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Quantum Mechanics
• Orbital (“electron cloud”)
– Region in space where there is 90% probability of finding an electron
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Electron Probability vs. Distance
Ele
ctro
n P
roba
bilit
y (%
)
Distance from the Nucleus (pm)
100 150 200 2505000
10
20
30
40
Orbital
90% probability offinding the electron
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Quantum Numbers
UPPER LEVEL
• Four Quantum Numbers:
– Specify the “address” of each electron in an atom
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Quantum Numbers
Principal Quantum NumberPrincipal Quantum Number ( nn )
Angular Momentum Quantum #Angular Momentum Quantum # ( ll )
Magnetic Quantum NumberMagnetic Quantum Number ( mmll )
Spin Quantum NumberSpin Quantum Number ( ms )
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Quantum Numbers
1. Principal Quantum NumberPrincipal Quantum Number ( nn )
– Energy level
– Size of the orbital
– n2 = # of orbitals in the energy level
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
1s
2s
3s
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1s orbital imagined as “onion”
Concentric spherical shells
Copyright © 2006 Pearson Benjamin Cummings. All rights reserved.
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Shapes of s, p, and d-Orbitals
s orbital
p orbitals
d orbitals
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Atomic Orbitals
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s, p, and d-orbitals
As orbitals:
Hold 2 electrons(outer orbitals ofGroups 1 and 2)
Bp orbitals:
Each of 3 pairs oflobes holds 2 electrons
= 6 electrons(outer orbitals of Groups 13 to 18)
Cd orbitals:
Each of 5 sets oflobes holds 2 electrons
= 10 electrons(found in elements
with atomic no. of 21and higher)
Kelter, Carr, Scott, , Chemistry: A World of Choices 1999, page 82
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Copyright © 2006 Pearson Benjamin Cummings. All rights reserved.
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(a) 1s (b) 2s (c) 3s
r r
21s
r r
22s
r r
23s
Distance from nucleus
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Quantum Numbers
px pz py
x
y
z
x
y
z
x
y
z
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Copyright © 2007 Pearson Benjamin Cummings. All rights reserved.
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Quantum Numbers
s p d f
2. Angular Momentum Quantum #Angular Momentum Quantum # ( ll )– Energy sublevel
– Shape of the orbital
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The azimuthal quantum number
Second quantum number l is called the azimuthal quantum number
– Value of l describes the shape of the region of space occupied by the electron
– Allowed values of l depend on the value of n and can range from 0 to n – 1
– All wave functions that have the same value of both n and l form a subshell
– Regions of space occupied by electrons in the same subshell have the same shape but are
oriented differently in space
Copyright © 2006 Pearson Benjamin Cummings. All rights reserved.
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Maximum Capacities of Subshells and Principal Shells
n 1 2 3 4 ...n
l 0 0 1 0 1 2 0 1 2 3
SubshellSubshelldesignationdesignation s s p s p d s p d f
Orbitals inOrbitals insubshell subshell 1 1 3 1 3 5 1 3 5 7
SubshellSubshellcapacity capacity 2 2 6 2 6 10 2 6 10 14
Principal shellPrincipal shellcapacity capacity 2 8 18 32 ...2n2
Hill, Petrucci, General Chemistry An Integrated Approach1999, page 320
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Quantum Numbers
3. Magnetic Quantum NumberMagnetic Quantum Number ( mmll )
– Orientation of orbital
– Specifies the exact orbital within each sublevel
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The magnetic quantum number
Third quantum is ml, the magnetic quantum number
– Value of ml describes the orientation of the region in space occupied by the electrons with
respect to an applied magnetic field
– Allowed values of ml depend on the value of l
– ml can range from –l to l in integral steps ml = l, -l + l, . . . 0 . . ., l – 1, l
– Each wave function with an allowed combination of n, l, and ml values describes an
atomic orbital, a particular spatial distribution for an electron
– For a given set of quantum numbers, each principal shell contains a fixed number of subshells, and each subshell contains a fixed number of orbitals
Copyright © 2006 Pearson Benjamin Cummings. All rights reserved.
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d-orbitals
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 336
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Quantum Numbers
4. Spin Quantum NumberSpin Quantum Number ( ms )
– Electron spin +½ or -½
– An orbital can hold 2 electrons that spin in opposite directions.
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Electron Spin: The Fourth Quantum Number
• When an electrically charged object spins, it produces a magnetic moment parallel to the axis of rotation and behaves like a magnet.
• A magnetic moment is called electron spin.
