נושא מס' 8: המבנה האלקטרוני של אטומים. Electronic Structure of Atoms. 1 Prof. Zvi C. Koren

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1 נושא מס' 8: המבנה האלקטרוני של אטומים Electronic Structure of Atoms 1 Prof. Zvi C. Koren

2 The Electron Spin From further experiments, it was evident that the e had additional magnetic properties associated with its internal movement. This movement was called spin, similar to the spin of a planet about its internal axis. Two such movements were detected, each with a different direction, and these gave a new quantum number for the electron with only two values: m s = (magnetic) spin quantum number = +½ or ½ (±½) (designates the direction of the spin of the e) 2 Prof. Zvi C. Koren

3 Pauli Schrodinger Quantum Numbers 4 Quantum Numbers are needed to characterize an electron Q.N. n l m l m s Property Name Principal q.n. Angular Momentum q.n. Magnetic q.n. Spin q.n. Property Related to the energy of the e orbiting about the nucleus Related to the angular momentm of the e orbiting about the nucleus Related to the magnetic property of the e orbiting about the nucleus Related to the magnetic property of the e spinning about its own axis Structural Name Shell Sub-shell Orbital e orientation Allowed Values 1, 2,, 0, 1, 2, 3, 4,, n 1 s, p, d, f, g, l,, 0,,+ l ± ½, or The 4 Q.N. s can be considered as the electron s: I.D. # or Address 3 Prof. Zvi C. Koren

Pauli Exclusion Principle Wolfgang Pauli (1900 1958, Austria & Switzerland) Nobel Prize in

(n, l, m l, m s ) electron 1 (n, l, m l, m s ) electron 2 No two electrons can have the same

4 Pauli Exclusion Principle Wolfgang Pauli ( , Austria & Switzerland) Nobel Prize in Physics, 1945 For polyelectronic atoms: Each electron has a unique set of 4 quantum numbers (n, l, m l, m s ) electron 1 (n, l, m l, m s ) electron 2 No two electrons can have the same set of four quantum numbers. The maximum # of e s in any orbital = 2 4 Prof. Zvi C. Koren

5 # of Electrons in Orbitals of a Subshell of a Shell n, Shell l values Subshells m l values Orbitals # of e s 1 0 1s 0 1s s 0 2s 2 1 2p -1, 0, 1 2p x, 2p y, 2p z 6 0 3s 0 3s p -1, 0, 1 3p x, 3p y, 3p z 6 2 3d -2, -1, 0, 1, 2 3dxy, 3dxz, 3dyz, 3d 2, 3d 2 10 x 2 z -y 4 5 (Complete this table) 5 Prof. Zvi C. Koren

6 שאלת "מה נשתנה": Why is H different from all other atoms? For H and H-like ions, from Schrödinger (and Bohr): E n = f(n) = (13.6 ev) Z 2 /n 2 For non-h atoms: E n,l = f(n,l) 4s- 7s- 6s- 5s- 3s- 2s- 1s- 6p--- 5p--- 4p--- 3p--- 2p--- 6d d d d----- H Atomic Subshell Energy Levels 6f f f ( Degenerate subshells) E Non-H (not to scale) 6p--- 5p--- 4p--- 3p--- 2p--- 6d d d d f f Note: For a given n, as l increases, E increases ( Degenerate orbitals) 1s- 2s- 3s- 4s- 5s- 6s- 7s- 6 Prof. Zvi C. Koren

7 Aufbau Principle via Triangulation and n+l values Order of Filling of Subshells 1s s 2p 3s 3p 3d n+l s 4p 4d 4f 5s 5p 5d 5f 5g 6s 6p 6d 6f 6g 6h 7s 7p... 7 The subshell with the lowest n+l value (and with the lower n ) is the most stable and gets filled first. Example: Write the electronic configuration of 88 Ra (radium). 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 5d 10 6p 6 7s 2 7 Prof. Zvi C. Koren

8 2s Hund s Rule (The Bus Seat Rule) Friedrich Hund ( , Germany) Consider the electronic configurations of: 7N, 8 O, 9 F, 10 Ne: 2p 2p 2p 2p 2s 2s 2s 1s 1s 1s 1s 7N 8O 9 F 10Ne 8 Prof. Zvi C. Koren

9 Atomic Electronic Configurations: 3 Different Representations 1A H Li 2A Be 3A B 4A C 5A N 6A O 7A F 8A He Ne Na Mg 3B 4B 5B 6B 7B 8B 1B 2B Al Si P S Cl Ar Full Line Notation (Spectroscopic Notation): 15P: 1s 2 2s 2 2p 6 3s 2 3p 3 Inner Outer e s e s Shorthand Notation (Noble Gas Notation): 15P: [Ne] 3s 2 3p 3 Orbital Energy Notation (Box Notation): 7N: 2p 2s 1s 9 Prof. Zvi C. Koren

10 Where Are the E s: Another Look 1A H Li 2A Be 3A B 4A C 5A N 6A O 7A F 8A He Ne Na Mg 3B 4B 5B 6B 7B 8B 1B 2B Al Si P S Cl Ar For 11 Na: 3s 2p 2s Recall: Orbitals are not solid physical structures, but probability functions. 1s 10 Prof. Zvi C. Koren

