular Mometum QN (l = 0 to -) - relates to shape of the orbital. Magetic QN (m l = l to -l) - relates to orietatio of the orbital i space relative to other orbitals. The agular mometum QNs ad correspodig letters used to desigate atomic orbitals Value of l (subshell) Letter used s p d f g Ex) for =5, fill the right table = 5, l = 0 (5s, orbital), (5p, 3), (5d, 5), 3 (5f, 7), 4(5g, 9)

21 Orbital Shapes ad Eergies Solutios of Schrödiger Equatio (for hydrogeic atoms) Y,l,ml = R,l (r)q l,ml (q,f) s orbitals surface that surrouds 90 % of the total electro probability # of total odes = -

22 Orbital Shapes ad Eergies Solutios of Schrödiger Equatio (for hydrogeic atoms) Y,l,ml = R,l (r)q l,ml (q,f) p x l # of total odes = - # of agular odes = l orietatio i space (ad phase iformatio) p orbitals degeeracy of p orbitals = 3

23 Orbital Shapes ad Eergies Solutios of Schrödiger Equatio (for hydrogeic atoms) Y,l,ml = R,l (r)q l,ml (q,f) p x l # of total odes = - # of agular odes = l orietatio i space (ad phase iformatio) Ex) shape of 3p z orbital? z total odes = xy plae agular ode = radial ode =

24 Orbital Shapes ad Eergies Solutios of Schrödiger Equatio (for hydrogeic atoms) 3d orbitals Y,l,ml = R,l (r)q l,ml (q,f) total odes =, agular odes = radial odes =0 p x l # of total odes = - # of agular odes = l orietatio i space (ad phase iformatio) 3d xy y x 3d x-y y degeeracy of d orbitals = 5 d z ( x y ) x

25 Orbital Shapes ad Eergies Solutios of Schrödiger Equatio (for hydrogeic atoms) 4f orbitals Y,l,ml = R,l (r)q l,ml (q,f) total odes = 3, agular odes = 3 radial odes =0 p x l # of total odes = - # of agulr odes = l orietatio i space (ad phase iformatio) degeeracy of f orbitals = 7

26 Orbital Shapes ad Eergies Solutios of Schrödiger Equatio (for hydrogeic atoms) Y,l,ml = R,l (r)q l,ml (q,f) how about this (Eergy)? E E Z J ( ) J ( ) Z 3.6eV ( ) 3.6eV ( ) (for H atom) H is perfectly solved!!

27 Electro Spi ad the Pauli Priciple Pauli (Nobel, 945) Exclusio Priciple (95) : No two electros i a atom ca have idetical quatum umbers. "But do't you see what this implies? It meas that there is a fourth degree of freedom for the electro. It meas that the electro has spi, that it rotates." - George Uhlebeck to Samuel Goudsmit i 95 o hearig of the Pauli priciple - Electro Spi QN (m s = +/, -/) - relates to the spi states of the electros. Therefore, a orbital ca hold oly two electros, ad they must have opposite spis. The state of a electro is completely described by a set of 4 quatum umbers (, l, m l, m s ).

28 Y Y hydrogeic atoms Polyelectroic Atoms Y Y Y Ze [si q ( r ) (si q ) ] Y( r, q, f) Y( r, q, f) u r si q r r q q si q f 4 r 0 Exact solutios => s, s,,p, 3s... polyelectroic atoms u i Y Y Y Ze e [si q ( ) (si q ) ] { } ( r, q, f) ( r, q, f) i ri i Y Y r si q r r q q si q f 4 r 4 r i i i i i i i i i 0 i j i 0 ij o exact solutio electro pathway is ot kow => r ij ot determied... approximatio : a field of charge that is the et result of the uclear attractio ad the average repulsio of all the other electros. + e - + 0e - Na Na + e - e - does ot feel + uclear charge because of shieldig of other electros hydrogeic orbitals with the same geeral shapes as for the hydrgeic orbitals, but with differet size ad eergies.

