:8 'סמ אשונ םימוטא לש ינורטקלאה הנבמה · K Ca Sc Ti V Cr Mn Fe Co Ni Cu...

© Prof. Zvi C. Koren1 19.07.10

:8' נושא מסהמבנה האלקטרוני של אטומים

Electronic Structure of Atoms


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:

ms = (magnetic) spin quantum number = +½ or –½ (±½)

(designates the “direction” of the “spin” of the e)


Quantum Numbers

Allowed ValuesStructural

NameProperty

Property

NameQ.N.

1, 2, …, ShellRelated to the energy of the

e orbiting about the nucleus

Principal

q.n.n

0, 1, 2, 3, 4,…, n – 1

s, p, d, f, g, …Sub-shell

Related to the angular

momentm of the e orbiting

about the nucleus

Angular

Momentum

q.n.

ℓ

–ℓ , …, 0, …,+ ℓ“Orbital”

Related to the magnetic

property of the e orbiting

about the nucleus

Magnetic

q.n.mℓ

± ½, or e orientation

Related to the magnetic

property of the e “spinning”

about its own axis

Spin q.n.ms

Sch

rod

ing

erP

auli

4 Quantum Numbers are needed to characterize an electron

The 4 Q.N.’s can be considered as the electron’s:

I.D. # or Address


(n, ℓ, mℓ, ms)electron 1 (n, ℓ, mℓ, ms)electron 2

“No two electrons can have the same set of

four quantum numbers.”

The maximum # of e’s in any orbital = 2

Pauli Exclusion Principle

Wolfgang Pauli(1900 – 1958, Austria & Switzerland)

Nobel Prize in Physics, 1945

For polyelectronic atoms:

Each electron has a unique set

of 4 quantum numbers


# of e’sOrbitalsmℓ valuesSubshellsℓ valuesn, Shell

21s01s01

22s02s02

62px, 2py, 2pz-1, 0, 12p1

23s03s0

3 63px, 3py, 3pz-1, 0, 13p1

10-2, -1, 0, 1, 23d2

4

5

# of Electrons in Orbitals of a Subshell of a Shell

(Complete this table)

222 zy-xyzxzxy 3d ,3d ,3d ,3d ,3d


":מה נשתנה" שאלתWhy is H different from all other atoms?

H

For H and H-like ions, from Schrödinger (and Bohr): En = f(n) = –(13.6 eV) Z2/n2

For non-H atoms: En,ℓ = f(n,ℓ)

Non-H (not to scale)

Atomic Subshell Energy Levels

1s-

2s-

3s-

4s-

5s-

6s-

7s-

2p---

3p---

4p---

5p---

6p---

3d-----

4d-----

5d-----

6d-----

4f-------

5f-------

1s-

2s-

3s-

4s-

5s-

6s-7s-

2p---

3p---

4p---

5p---

6p---

3d-----

4d-----

5d-----

6d-----

4f-------

5f-------

6f-------

(“Degenerate” subshells)

(“Degenerate” orbitals)

Note:For a given n,as ℓ increases,

E increases

E


1s

2s 2p

3s 3p 3d

4s 4p 4d 4f

5s 5p 5d 5f 5g

6s 6p 6d 6f 6g 6h

7s 7p ...

Aufbau Principlevia

Triangulation and “n+ℓ” values

1

32

45

67

n+ℓ

Order of Filling of Subshells

Example: Write the electronic configuration of 88Ra (radium).

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2

The subshell with the

lowest “n+ℓ” value

(and with the lower “n”)

is the most stable and

gets filled first.


Hund’s Rule

(The “Bus Seat” Rule)

Friedrich Hund

(1896 – 1997, Germany)

Consider the electronic configurations of:

7N, 8O, 9F, 10Ne:

1s

2s

2p

1s

2s

2p

1s

2s

2p

1s

2s

2p

7N 8O 9 F 10Ne


Atomic Electronic Configurations:

3 Different Representations

Full Line Notation

(Spectroscopic Notation):

15P: 1s2 2s2 2p6 3s2 3p3

Shorthand Notation

(Noble Gas Notation):

15P: [Ne] 3s2 3p3

Orbital Energy Notation (Box Notation):

1s

2s

2p

Innere’s

Outere’s

8A1A

He7A6A5A4A3A2A

H

NeFONCBBeLi

ArClSPSiAl2B1B8B7B6B5B4B3B

MgNa

7N:


8A1A

He7A6A5A4A3A2A

H

NeFONCBBeLi


MgNa

Where Are the E’s: Another Look

For 11Na:

1s

2s

2p

3s

Recall:Orbitals are notsolid physical structures, but

probability functions.


pds

8APeriodic Table

of the

Elements

1A

He7A6A5A4A3A2A

H

NeFONCBBeLi


MgNa

KrBrSeAsGeGaZnCuNiCoFeMnCrVTiScCaK

XeITeSbSnInCdAgPdRhRuTcMoNbZrYSrRb

RnAtPoBiPbTlHgAuPtIrOsReWTaHfLu*BaCs

UuoUusUuhUupUuqUutUubRgDsMtHsBhSgDbRfLr*

*RaFr

fYbTmErHoDyTbGdEuSmPmNdPrCeLa*

NoMdFmEsCfBkCmAmPuNpUPaThAc*

*

Electronic Structures of the Atoms:Periodic Blocks of the Periodic Table

(Find the shorthand noble-gas configurations of some elements.)


