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1Figure 12.23 - Zumdahl - Chemical Principles (4/e)
Energy Level Scheme of 1-electron (Hydrogenic) Atoms:En ~ 1/n2 (n- only)
2
HANDOUT: “QM & PT”:QUANTUM MECHANICS & PERIODIC TABLE (page 1)
• Schrödinger Wave Equation (SWE) for MULTI-ELECTRON ATOMS … contains potential energy terms which include interactions BETWEEN electrons…
Nuclear attraction = ! Z • e2
r1
! Z • e2
r2
, where Z = 2 for He
Electron!Electron Re pulsion = Electron Correlation = + e2
| r1 ! r2 |
This last term correlates (couples) electron behavior…SWE can NOT be solved exactly … APPROXIMATIONS…
3
“QM & PT”: (page 1)
Nuclear attraction = ! Z • e2
r1
! Z • e2
r2
, where Z = 2 for He
Electron!Electron Re pulsion = Electron Correlation = + e2
| r1 ! r2 |
2p+
e1-
e2-
e-e repulsion(correlation)
nuclearattraction
nuclearattraction
4
“QM & PT”: (page 2)
• PRESUME that e!ect of e-e repulsion was “INDIRECT”, I.e, Each electron “separately” a"racts the nucleus…BUT…
• The specific amount of nuclear charge “felt” varied with EACH electron’s SUBSHELL designation (n & l).
• This ATTENUATED NUCLEAR CHARGE is termed EFFECTIVE NUCLEAR CHARGE (Ze! = (Z - s) < Z) - subshell dep. Energy of subshell = En l = - Ze!,nl
2•Ry/n2 , n = 1, 2, 3, …
• Otherwise, each electron occupies a hydrogenic atomic orbital - !nlml(r,",#) = Rnl(r)•Ylml(",#) …same pictures from before.
5
“QM & PT”: (pages 2-3)
• !nlml(r,",#) = Rnl(r)•Ylml(",#). Rnl(r) - expresses the radial behavior [RDF’s].
• Radial behavior (pictures) RATIONALIZE SUBSHELL ENERGY DEPENDENCE.
• Ze! = Z - s ; where “s” is the SCREENING or SHIELDING.
• Energy of subshell = En l = - Ze!,nl2•Ry/n2 , n = 1, 2, 3, …
• Ze! - for a given “n” - DECREASES as l INCREASES. “s” feels “greatest” & “f” the “least”…. SEE RDF’s …
6
Figure 12.33 - Zumdahl - Chemical Principles (4/e)
Radial Distributions {4#r2•[Rnl(r)]2}: n = 3 orbitalsFor the same n value, lower l value has
greater degree of “penetration”[ns (greatest) > np > nd > nf (least)]
7Figure 8.10 - Hill & Petrucci - General Chemistry (3/e)
E!ective Nuclear Charge (Ze!) & Multi-electron Atoms:Ze!, n,l = Z - sn,l depends on (n,l) - subshell:
• ENERGY of e- SUBSHELL: En,l = -Ze!2•Ry/n2 .
• IONIZATION ENERGY of e- in subshell:IEn,l = Ef - Ei = 0 -En,l = +Ze!
2•Ry/n2
8Figure 8.1 - Hill & Petrucci - General Chemistry (3/e)
Energy Level Scheme of Multi-electron Atoms:Depends on (n,l) - subshell - En,l = -Ze!
2•Ry/n2 .
9
Figure 12.33 - Zumdahl - Chemical Principles (4/e)
Radial Distributions {4#r2•[Rnl(r)]2}: 3d vs 4s subshellsE4s (more stable) < E3d (less stable) :
10Figure 7.29 - Hill & Petrucci - General Chemistry (3/e)
“QM & PT”: (page 4)How do we pile e-’s in orbitals?
First … one more quantum # …“Spin” Quantum # (ms) - 4th Quantum #:
ms = +1/2 or -1/2
11
“QM & PT”: (page 4)“Spin” Quantum # (ms) = +1/2 or -1/2
RESTRICTS Orbital Population:Pauli Exclusion Principle (PEP):
(Di!erent ways of saying the same thing):
• NO 2 e-’s are allowed (zero probability) to have the SAME set of 4 quantum #’s (n, l, ml , ms).
• IF 2 e-’s are in the SAME ORBITAL (same n, l, ml ), each MUST have DIFFERENT ms values, i.e., they MUST have “OPPOSITE” SPINS”.