• An electron has two possible orientations in an external magnetic field, which are described by a fourth quantum number ms.
• For any electron, ms can have only two possible values, designated + (up) and – (down), indicating that the two orientations are opposite and the subscript s is for spin.
• An electron behaves like a magnet that has one of two possible orientations, aligned either with the magnetic field or against it.
Copyright © 2006 Pearson Benjamin Cummings. All rights reserved.
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Quantum Numbers
1. Principal #
2. Ang. Mom. #
3. Magnetic #
4. Spin #
energy level
sublevel (s,p,d,f)
orbital
electron
• Pauli Exclusion PrinciplePauli Exclusion Principle
– No two electrons in an atom can have the same 4 quantum numbers.
– Each electron has a unique “address”:
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Wolfgang Pauli
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Level n 1 2 3
Sublevel l Orbital ml
Spin ms
0 0
0 0 1 0 -1 0 1 0 -1 2 1 0 -1 -2
2101
= +1/2
= -1/2
Allowed Sets of Quantum Numbers for Electrons in Atoms
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Electron Orbitals:
Electronorbitals
EquivalentElectronshells
(a) 1s orbital (b) 2s and 2p orbitals c) Neon Ne-10: 1s, 2s and 2p
1999, Addison, Wesley, Longman, Inc.
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What sort of covalent bonds are seen here?
H H
H
H
O H
H
H
HO
OO O O
(b) O2
(d) CH4(c) H2O
O H
H
(a) H2
H H
C H
H
H
H
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H = 1s1
1s
He = 1s2
1s
Li = 1s2 2s1
1s 2s
Be = 1s2 2s2
1s 2s
C = 1s2 2s2 2p2
1s 2s 2px 2py 2pz
S = 1s2 2s2 2p63s2 3p4
1s 2s 2px 2py 2pz 3s 3px 3py 3pz
THIS SLIDE IS ANIMATEDIN FILLING ORDER 2.PPT
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Fe = 1s1 2s22p63s23p64s23d6
1s 2s 2px 2py 2pz 3s 3px 3py 3pz
+26
e-
e-
e-
e-
4s 3d 3d 3d 3d
Iron has ___ electrons.26
3d
ArbitraryEnergy Scale
18
18
32
8
8
2
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
e-
e-e-
e-
e- e-
e-
e-
e-
e-
e-
e-
e-e-
e-
e-
e-
e-
e- e-
e-
e-
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Orbital Filling
Element 1s 2s 2px 2py 2pz 3s Configuration
Orbital Filling
Element 1s 2s 2px 2py 2pz 3s Configuration
Electron ConfigurationsElectron
H
He
Li
C
N
O
F
Ne
Na
1s1
1s22s22p63s1
1s22s22p6
1s22s22p5
1s22s22p4
1s22s22p3
1s22s22p2
1s22s1
1s2
NOT CORRECTViolates Hund’s
Rule
Electron ConfigurationsElectron
H
He
Li
C
N
O
F
Ne
Na
1s1
1s22s22p63s1
1s22s22p6
1s22s22p5
1s22s22p4
1s22s22p3
1s22s22p2
1s22s1
1s2
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Orbital Filling
Element 1s 2s 2px 2py 2pz 3s Configuration
Electron ConfigurationsElectron
H
He
Li
C
N
O
F
Ne
Na
1s1
1s22s22p63s1
1s22s22p6
1s22s22p5
1s22s22p4
1s22s22p3
1s22s22p2
1s22s1
1s2
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Filling Rules for Electron Orbitals
Aufbau Principle: Electrons are added one at a time to the lowest energy orbitals available until all the electrons of the atom have been accounted for.
Pauli Exclusion Principle: An orbital can hold a maximum of two electrons.To occupy the same orbital, two electrons must spin in opposite directions.
Hund’s Rule: Electrons occupy equal-energy orbitals so that a maximum number of unpaired electrons results.
*Aufbau is German for “building up”
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Filling Rules for Electron Orbitals
Aufbau Principle: Electrons are added one at a time to the lowest energy orbitals available until all the electrons of the atom have been accounted for.
Pauli Exclusion Principle: An orbital can hold a maximum of two electrons.To occupy the same orbital, two electrons must spin in opposite directions.
Hund’s Rule: Electrons occupy equal-energy orbitals so that a maximum number of unpaired electrons results.
*Aufbau is German for “building up”
ArbitraryEnergy Scale
18
18
32
8
8
2
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
North
S
South
N
- -
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Spin Quantum Number, ms
North
South
The electron behaves as if it were spinning about an axis through its center.This electron spin generates a magnetic field, the direction of which dependson the direction of the spin.