78 0 8 Z J( ) the higher uclear charge, the lower eergy level higher

29 Polyelectroic Atoms Peetratio ad shieldig s, p 3s, 3p, 3d peetratio of s orbital effective uclear charge 3s > 3p > 3d shieldig o p orbital E Z J( ) the higher uclear charge, the lower eergy level higher effective uclear charge for electro i s orbital tha i p E s < E p < E d < E f...

30 Polyelectroic Atoms Hydrogeic atoms Polyelectroic atoms Pricipal quatum umber (QN) ( =,, 3,...) - related to size ad eergy of the orbital. Agular Mometum QN (l = 0 to -) - relates to shape of the orbital. Pricipal quatum umber (QN) ( =,, 3,...) - related to size ad eergy of the orbital. Agular Mometum QN (l = 0 to -) - relates to shape of the orbital ad cotributes to eergy.

31 The Histroy of Periodic Table Cotributor Date Cotributio Aristotle ~330 BC Four elemet theory: earth, air, fire & water Atoie Lavoisier Jös Jakob Berzelius Joha Döbereier Joh Newlads ~ Wrote the first extesive list of elemets cotaiig 33 elemets. Distiguished betwee metals ad o-metals. Developed a table of atomic weights. Itroduced letters to symbolize elemets. Developed 'triads', groups of 3 elemets with similar properties. Lithium, sodium & potassium formed a triad. Calcium, strotium & barium formed a triad. Chlorie, bromie & iodie formed a triad. Law of triad: The Middle elemet i the triad had atomic weight that was the average of the other two members. The kow elemets (>60) were arraged i order of atomic weights ad observed similarities betwee the first ad ith elemets, the secod ad teth elemets etc. He proposed the 'Law of Octaves'. from

The Histroy of Periodic Table Cotributor Date Cotributio Lothar Meyer Dmitri Medeleev 869 869 Compiled a Periodic Table of 56 elemets based o the periodicity of properties such

Produced a table based o atomic weights but arraged 'periodically' with elemets with similar properties uder each other.

32 The Histroy of Periodic Table Cotributor Date Cotributio Lothar Meyer Dmitri Medeleev Compiled a Periodic Table of 56 elemets based o the periodicity of properties such as molar volume whe arraged i order of atomic weight. Almost the same as Medeleev's. Produced a table based o atomic weights but arraged 'periodically' with elemets with similar properties uder each other. Gaps were left for elemets that were ukow at that time ad their properties predicted (the elemets were gallium, scadium ad germaium). The order of elemets was re-arraged if their properties dictated it, eg, tellerium is heavier tha iodie but comes before it i the Periodic Table. from org/~ethall/period /period.htm

33 Cotributor Date Cotributio William Ramsay Hery Moseley Gle Seaborg The Histroy of Periodic Table Discovered the Noble Gases (Ar) of which the properties are differet from others. Expad the periodic table. Determied the atomic umber of each of the elemets. He modified the 'Periodic Law' to read that the properties of the elemets vary periodically with their atomic umbers. Sythesised trasuraic elemets (the elemets after uraium i the periodic table) Expad the periodic table. from

34 The Aufbau Priciple ad the Periodic Table Aufbau Priciple (Buildig-Up Priciple) : determies the electro cofiguratio of a atom, molecule or io. The priciple postulates a hypothetical process i which a atom is "built up" by progressively addig electros. As they are added, they assume their most stable coditios (electro orbitals) with respect to the ucleus ad those electros already there. s s p He:s Li:s s Be:s s B:s s p C:s s p N:s s p 3 Pauli exclusio priciple Hud's rule: The lowest eergy cofiguratio for a atom is the oe havig the maximum umber of upaired electros allowed by the Pauli priciple i a particular set of degeerate orbitals s s p F:s s p 5 Ne:s s p 6 [Ne] Na:[Ne]3s Mg:[Ne]3s Al:[Ne]3s 3p

H:s s s p He:s Li:s s Be:s s B:s s p The Aufbau Priciple ad the Periodic Table Valece electros: The electros i the outermost priciple quatum level of a atom.