• Any orbital can have, at MOST, ONLY 2 e-’s; 1 e- with ms = +1/2 ($) & 1 e- with ms = -1/2 (%), i.e., $ % .
12
Aufbau Ordering ofEnergies of Subshells of Multi-electron Atoms:
[1s subshell through 6s subshell]
En,l = - (Zeffective)2•Ry/n21s2s
2p3s
3p4s
3d4p
5s
6s
4d5p
Aufbau orderingof subshell energies.
Energy
En,l
Not to scale.
13
GROUND STATE (Most Stable) electron configurations:[H, He, Li, Be, & B] - Orbital Box Diagram
Lowest energy ----> Highest energy (Obey PEP)
En,l = - (Zeffective)2•Ry/n2
Energy
En,l
1s
2s
2p
{ H , He }
{ Li , Be }
Not to scale.
Aufbau ordering:(Ground StateConfigurations)
{ B}
14
GROUND STATE (Most Stable) electron configurations:
Populating subshells containing energy-degenerate orbitals…
Do NOT “bunch up” … “spread out” …
En,l = - (Zeffective)2•Ry/n2
Energy
En,l
1s
2s
2p
{ H , He }
{ Li , Be }
Not to scale.
Carbon? ... NOT a Lowest EnergyGround State Config. ... actuallyan Excited State Config.!!
15
GROUND STATE (Most Stable) electron configurations:Populating subshells containing energy-degenerate orbitals…
Ground State configuration of Carbon:Hund’s Rule (preference) for Ground State Configurations:
“Singly occupy all orbitals [$ $ ] of same energy -with SAME spin … BEFORE filling any of them [$% ]).”
En,l = - (Zeffective)2•Ry/n2
Energy
En,l
1s
2s
2p
{ H , He }
{ Li , Be }
Not to scale.
Aufbau ordering:(Ground StateConfigurations)
Carbon: Hund'sRule
16
GROUND STATE (Most Stable) electron configurations:Populating subshells containing energy-degenerate orbitals…
Ground State configuration of Nitrogen:Hund’s Rule (preference) for Ground State Configurations:
En,l = - (Zeffective)2•Ry/n2
Energy
En,l
1s
2s
2p
{ H , He }
{ Li , Be }
Not to scale.
Aufbau ordering:(Ground StateConfigurations)
Nitrogen: Hund'sRule
17
GROUND STATE (Most Stable) electron configurations:
2nd Row: [Li, Be, B, C, N, O, F, Ne]Lowest energy ----> Highest energy (Obey PEP, & Hund’s Rule)
En,l = - (Zeffective)2•Ry/n2
Energy
En,l
1s
2s
2p
{ H , He }
{ Li , Be }
{ B,C,O,N,F,Ne}
Not to scale.
Aufbau ordering:(Ground StateConfigurations)
18
GROUND STATE (Most Stable) electron configurations:
3rd Row: [Na, Mg, Al, Si, P, S, Cl, Ar]Lowest energy ----> Highest energy (Obey PEP, & Hund’s Rule)
En,l = - (Zeffective)2•Ry/n2
Energy
En,l
1s
2s
2p
3s
3p
{ H , He }
{ Li , Be }
{ B,C,O,N,F,Ne}
{ Na , Mg}
{Al,Si,P,S,Cl,Ar}
Not to scale.
Aufbau ordering:(Ground StateConfigurations)
19
Figure 12.26 - Zumdahl - Chemical Principles (4/e)
Electron Configuration Correlated with Periodic Table:[Ground State (Lowest Energy) Configurations]
20
GROUND STATE (Most Stable) electron configurations:4th Row - Includes 1st period of Transition Metals:
[K, Ca, Sc, Ti, V, Cr*, Mn, Fe, Co, Ni, Cu*, Zn, Ga, Ge, As, Se, Br, Kr]Lowest energy ----> Highest energy (Obey PEP, & Hund’s Rule)
En,l = - (Zeffective)2•Ry/n2
Energy
En,l
1s
2s
2p
3s
3p
4s
3d
4p
{ H , He }
{ Li , Be }
{ B,C,O,N,F,Ne}
{ K , Ca }
{ Na , Mg}
{Al,Si,P,S,Cl,Ar}
{Ga,Ge,As,Se,Br,Kr}
{Sc,Ti,V,Cr*,Mn,Fe,Co,Ni,Cu*,Zn}
Not to scale.