Brown, LeMay, Bursten, Chemistry The Central Science, 2000, page 208
- -S
N
Electron aligned with magnetic field,
ms = + ½
Electron aligned against magnetic field,
ms = - ½
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Energy Level Diagram of a Many-Electron Atom
ArbitraryEnergy Scale
18
18
32
8
8
2
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
O’Connor, Davis, MacNab, McClellan, CHEMISTRY Experiments and Principles 1982, page 177
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Maximum Number of Electrons In Each SublevelMaximum Number of Electrons In Each Sublevel
Maximum Number Sublevel Number of Orbitals of Electrons
s 1 2
p 3 6
d 5 10
f 7 14
LeMay Jr, Beall, Robblee, Brower, Chemistry Connections to Our Changing World , 1996, page 146
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Quantum Numbers
n shell
l subshell
ml orbital
ms electron spin
1, 2, 3, 4, ...
0, 1, 2, ... n - 1
- l ... 0 ... +l
+1/2 and - 1/2
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Order in which subshells are filled with electrons
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
3d
4d
5d
6d
4f
5f
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d … 2 2 6 2 6 2 10 6 2 10
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
Bohr Model
Electron Configuration
CLICK ON ELEMENT TO FILL IN CHARTS
N
H He Li C N Al Ar F Fe La
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
Bohr Model
Electron Configuration
CLICK ON ELEMENT TO FILL IN CHARTS
N
H = 1s1
Hydrogen
H He Li C N Al Ar F Fe La
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
Bohr Model
Electron Configuration
CLICK ON ELEMENT TO FILL IN CHARTS
N
He = 1s2
Helium
H He Li C N Al Ar F Fe La
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
Bohr Model
Electron Configuration
CLICK ON ELEMENT TO FILL IN CHARTS
N
Li = 1s22s1
Lithium
H He Li C N Al Ar F Fe La
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
Bohr Model
Electron Configuration
CLICK ON ELEMENT TO FILL IN CHARTS
N
C = 1s22s22p2
Carbon
H He Li C N Al Ar F Fe La
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
Electron Configuration
CLICK ON ELEMENT TO FILL IN CHARTS
N
N = 1s22s22p3
Bohr Model
Nitrogen
Hund’s Rule “maximum number of unpaired
orbitals”.
H He Li C N Al Ar F Fe La
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
Bohr Model
Electron Configuration
CLICK ON ELEMENT TO FILL IN CHARTS
N
F = 1s22s22p5
Fluorine
H He Li C N Al Ar F Fe La
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
Bohr Model
Electron Configuration
CLICK ON ELEMENT TO FILL IN CHARTS
N
Al = 1s22s22p63s23p1
Aluminum
H He Li C N Al Ar F Fe La
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
Electron Configuration
CLICK ON ELEMENT TO FILL IN CHARTS
N
Ar = 1s22s22p63s23p6
Bohr Model
Argon
H He Li C N Al Ar F Fe La
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
CLICK ON ELEMENT TO FILL IN CHARTS
Fe = 1s22s22p63s23p64s23d6
N
H He Li C N Al Ar F Fe La
Bohr Model
Iron
Electron Configuration
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Energy Level Diagram
Arb
itrar
y E
nerg
y S
cale
1s
2s 2p
3s 3p
4s 4p 3d
5s 5p 4d
6s 6p 5d 4f
NUCLEUS
CLICK ON ELEMENT TO FILL IN CHARTS
La = 1s22s22p63s23p64s23d10
4s23d104p65s24d105p66s25d1
N
H He Li C N Al Ar F Fe La
Bohr Model
Lanthanum
Electron Configuration
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neon's electron configuration (1s22s22p6)
Shorthand Configuration
[Ne] 3s1
third energy level
one electron in the s orbital
orbital shape
Na = [1s22s22p6] 3s1 electron configuration
AA
BB
CC
DD
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Shorthand Configuration
[Ar] 4s2
Electron configurationElement symbol
[Ar] 4s2 3d3
[Rn] 7s2 5f14 6d4
[He] 2s2 2p5
[Kr] 5s2 4d9
[Kr] 5s2 4d10 5p5
[Kr] 5s2 4d10 5p6
[He] 2s22p63s23p64s23d6
Ca
V
Sg
F
Ag
I
Xe
Fe [Ar] 4s23d6
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General Rules
• Pauli Exclusion PrinciplePauli Exclusion Principle
– Each orbital can hold TWO electrons with
opposite spins.