11 1A H Li Na K Rb Cs Fr s 2A Be Mg Ca Sr 3B Sc Y Ba * Lu * Ra Lr * Electronic Structures of the Atoms: Periodic Blocks of the Periodic Table 4B Ti Zr Hf Rf 5B V Nb Ta Db 6B Cr Mo W Sg d Periodic Table of the Elements 7B Mn Tc Re Bh Fe Ru Os Hs 8B Co Rh Ir Mt f 11 Prof. Zvi C. Koren Ni Pd Pt Ds 1B Cu Ag Au Rg 2B Zn Cd Hg 3A B Al Ga In Tl 4A C Si Ge Sn Pb 5A N P As Sb Bi p 6A O S Se Te Po 7A F Cl Br I At 8A He Ne Ar Kr Xe Rn Uub Uut UuqUupUuh Uus Uuo * La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm * Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md * (Find the shorthand noble-gas configurations of some elements.) Yb No

Radial Probability Functions Penetration vs. Shielding (Screening) Effective Nuclear Charge: Z eff or Z* = Z - S 1s 2s 2p (radius by Bohr: 0.529 Å) What is Z* for each e in 3 Li?

12 Radial Probability Functions Penetration vs. Shielding (Screening) Effective Nuclear Charge: Z eff or Z* = Z - S 1s 2s 2p (radius by Bohr: Å) What is Z* for each e in 3 Li? In a given shell, n: As l increases, E increases. Why? (As Z* increases e is more stable.) 3s 3p 3d E: 4s < 3d because 4s penetrates more than 3d (a o = Bohr radius = Å) 12 Prof. Zvi C. Koren

13 1A H Li Na K Anomalies in the Atomic Electronic Configurations 2A 3A 4A 5A 6A 7A Be B C N O F Mg Ca 3B 4B 5B 6B 7B 8B 1B 2B Sc Ti V Cr Mn Fe Co Ni Cu Zn Al Si P S Cl Ga Ge As Se Br 8A He Ne Ar Kr Cr expected: [Ar] 4s 2 3d 4 Cr actual: [Ar] 4s 1 3d 5 4s 3d 4s 3d Note: 2 e s in same orbital (4s) In Cr: E 4s E 3d Note: e s more dispersed (2 half-filled subshells) The key: One e makes the difference between 2 closely spaced subshells 13 Prof. Zvi C. Koren

14 1A H Li Na K Anomalies in the Atomic Electronic Configurations 2A 3A 4A 5A 6A 7A Be B C N O F Mg Ca 3B 4B 5B 6B 7B 8B 1B 2B Sc Ti V Cr Mn Fe Co Ni Cu Zn Al Si P S Cl Ga Ge As Se Br 8A He Ne Ar Kr Cu expected: [Ar] 4s 2 3d 9 Cu actual: [Ar] 4s 1 3d 10 4s 3d 4s 3d Note: 2 e s in same orbital (4s) In Cu: E 4s E 3d Note: 3d orbital can accommodate a pair of e s better than the 4s because a 3d orbital is more dispersed (4 lobes); 1 full subshell + 1 half-filled subshell The key (again): One e makes the difference between 2 closely spaced subshells 14 Prof. Zvi C. Koren

15 Diamagnetism vs. Paramagnetism vs. Ferromagnetism A spinning electron has a magnetic moment, meaning it acts like a little bar magnet. When two e s occupy the same orbital, they have opposed spins and so opposed magnetic moments, and their magnetic effect cancels out. However, if an element has orbitals with only one electron, the atom inherits a magnetic moment from the unpaired electrons. normal Paramagnetism (at least one unpaired e) Atoms with an unpaired e normally align themselves randomly so that the atoms magnetic fields cancel each other When weighed in a very strong external magnetic field, a paramagnetic substance has a small apparent weight gain due to attraction of the material into the external field. Diamagnetism (all e s paired) << Paramagnetism An external magnetic field induces an electric current into the material, with the electric current setting up an opposed magnetic field. When weighed in a very strong external magnetic field, a diamagnetic substance has a very slight apparent weight loss due to repulsion of the substance away from the external field. 15 Prof. Zvi C. Koren Ferromagnetism (Fe, Ni, Co,...) After an external magnetic field is applied, all the magnetic moments stay aligned even after the external field is turned off. in a field

16 Prof. Zvi C. Koren

17 Electronic Configurations of Ions Main Group Atoms Octet Rule: Metallic atoms will lose e s Non-metals will accept e s 1A H Li 2A Be to attain a Noble Gas configuration 3A 4A B C 5A N 6A O 7A F 8A He Ne Na K Mg Ca 3B Sc 4B Ti 5B V 6B Cr 7B Mn Fe 8B Co Ni 1B Cu 2B Zn Al Ga Si Ge P As S Se Cl Br Ar Kr Cations e Na: [Ne] 3s 1 Na + : [Ne] Na + is isoelectronic with Ne Anions S: [Ne] 3s 2 3p +2e 4 S 2 : [Ne] 3s 2 3p 6 = [Ar] S 2 is isoelectronic with Ar 17 Prof. Zvi C. Koren