1s

2s

2p

3s

3p

3d

(ao = Bohr radius = 0.529 Å)

RadialProbabilityFunctions

EffectiveNuclearCharge:Zeff or Z*

= Z - S

Penetrationvs.

Shielding(Screening)

(radius by Bohr: 0.529 Å)

In a givenshell, n:

As ℓ increases,E increases.

Why?(As Z* increasese is more stable.)

What is Z*for each e

in 3Li?

E: 4s < 3dbecause 4spenetratesmore than

3d


In Cr: E4s E3d

Note: e’s more dispersed

(2 half-filled subshells)

Note: 2 e’s in same orbital (4s)

The key: One e makes the difference

between 2 closely spaced subshells

Anomalies in the Atomic Electronic Configurations8A

1A

He7A6A5A4A3A2A

H

NeFONCBBeLi


MgNa


Cr expected: [Ar] 4s2 3d4

4s3d

Cr actual: [Ar] 4s1 3d5

4s3d


Note: 2 e’s in same orbital (4s)

The key (again): One e makes the difference

between 2 closely spaced subshells

Anomalies in the Atomic Electronic Configurations8A

1A

He7A6A5A4A3A2A

H

NeFONCBBeLi


MgNa


Cu expected: [Ar] 4s2 3d9

4s3d

Cu actual: [Ar] 4s1 3d10

4s3d

In Cu: E4s E3d

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


Diamagnetism vs. Paramagnetism vs. Ferromagnetism

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.

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

Paramagnetism (at least one unpaired e)

Atoms with an unpaired e normally align themselves randomly so that the atoms’ magnetic fields cancel each other

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.

An external magnetic field induces an electric current into the material, with the electric current setting up an opposed magnetic field.

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.

normalin afield


Electronic Configurations of Ions – Main Group Atoms

Octet Rule:

Metallic atoms will lose e’s

to attain a Noble Gas configuration

Non-metals will accept e’s

8A1A

He7A6A5A4A3A2A

H

NeFONCBBeLi


MgNa


Na: [Ne] 3s1 Na+: [Ne]

Na+ is isoelectronic with Ne

–eS: [Ne] 3s2 3p4

+2eS2–: [Ne] 3s2 3p6

= [Ar]

S2– is isoelectronic with Ar

Cations Anions


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)8A1A

He7A6A5A4A3A2A

H

NeFONCBBeLi


MgNa


26Fe: [Ar] 4s2 3d6

Cationization occurs with the removal of the e’s

in the highest “n” value (and the higher ℓ)

4s 3d

Order of removal and the order of filling

are not necessarily the same

26Fe2+: [Ar] 3d6

4s 3d

Note: E4s E3d


Metallicity

Non-metallicity

Atomic Properties & Periodic Trends:Metallic vs. Non-metallic Trends in the Periodic Table

Electronegativity also follows this trend (later)


Atomic Properties & Periodic Trends:Atomic Size or Atomic Radii

The size, or radius, of an atom is not fixed, as the e’s can havestatistically varying positions around the nucleus (Schrödinger):

Here, we are discussing a statistical size, e.g., theaverage or most probable distance between the nucleus and the furthest e.

SIZE

Z vs. n

Z increasesBut

n increases

n constant (or decreases)But Z increases

Size: cation < free atom, anion > free atom

(Problem: Compare the sizes of the following isoelectronic species: O2–, F–, Na+, Mg2+)

O F

Na Mg


I.E.

Atomic Properties & Periodic Trends:Ionization Energies (or Ionization Potentials)

I.E.

SIZE

M(g) + I.E. M+(g) + e–Recall:

(Careful: The trend is not monotonic)

(The trend in sizes is more

monotonic than with I.E.’s.)

Metals

Non-metals


Why Does Mg form Mg2+ and not Mg+ or Mg3+ Ions?

Mg(g) Mg+(g) + e– 1st I.E. IE1 = 738 kJ/mol

[Ne]3s2

Mg+(g) Mg2+(g) + e– 2nd I.E. IE2 = 1451 kJ/mol

[Ne] 3s1

Mg2+(g) Mg3+(g) + e– 3rd I.E. IE3 = 7733 kJ/mol

[Ne]

8A1A

He7A6A5A4A3A2A

H

NeFONCBBeLi

ArClSPSiAlMgNa

The higher the charge, the stronger the ionic bond. So, why isn’t there Mg3+

Extremely high energy cost in forming the higher ionic charge (+3)


Experimental Evidence for Orbtal Energies8A1A

He7A6A5A4A3A2A

H

NeFONCBBeLi

2s1 2s2 2s22p1 2s22p2 2s22p3 2s22p4 2s22p5 2s22p6

1st IE(kJ/mol)

IE: Be > Beasier to remove e from 2p than 2s

IE: N > Oeasier to removea paired e in 2p4

than anunpaired e


Atomic Size & Ionization Energies of Transition Metals

1 pm = 10– 12 m

1 Å = 10– 10 m1 Å = 100 pm

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.


Lanthanide Contraction

Why is the atomic size of Au similar to Ag (and not greater)?

4f14

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.


Electron Affinities

X(g) + e– X–(g) + EA

IE

IE

EA

EA

EA’s show

many

exceptions to

the general

trend

Note: Both IE and EA are defined as positive quantities. BUT

IE is defined for an endothermic process and EA for an exothermic one.


Electronegativities

Ability of a bonded atom to attract bonding e’s

Pauling

Scale

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