Chapter One (continued)
Many Electron Atoms
and The Periodic Table
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Multielectron Atoms
• In the hydrogen atom, all subshells of a principal
shell are at the same energy level.
• In a multielectron atom, several electrons are
attracted to the nucleus while simultaneously
repelling one another.
• Orbital energies are lower in multielectron atoms
than in the hydrogen atom.
• In a multielectron atom the various subshells of a
principal shell are at different energy levels.
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Orbital Energy Diagrams
E =−
n 2 h2
8mL2
Z 2 me 4
E =− 2 2
2n h
2
E=−
Z eff me4
2n 2 h 2
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Penetration Effect
3s > 3p > 3d
Shielding Effect
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Slater’s Rule
• Slater's Rule determines the shielding constant which is
represented by S. To determine the effective nuclear charge use
this equation:
Z*=Z-S.
• According to Slater's rule, the electrons are grouped like:
(1s)(2s,2p)(3s,3p)(3d)(4s,4p)(4d)(4f)(5s,5p)(5d)(5f)...
• Electrons to the right of the electron you have chosen do not
contribute because they don't shield.
• In the same group, each electron shields 0.35.
• If the desired electron is in the (s,p) orbital, each electron in n-1
contribute 0.85.
• Electrons in n-2 contribute 1.00
• If the desired electron is in the (d,f) orbital, anything to the left
shields completely and therefore has a value of 1.0.
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Example 1: Na (Z= 11)
(1s)2(2s,2p)8(3s,3p)1
from a 3s perspective
S(3s)=8 x 0.85 + 2 x 1.0 = 8.8
So, Z(3s)*=11-8.8 = 2.2
from a 2s perspective
S(2s)=7 x 0.35 + 2 x 0.85 = 4.15
So, Z(3s)*=11-4.15 = 6.85
Example 2: Sc (Z= 21)
(1s)2(2s,2p)8(3s,3p)8(3d)1(4s,4p)2
from a 4s perspective
S(4s) = 1 x (0.35) + 1 x 0.85 + 18 x 1.0
= 19.2
So, Z(4s)*=21-19.2 = 1.8
from a 3d perspective
S(3d) = 8 x 1.0 + 10 x 1.0 = 18
So, Z(4s)*=21-18 = 3
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Principles of atom building
(the Aufbau Principle)
–
–
–
Quantum number principle
The hydrogen atom quantum numbers can be
used to describe electron states in any atoms
Minimum energy principle
place electrons in the states which lead atom
having the lowest energy
Pauli exclusion principle
No two electrons in the same atom may have
all four quantum numbers alike
(An atomic orbital can accommodate only two
electrons, and these electrons must have
opposing spins)
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Principles of atom building (continued)
–
Hund’s rule
For orbitals of half-filled or less than half-filled,
electrons will go into separate orbitals of the
same energy (degenerate orbitals) with parallel
spins
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Electron Configurations
• Electron configuration describes the distribution of
electrons among the various orbitals in the atom
• Electron configuration is represented in two ways
– The s, p, d, f notation
(Z = 1) H 1s1
(Z = 2) He 1s2
(Z = 3) Li 1s22s1 or, [He]2s1 Mn 1s22s22p63s23p64s23d5
C 1s22s22p2 or, [He]2s22p2
or
– An orbital diagram
3d
4s
Slide 11 of 39
(ml)
(0)
(0) (-1, 0, +1)
Slide 12 of 39
Subshell Filling Order
Slide 13 of 39
2
E=−
Z eff me4
2
2n h
2
Sc Z=21
In higher numbered principal
shells of a multielectron atom,
some subshells of different
principal shells have nearly
identical energies.
Slide 14 of 39
Ca [Ar]4s2
Ti [Ar]4s23d2
Ti+ [Ar]4s13d2
Ti2+ [Ar]3d2
Fe2+ [Ar]3d6
Slide 15 of 39
Exceptions to the Aufbau Principle
• Elements will fill out a lower subshell to obtain a lower
energy state
• Cr and Cu fill out their 3d shell before the 4s shell.
Elements in the same family as Cr and Cu behave in a
similar way.