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Wolfgang Pauli
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General Rules
Aufbau PrincipleAufbau Principle
– Electrons fill the lowest energy orbitals first.
– “Lazy Tenant Rule”
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
2s
3s
4s
5s
6s
7s
1s
2p
3p
4p
5p
6p
3d
4d
5d
6d
4f
5f
1s
2s
2p
3s
3p
4s
4p
3d
4d5s
5p6s
7s
6p
6d
4f
5f
5d
En
erg
y
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RIGHTWRONG
General Rules
• Hund’s RuleHund’s Rule
– Within a sublevel, place one electron per orbital before pairing them.
– “Empty Bus Seat Rule”
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
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O
8e-
• Orbital Diagram
• Electron Configuration
1s1s22 2s2s22 2p2p44
Notation
1s 2s 2p
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
O15.9994
8
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• Shorthand Configuration
S 16e-
Valence ElectronsValence ElectronsCore ElectronsCore Electrons
S 16e- [Ne] 3s2 3p4
1s2 2s2 2p6 3s2 3p4
Notation
• Longhand Configuration
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
S32.066
16
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sp
d (n-1)
f (n-2) 67
Periodic Patterns
11ss
22ss
33ss
44ss
55ss
66ss
77ss
33dd
44dd
55dd
66dd
11ss
22pp
33pp
44pp
55pp
66pp
77pp
44ff
55ff
1234567
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Periodic Patterns
• Period #– energy level (subtract for d & f)
• A/B Group # – total # of valence e-
• Column within sublevel block– # of e- in sublevel
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
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s-block1st Period
1s11st column of s-block
Periodic Patterns
• Example - Hydrogen
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
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1
2
3
4
5
6
7
Periodic Patterns
• Shorthand Configuration– Core electrons:
• Go up one row and over to the Noble Gas.
– Valence electrons: • On the next row, fill in the # of e- in each sublevel.
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
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[Ar] 4s2 3d10 4p2
Periodic Patterns
• Example - GermaniumGermanium
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Ge72.61
32
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• Full energy level
1
2
3
4
5
6
7
• Full sublevel (s, p, d, f)• Half-full sublevel
Stability
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This fills the valenceshell and tends to givethe atom the stabilityof the inert gasses.
The Octet Rule
Atoms tend to gain, lose, or share electrons until they have eight valence electrons.
8
ONLY ss- and pp-orbitals are valence electrons.
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Write out the complete electron configuration for the following:1) An atom of nitrogen
2) An atom of silver
3) An atom of uranium (shorthand)
Fill in the orbital boxes for an atom of nickel (Ni)
2s 2p 3s 3p 4s 3d1s
Which rule states no two electrons can spin the same direction in a single orbital?
Extra credit: Draw a Bohr model of a Ti4+ cation.
Ti4+ is isoelectronic to Argon.
POP QUIZ
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Write out the complete electron configuration for the following:1) An atom of nitrogen
2) An atom of silver
3) An atom of uranium (shorthand)
Fill in the orbital boxes for an atom of nickel (Ni)
2s 2p 3s 3p 4s 3d1s
Which rule states no two electrons can spin the same direction in a single orbital?
1s22s22p3
1s22s22p63s23p64s23d104p65s24d9
[Rn]7s26d15f3
Extra credit: Draw a Bohr model of a Ti4+ cation. 22+n = n
Pauli exclusion principle
Ti4+ is isoelectronic to Argon.
Answer Key
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Electron Configurations of First 18 Elements:Hydrogen
1H
Lithium
3Li
Sodium
11NaMagnesium
12Mg
Boron
5B
Aluminum
13Al
Carbon
6C
Silicon
14SiPhosphorous
15P
Oxygen
8O
Sulfur
16S
Fluorine
9F
Chlorine
17Cl
Neon
10Ne
Argon
18Ar
Beryllium
4BeNitrogen
7N
Helium
2He
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Electron Dot Diagrams
H
Li
Na
K
Be
Mg
Ca
B
Al
Ga
C
Si
Ge
N
P
As
O
S
Se
F
Cl
Br
Ne
Ar
Kr
He
Group
1A 2A 3A 4A 5A 6A 7A 8A
= valence electron
s1 s2 s2p2 s2p3 s2p4 s2p5 s2p6s2p1
1 2 13 14 15 16 17 18
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V. Outer Level e-’s
• Valence electrons
• Usually involved in chemical changes
• Dot diagram–Symbol represents the nucleus
–Dots represent the outer e-’s
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