Aufbau ordering:(Ground StateConfigurations)
21
Figure 12.27 - Zumdahl - Chemical Principles (4/e)
Electron Configuration Correlated with Periodic Table:[4th Row (Period) - Ground State (note 24Cr & 29Cu)]:
22
“Condensed” Formats to Represent Electron Configurations:[page 7 of “QM & PT” handout]
Example: Sulfur (S) [For Orbital Box Diagram - see below]• Spectroscopic: 1s2 2s2 2p6 3s2 3p4 [in order of $ energy]• Noble gas core abbreviation : [Ne] 3s2 3p4
(3s & 3p e-’s are the VALENCE electrons)
En,l = - (Zeffective)2•Ry/n2
Energy
En,l
1s
2s
2p
3s
3p
Not to scale.
Aufbau ordering:(Ground StateConfigurations)
SULFUR (S)
23
Figure 12.28 - Zumdahl - Chemical Principles (4/e)
Electron Configuration Correlated with Periodic Table:
24
“Follow” the Periodic Table to Determine Ground StateElectron Configurations:
[page 5 of “QM & PT” handout]
• Transition metals: [Noble gas core] ns2 (n-1)d1 --> 10 (n = row #)[Some exceptions … Cr = [Ar] 4s1 3d5 , Cu = [Ar] 4s1 3d10]
• Lanthanides (Between 57La & 72Hf - 6th row): [Xe] 6s2 5d1 4f1 ---> 14 [58Ce through 71Lu]. [Some exceptions … Don’t worry about exceptions.]
• Actinides (Between 89Ac & 104Rf - 7th row): [Rn] 7s2 6d1 5f1 ---> 14 [90Th through 103Lr]. [Some exceptions … Don’t worry about exceptions.]
25
Figure 12.29 - Zumdahl - Chemical Principles (5/e)
Electron Configuration Correlated with Periodic Table:
26
Main Group Elements & Valence Shell Electron Configuration[page 8 of “QM & PT” handout]
Group Valence Shell e- Config*. # of Valence e-’s1A ns1 12A ns2 23A ns2 np1 34A ns2 np2 45A ns2 np3 56A ns2 np4 67A ns2 np5 78A ns2 np6 8
*[n is the row # (period) of the element in the group.]
27
Ground State Electron Configuration of Ions[page 8 & page 9 of “QM & PT” handout]
Cations:• Construct ground state electron configuration of NEUTRAL atom first.• Remove e-’s from populated shell of HIGHEST principal quantum # (n) until proper cation charge is achieved*. * If more than one subshell of highest principal quantum # is populated, BEGIN with subshell of HIGHEST l quantum #. (i.e., subshell that is MOST [<--- corrected] shielded.) *[n is the row # (period) of the element in the group.]Examples: Fe+2 & Pb+4:1st Fe: [Ar] 4s2 3d6 , then, Fe+2 : [Ar] 3d6 (NOT [Ar] 4s2 3d4).1st Pb: [Xe] 6s2 4f14 5d106p2 , then, Pb+4 : [Xe] 4f14 5d10 (NOT [Xe] 6s2 4f14 5d8).
28
Ground State Electron Configuration of Ions[page 8 & page 9 of “QM & PT” handout]
Anions (page 9):• Typically involve non-metals in the p-block.
• Construct ground state electron configuration of NEUTRAL atom first.
• Continue to add electrons consistent with the Aufbau ordering scheme.
Example: O-2 (oxide anion)1st O: [He] 2s2 2p4 , then O-2 : [He] 2s2 2p6
= [Ne] (isolectronic with Ne).
29
Paramagnetism & Diamagnetism(unpaired e-’s vs all e-’s paired )
[page 9 & page 10 (diagram) of “QM & PT” handout]
Weights
Sample - suspendedfrom one side of balance.
Magnet
Balance
SN
30
Paramagnetism & Diamagnetism(unpaired e-’s vs all e-’s paired )
[page 9 & page 10 (diagram) of “QM & PT” handout]
• Construct electron configuration of species & determine if there are any unpaired e-’s [orbital box diagram.]• If ANY unpaired e-’s & PARAMAGNETIC. Species is ATTRACTED by a magnetic field. # of unpaired electrons determines “degree of paramagnetism”. As # of unpaired e-’s $, degree of paramagnetism $’s. Species is a"racted more strongly by magnetic field.• If NO unpaired e-’s, i.e., all are paired & DIAMAGNETIC. Species is NOT a"racted by a magnetic field.
31
Figure 12.38 - Zumdahl - Chemical Principles (4/e)
Atomic Radii (in pm) (Main Group Elements): [pp. 11 - 16.]
32
Figure 13.7 - Zumdahl - Chemical Principles (4/e)
Ionic Radii (in pm) (Main Group Elements): [pp. 11 - 16.]