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Main Group and Transition Elements
• Elements in which the orbitals being filled in the aufbau
process are either s or p orbitals of the outermost shell
are called main group elements
• The first 20 elements are all main group elements
• In transition elements, the d subshell being filled in the
aufbau process is in an inner principal shell
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The Periodic Table
Slide 18 of 39
Valence Electrons and Core
Electrons
• The valence shell is the outermost occupied shell
• Valence electrons are those with the highest
principal quantum number
– They occupy the outermost principal shell of an
atom
• Electrons in inner shells are called core electrons
– Their principal quantum number are less than n
• In the calcium atom with the electron configuration of
[Ar]4s2, the 4s electrons are valence electrons and
those in the [Ar] configuration are core electrons
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Electron Configurations of
Some Metal Ions
[Ar]3d10
[Kr]4d10
[Xe]5d10
Inert Pair Effect
(6s2)
Slide 20 of 39
Periodic Atomic Properties of The
Elements
The distance between the nuclei of two atom is the
atomic radius
– The covalent radius is one-half the distance
between the nuclei of two identical atoms joined
into a molecule
– The metallic radius is half the distance between
the nuclei of adjacent atoms in a solid metal
• Atomic radii increase from top to bottom within a
group of the periodic table and decrease from left to
right in a period of the periodic table
•
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Covalent Radius of Iodine
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Atomic Radii of the Elements
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Ionic Radii
• The ionic radius of each ion is the portion of the distance
between the nuclei occupied by that ion
– Cations are smaller than the atoms from which they are
formed; The nucleus attracts the remaining electrons
more strongly
– Anions are larger than the atoms from which they are
formed;The greater number of electrons repel more
strongly
• Isoelectronic defines elements that all have the same
number of electrons
• For a series of isoelectronic species with the same electron
configuration, the great the nuclear charge, the smaller the
species
Slide 26 of 39
The Ionic Radii of Mg2+ and O2-
Slide 27 of 39
Slide 28 of 39
Representative Atomic and Ionic
Radii
Effective
nuclear
charges are
similar
Slide 29 of 39
Ionization Energy
• Ionization energy is the energy required to remove
an electron from a ground state atom in the gaseous
state
A(g) → A+(g) + e- ∆H > 0, IE = ∆H
– The quantity of energy is usually expressed in
terms of a mole of atoms
– With the continual removal of electrons, ionization
energy greatly increases
• Removing a core electron takes impressively more
energy than removing a valence electron
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Selected Ionization Energies
•IE(2p) < IE(2s)
•IE of half-filled orbitals is higher
because it has less e--e- repulsion
1 eV = 96.485 kJ/mol
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First Ionization Energies
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Boron (B), electron configuration 1s22s22p1
B(g) → B+(g) + e-
IE(1) =
B+(g) → B2+(g) + e-
IE(2) = 2,427 kJ/mol
B2+(g) → B3+(g) + e-
IE(3) = 3,660 kJ/mol
B3+(g) → B4+(g) + e-
IE(4) = 25,025 kJ/mol
B4+(g) → B5+(g) + e-
IE(5) = 32,822 kJ/mol
801 kJ/mol
Valence
electrons
Core
electrons
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Electron Affinity
• Electron affinity is the energy change that occurs
when an electron is added to a gaseous atom
A(g) + e- → A-(g)
generally ∆H < 0, EA = - ∆H
– Electron affinities are generally expressed as
positive, although the process is exothermic
– Electron affinity increases to the right and up the
periodic table
Slide 34 of 39
Selected Electron Affinities
1 eV = 96.485 kJ/mol
Slide 35 of 39
Electronegativity
• Electronegativity (EN, expressed as χ), is a measure of
the ability of an atom to attract bonding electrons to itself
when the atom is in a molecule.
• Mulliken’s EN
Absolute EN, χM = (IE + EA)/2
• Pauling’s EN
define χ(H) = 2.2
∆ χ = χ(A) - χ(B) = [∆ ΑΒ(kJ)/96.49]1/2 = [∆ΑΒ(kcal)/23.06]1/2
∆ΑΒ = D(A-B) - [D(A-A) x D(B-B)]1/2
Bond dissociation energy of A-B
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Pauling’s Electronegativities
2.2
χP = 1.35 χM½ -1.37
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Polarizability (α)- the ability of electron
distribution to be distorted by an electric field
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Polarizability (α) ↑ Hardness (η) ↓
Absolute hardness, η = (IE –EA) /2
Y → Y+ + e
Y + e → Y-
∆H1 = IE
∆H2 = -EA
2Y → Y+ + Y-
∆H1 + ∆H2 = IE – EA
Y → ½ (Y+ + Y-)
½ (∆H1 + ∆H2) = (IE – EA)/2 = η
e.g. η(Li) = (IE –EA) /2 = (520-60)/2 =230 kJ/mol
η(Cs) = (376-46)/2 =165 kJ/mol
=> Li is harder than Cs, or Cs is softer than Li.
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