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© Prof. Zvi C. Koren1 19.07.10
:8' נושא מסהמבנה האלקטרוני של אטומים
Electronic Structure of Atoms
© Prof. Zvi C. Koren2 19.07.10
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)
© Prof. Zvi C. Koren3 19.07.10
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
© Prof. Zvi C. Koren4 19.07.10
(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
© Prof. Zvi C. Koren5 19.07.10
# 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
© Prof. Zvi C. Koren6 19.07.10
":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
© Prof. Zvi C. Koren7 19.07.10
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.
© Prof. Zvi C. Koren8 19.07.10
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
© Prof. Zvi C. Koren9 19.07.10
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:
© Prof. Zvi C. Koren10 19.07.10
8A1A
He7A6A5A4A3A2A
H
NeFONCBBeLi
ArClSPSiAl2B1B8B7B6B5B4B3B
MgNa
Where Are the E’s: Another Look
For 11Na:
1s
2s
2p
3s
Recall:Orbitals are notsolid physical structures, but
probability functions.
© Prof. Zvi C. Koren11 19.07.10
pds
8APeriodic Table
of the
Elements
1A
He7A6A5A4A3A2A
H
NeFONCBBeLi
ArClSPSiAl2B1B8B7B6B5B4B3B
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.)
© Prof. Zvi C. Koren12 19.07.10
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
© Prof. Zvi C. Koren13 19.07.10
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
ArClSPSiAl2B1B8B7B6B5B4B3B
MgNa
KrBrSeAsGeGaZnCuNiCoFeMnCrVTiScCaK
Cr expected: [Ar] 4s2 3d4
4s3d
Cr actual: [Ar] 4s1 3d5
4s3d
© Prof. Zvi C. Koren14 19.07.10
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
ArClSPSiAl2B1B8B7B6B5B4B3B
MgNa
KrBrSeAsGeGaZnCuNiCoFeMnCrVTiScCaK
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
© Prof. Zvi C. Koren15 19.07.10
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
© Prof. Zvi C. Koren
© Prof. Zvi C. Koren17 19.07.10
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
ArClSPSiAl2B1B8B7B6B5B4B3B
MgNa
KrBrSeAsGeGaZnCuNiCoFeMnCrVTiScCaK
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
© Prof. Zvi C. Koren18 19.07.10
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
ArClSPSiAl2B1B8B7B6B5B4B3B
MgNa
KrBrSeAsGeGaZnCuNiCoFeMnCrVTiScCaK
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
© Prof. Zvi C. Koren19 19.07.10
Metallicity
Non-metallicity
Atomic Properties & Periodic Trends:Metallic vs. Non-metallic Trends in the Periodic Table
Electronegativity also follows this trend (later)
© Prof. Zvi C. Koren20 19.07.10
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
© Prof. Zvi C. Koren21 19.07.10
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
© Prof. Zvi C. Koren22 19.07.10
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)
© Prof. Zvi C. Koren23 19.07.10
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
© Prof. Zvi C. Koren24 19.07.10
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.
© Prof. Zvi C. Koren25 19.07.10
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.
© Prof. Zvi C. Koren26 19.07.10
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.
© Prof. Zvi C. Koren27 19.07.10
Electronegativities
Ability of a bonded atom to attract bonding e’s
Pauling
Scale