18 1A H Li Na K Electronic Configurations of Transition Metal Cations E of an e in subshell n,l in an atom/ion with nuclear charge Z = f(z, total # and locations (orbitals) of all the e s, n, l) 2A Be Mg Ca 3B Sc 4B Ti 5B V 6B Cr 7B Mn Fe 8B Co Ni 1B Cu 2B Zn 3A B Al Ga 4A C Si Ge Cationization occurs with the removal of the e s in the highest n value (and the higher l) 5A N P As 6A O S Se 7A F Cl Br 8A He Ne Ar Kr 26Fe: [Ar] 4s 2 3d 6 4s 3d 26Fe 2+ : [Ar] 3d 6 4s 3d Note: E 4s E 3d Order of removal and the order of filling are not necessarily the same 18 Prof. Zvi C. Koren

19 Atomic Properties & Periodic Trends: Metallic vs. Non-metallic Trends in the Periodic Table Non-metallicity Metallicity Electronegativity also follows this trend (later) 19 Prof. Zvi C. Koren

20 Atomic Properties & Periodic Trends: Atomic Size or Atomic Radii The size, or radius, of an atom is not fixed, as the e s can have statistically varying positions around the nucleus (Schrödinger): Here, we are discussing a statistical size, e.g., the average or most probable distance between the nucleus and the furthest e. Size: cation < free atom, anion > free atom n constant (or decreases) But Z increases Z vs. n Z increases But n increases Na Mg O F SIZE (Problem: Compare the sizes of the following isoelectronic species: O 2, F, Na +, Mg 2+ ) 20 Prof. Zvi C. Koren

Atomic Properties & Periodic Trends: Ionization Energies (or Ionization Potentials) Recall: M(g) + I.E. M + (g) + e I.E. I.E. SIZE (The trend in sizes is more monotonic than with I.

21 Atomic Properties & Periodic Trends: Ionization Energies (or Ionization Potentials) Recall: M(g) + I.E. M + (g) + e I.E. I.E. SIZE (The trend in sizes is more monotonic than with I.E. s.) (Careful: The trend is not monotonic) Non-metals Metals 21 Prof. Zvi C. Koren

22 1A H Li Na Why Does Mg form Mg 2+ and not Mg + or Mg 3+ Ions? The higher the charge, the stronger the ionic bond. So, why isn t there Mg 3+ 2A 3A 4A 5A 6A 7A Be B C N O F Mg Al Si P S Cl 8A He Ne Ar Mg(g) Mg + (g) + e 1 st I.E. IE 1 = 738 kj/mol [Ne]3s 2 Mg + (g) Mg 2+ (g) + e [Ne] 3s 1 Mg 2+ (g) Mg 3+ (g) + e [Ne] 2 nd I.E. IE 2 = 1451 kj/mol 3 rd I.E. IE 3 = 7733 kj/mol Extremely high energy cost in forming the higher ionic charge (+3) 22 Prof. Zvi C. Koren

23 1A H Li 2A Be Experimental Evidence for Orbtal Energies 3A 4A 5A B C N 6A O 7A F 8A He Ne 1 st IE (kj/mol) 2s 1 2s 2 2s 2 2p 1 2s 2 2p 2 2s 2 2p 3 2s 2 2p 4 2s 2 2p 5 2s 2 2p 6 IE: Be > B easier to remove e from 2p than 2s IE: N > O easier to remove a paired e in 2p 4 than an unpaired e 23 Prof. Zvi C. Koren

24 Atomic Size & Ionization Energies of Transition Metals Z increases, so size decreases and IE increases. BUT, the e s that fill the 3d subshell repel the 4s e s and offset somewhat the increasing Z. Thus the 4s e s are held only slightly more tightly across the periodic row. 1 pm = m 1 Å = m 1 Å = 100 pm 24 Prof. Zvi C. Koren

25 Lanthanide Contraction Why is the atomic size of Au similar to Ag (and not greater)? 4f 14 The 4f e s do not shield the higher shell e s very well. So, the increase in Z by +14 is not offset by much. This lanthanide contraction results in Au s 6s orbital being similar size as Ag s 5s orbital. Thus, the density of Au >> density of Ag. 25 Prof. Zvi C. Koren

26 Electron Affinities IE X(g) + e X (g) + EA Note: Both IE and EA are defined as positive quantities. BUT IE is defined for an endothermic process and EA for an exothermic one. IE EA s show many exceptions to the general trend EA EA 26 Prof. Zvi C. Koren

27 Electronegativities Ability of a bonded atom to attract bonding e s Pauling Scale 27 Prof. Zvi C. Koren

MANY ELECTRON ATOMS Chapter 15

MANY ELECTRON ATOMS Chapter 15 Electron-Electron Repulsions (15.5-15.9) The hydrogen atom Schrödinger equation is exactly solvable yielding the wavefunctions and orbitals of chemistry. Howev er, the Schrödinger