33
Figure 12.35 - Zumdahl - Chemical Principles (4/e)
1st IE’s (Main Group Elements): [pp. 11 - 16.]M(gas) -----> M+(gas) + e- ; $E =IE1 (+)
34
Figure 12.36 - Zumdahl - Chemical Principles (4/e)
Electron A%nities (EA) (Main Group Elements): [pp. 11 - 16.]A(gas) + e- -----> A-(gas) ; $E = EA (+ or -)
35
Figure 13.3 - Zumdahl - Chemical Principles (4/e)
Electronegativities (Pauling Values):
36
PERIODIC TRENDS - SUMMARY[See QM & Periodic Table - pages 11-14]
Radius, Diameter, Size [Fig. 12.38, Zumdahl] :• DECREASES L ---> R across a row (period) - generally. [Ze! increases].
• INCREASES Top ---> Bo"om down a column (group). [Ze! “decreases” … outermost e-’s “farther away” from nucleus.]
Ionic Radius, Diameter, Size [Fig. 13.7, Zumdahl] :• Radius of CATION < corresponding NEUTRAL ATOM.
• Radius of ANION > corresponding NEUTRAL ATOM.
37
PERIODIC TRENDS - SUMMARY[See QM & Periodic Table - pages 11-14]
IONIZATION ENERGY (1st IE) :A(gas) ' A+(gas) + e- IE of A = $E of reaction (+).• INCREASES L ---> R across a row (period) - generally. [Ze! increases]. “Glitches”. Look at (ground state) e- configs. IE1 values [3rd row (period)] (in kJ/mol): Na Mg Al Si P S Cl Ar 500 740 580 790 1060 1000 1260 1520 3s1 3s2 3p1 3p2 3p3 3p4 3p5 3p6 [before] 3s0 3s1 3p0 3p1 3p2 3p3 3p4 3p5 [after]
• DECREASES Top ---> Bo"om down a column (group). IE1 values [Group 2A)] (in kJ/mol): Be (900) ; Mg (740) ; Ca (590) ; Sr (550) ; Ba (500)
38
PERIODIC TRENDS - SUMMARY[See QM & Periodic Table - page 13]
SUCCESSIVE IONIZATION ENERGIES (IE1 … IEn). • Example - Aluminum (Al) :
Al(gas) ' Al+(gas) + e- IE1 = 580 kJ/mol [3p1 ----> 3p0].
Al+(gas) ' Al+2(gas) + e- IE2 = 1,820 kJ/mol [3s2 ----> 3s1].
Al+2(gas) ' Al+3(gas) + e- IE3 = 2,740 kJ/mol [3s1 ----> 3s0].
Al+3(gas) ' Al+4(gas) + e- IE4 = 11,580 kJ/mol [2p6 ---->2p5].
39
PERIODIC TRENDS - SUMMARY[See QM & Periodic Table - page 15]
ELECTRON AFFINITY (EA) - energy change of reaction: A(gas) + e- ' A-(gas) EA of A = $E (+ or -).• More negative - more exothermic acquisition.• More negative (generally) L ---> R . across a row (period). “Quirky”.• Less negative (generally) Top ---> Bo"om down a column (group). “Quirky”. Li Be B C N O F-59.6 (+) -26.7 -122 (+) -141 -328 Na Mg Al C P S Cl-59.6 (+) -43 -134 -72 -200 -349 Br -325
40
PERIODIC TRENDS - SUMMARY[See QM & Periodic Table - page 16]
ELECTRONEGATIVITY (x) - measure of ability for atom to “draw” electron density from an atom to which it ischemically bonded.
• F = greatest = 4.0 , H = 2.1 , Group 1A metals - “least”.
• INCREASES L ---> R across a row (period). [“closer to F”]
• DECREASES Top ---> Bo"om down a column (group). [“farther away from F”] continued …
41
PERIODIC TRENDS - SUMMARYElectronegativity Di!erence ($x) &• Covalent versus Ionic Bonds:xA & xB = electronegativity of atoms A & B, respectively.(x = | xA - xB | = magnitude of the electronegativity di!erence between atoms A & B.If (x = 0 (Exactly) AB bond is purely covalent (or non-polar).If 0 < (x & 1.7 AB bond is polar covalent, i.e., the electrons are “polarized” toward with larger x.If (x > 1.7 AB bond is ionic, i.e., the electrons in the bond are“totally owned” by atom with larger x (anion) & “totallylost” by atom with smaller x (cation).