35 H:s s s p He:s Li:s s Be:s s B:s s p The Aufbau Priciple ad the Periodic Table Valece electros: The electros i the outermost priciple quatum level of a atom. Core electros: Ier electros C:s s p N:s s p 3 O:s s p 4 [He] [Ne] [He]s [Ne]3s F:s s p 5 Ne:s s p 6 The elemets i the same group have the same valece electro cofiguratio. Na: [Ne]3s Mg: [Ne]3s Al: [Ne]3s 3p

36 K: s s p 6 3s 3p 6 4s = [Ar]4s Ca: [Ar]4s Sc: [Ar]4s 3d Ti: [Ar]4s 3d : : The Aufbau Priciple ad the Periodic Table Catios K + : [Ar] Ca + : [Ar]4s V + : [Ar]3d 3 M + : [Ar]3d 5 Co + : [Ar]3d 7 Cu + : [Ar]3d 9 Cr + : [Ar]3d 4 Fe + : [Ar]3d 6 Ni + : [Ar]3d 8 Z + : [Ar]3d 0 always s electros are out first. trasitio metals [Ar] [Ar]4s [Ar]4s 3d 0

37 The Aufbau Priciple ad the Periodic Table the order i which the orbitals fill i polyelectroic atoms with some exceptios Lataide series Actiide series

38 The Aufbau Priciple ad the Periodic Table mai group elemets mai group elemets IUPAC America alkali metals alkalie earth metals oble gases haloges

X(g) X + (g) + e - e - Al(g) Al + (g) + e - Al + (g) Al + (g) + e - Al + (g) Al 3+ (g) +

39 Periodic Treds i Atomic Properties Ioizatio Eergy: The quatity of eergy required to remove a electro from the gaseous atom or io. X(g) X + (g) + e - e - Al(g) Al + (g) + e - Al + (g) Al + (g) + e - Al + (g) Al 3+ (g) + e - Al 3+ (g) Al 4+ (g) + e - I = 580 kj/mol I = 85 kj/mol I 3 = 740 kj/mol I 4 =,600 kj/mol first ioizatio eergy secod ioizatio eergy :

40 Ioizatio Eergy Periodic Treds i Atomic Properties IE N(g) N + (g) + e - N:s s p 3 N + :s s p O(g) O + (g) + e - O:s s p 4 O + :s s p 3 Be(g) Be + (g) + e - Be:s s Be + :s s B(g) B + (g) + e - B:s s p B + :s s

41 Ioizatio Eergy Periodic Treds i Atomic Properties

42 Periodic Treds i Atomic Properties Electro Affiity : The eergy chage associated with the additio of a electro to a gaseous atom. e - X(g) + e - X - (g) Be careful o the defiitio of the directio of the process. The more exothermic, the easier to accept electro. EA (egatively) He, Be, N, Ne, Mg, Ar whose atoms do ot add a electro exothermically ad thus do ot form stable, isolated X - ios. IE > 0, EA > 0 or < 0

Atomic Radius Periodic Treds i Atomic Properties radius?? Covalet atomic radius : half the distace betwee the uclei i a diatomic molecule with a sigle bod.

43 Atomic Radius Periodic Treds i Atomic Properties radius?? Covalet atomic radius : half the distace betwee the uclei i a diatomic molecule with a sigle bod. (for ometals with o such case, r is estimated) Metallic radius : half the distace betwee the uclei i solid metal closepackig crystal (for metals woth o such case r is estimated) r x > r x+ r x < r x-

Properties of a Group: The Alkali Metals Iformatio Cotaied i the Periodic Table. Each group member has the same valece electro cofiguratio (these electros primarily determie a atom s chemistry).

44 Properties of a Group: The Alkali Metals Iformatio Cotaied i the Periodic Table. Each group member has the same valece electro cofiguratio (these electros primarily determie a atom s chemistry).. The electro cofiguratio of ay represetative elemet. 3. Certai groups have special ames (alkali metals, haloges, etc). 4. Metals ad ometals are characterized by their chemical ad physical properties. - metals with low ioizatio eergy (easier to be catios). - oemtals with high ioizatio eergy ad the most egative electro affiities (ability to gai oe or more electros to form a aio whe reactig with a metal)

45 Properties of a Group: The Alkali Metals The Alkali Metals The most chemically reactive of metals. Na K Cs M(s) + H O(l) H (g) + M + (aq) + OH - (aq) + eergy

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