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Chemistry 285 Advanced Inorganic Chemistry Lecture Notes Assoc. Prof. Joel R. Salazar

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### Transcript of Atomic Structure

Chemistry

Lecture Notes

Assoc. Prof. Joel R. Salazar

Chapter 1

Atomic Structure

Common Applications of Inorganic Chemistry

Polyelectronic Atom

Semi-empirical Method and Ab –initio Approximations : Hartree Fock Method (SCF) Assumptions1.) one reasonable φ for each electron2.) shielding or screeningNote: these assumptions are used to explain periodic

properties:a.) radius b.) electron affinity c.) ionization energy d.) electronegativity

Hartree – Fock SCF Orbitals Iterative method for solving the many-electron

Schrödinger equation

developed by D.R. Hartree (1928)

Effective Nuclear Charge

Sample Problem

What is the Zeff for P15

Ans: Zeff = 4.8

Sample Problem

2.) Calculate the Ionization energy for 13 Al.

13Al =1s2 (2s2p)8 3s23p1

Ans. 10.73 Kj

Solution

Alo = 1s2 (2s2p)8 (3s2 3po) = 2(0.35) + 8 (0.85) +2 (1.0) = 9.5

Al+ = 1s2 (2s2p)8 (3s1 ) = 1(0.35) + 8 (0.85) + 2(1.0) = 9.15

B.E. = 13.6 (Z –δ/n)2

B.E.Al (o) = 3 (13.6) (13 – 9.5/3)2 = 55.53

B.E.Al(+) = 2 (13.6) (13 – 9.15/3)2 = 44.80

I.E. = B.E. (Alo) - B.E.(Al+) = 10.73 Kj

What is the Zeff for Nickel

3d and 4s

3d = 7.55

4s = 4.05

Atomic Energy States

Term symbols: a shorthand notation that describes the electron distribution in atoms or ions, i.e. the ml and ms quantum numbers. Spectroscopists most frequently use these.

Microstate = defined as the different ways of putting the electrons in orbitals while taking into account the electron –electron repulsion

The result of calculation is called Russell –Saunders coupling and presented as an atomic term symbol

Spin- orbit Coupling = the spin and orbital angular momenta of individual electrons are strongly coupled together

The possible term symbols for various electron configurationElectron Configuration Term Symbol

s1 2S (2)

p1 2P (6)

p2 and p4 1S,1D,3P (15)

p3 2P,2D, 4S (20)

p1 and p5 2P (6)

d1 andd9 2D (10)

d2 and d8 1S,1D,1G,3P,3F (45)

d3 and d7 2P,2D,2F,2G,2H,4P,4F

d4 and d6

d5

Terms for Equivalent electrons

Terms for configuration

P6-n is the same as pn (p4 and p2; p1 and p5; p3

and p6)

D10-n is the same as dn ( d1 and d9, d2 and d8 etc.)

Term Symbols for nd2

Term Number of State

1G 9x1 =9

3F 7x3 =21

1D 5x1 =5

3P 3x3 =9

1S 1x1 =1

Total =45 (microstates)

Multiplicity

s1 l = 0 and s = ½

Term Symbol : 2S

2S +1 = 2(1/2) + 1 =2

p1 l =1 and s = ½

2S + 1 = 2 (1/2) + 1 = 2

Term Symbol : 2P

s1p1 parallel (3P)and antiparallel (1P)

Microstates (d2)

1.) ‖ _ _ _ _ L = 4 1G

2.) I I _ _ _ L = 3 3F

3.) _ ‖ _ _ _ L = 2 1D

4.) _ I I _ _ L = 1 3P

5.) _ _ ‖ _ _ L = 0 1S

What is the ground term of the configurations 3d5 of Mn2+ and 3d3 of Cr3+

Ans. 6S and 4F

The ML and Ms are tabulated in array

2 11 1 2 1

ML 0 1 3 1-1 1 2 1-2 1

-1 0 +1MS

Highest ML = 2 (the array ML = 2,1,0,-1,-2 exists

corresponding to L = 2)These values occur for Ms = 0A term with L = 2; S = 0 or1D

Term Symbols

The array after subtracting the microstate 1D2

1 1 1 1

Ml 0 0 1 2 1-1 1 1 1-2

-1 0 1

Ms

From the highest remaining ML = 1

The array ML = -1, 0, +1+ exists corresponding to L =1

These values occur for Ms = 1, 0 ,-1L = 1; and S = 1 or 3P

Term Symbols

The array after subtracting the microstate 3P

2

1

Ml 0 1

-1

-2

-1 0 1

Ms

Ml =0 and MS = 0 and 1S

Sample Problem

Use Hund’s rules to deduce the lowest energy state of an excited state of a Be atom whose electron configuration is 1s2 2s1 3s1 and of the ground state of a carbon atom 1s22s22p2

Ans: 3S1

3Po

Sample Problem

Identifying Ground State

3d2 Ans. 3F2

3d5 Ans. 6S5/2

3d8 Ans. 3F4

Sample problem

Show that the term symbol corresponding to an nd10

electron configuration is 1So

Note : Same as ns2 and np6

Sample Problem

Deduce the values of J associated with the term symbols 2S, 3D and 4F.

Problem Set 1

1.) a.) Determine the number of microstates associated with electron configuration p1d1

b.) Find out all the term symbols for this electron configuration

The Periodic Table

Lanthanide contraction

Note that although there is a significant increase in radius in going from the 3d to the 4d metals, the 4d and 5d metals are remarkably similar in size – a result of Lanthanide contraction

Electron Affinity = the energy change associated with the process in which the electron is added to a gaseous atom.

A(g) + e- ==== A-(g)

Measuring Electronegativity

1.) Mulliken ElectronegativityAssumption:

if the atoms I and EA are both low, then the atom will tend to lose electrons than gain them

χM = 1/2 (I + EA)Conversion between Pauling and Mulliken electronegativity

χP = 1.35 (χM)1/2 – 1.372.) Allred –Rochow DefinitionAssumption: Elements with high electronegativity are those with high

effective nuclear charge and with smaller covalent radius

χAR = 0.744 + 35.90 Zeff/ (r/pm)2

Polarizability (α)

Polarizability of an atom is its ability to be distorted by an electric field( such as that of the neighboring ion)

A polarizable atom or ion is one with orbitals that lie close in energy

Polarizability is likely to be high if the separation of the frontier orbitals is small

Large, heavy atoms and ions tend to be highly polarizable (closely separated frontier orbital)

Sample Problem

Which would be the more polarizable: an F- an I- ion?

Which would be more polarizing, Na+ or Cs+?Species that effectively distort the electron distribution of a neighboring atom or anion are described as having polarizing ability.

Fajans Rule (factors that affect polarization)1.) Small, highly charged cations have polarizing ability2.) Large, highly charged anions are easily polarized3.) Cations that do not have a noble –gas electron configuration are

easily polarized (important for d –block element)