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Chemistry 281(01) Winter 2014
10:00-11:15 am
Instructor: Dr. Upali Siriwardane
CTH 277
E-mail: [email protected]
Office: 311 Carson Taylor Hall ; Phone: 318-2574941;
Office Hours: MTW 8:00 am - 10:00 am;
TR 8:30 - 9:30 am & 1:00-2:00 pm.
January 14, 2014 Test 1 (Chapters 1&,2),
February 6, 2014 Test 2 (Chapters 3 &4)
February 25, 2014, Test 3 (Chapters 5 & 6),
Comprehensive Final Make Up Exam: February
27, 2012 9:30-10:45 AM, CTH 311.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-1
Chapter 1. Atomic Sturcture
Chapter 1. Atomic structure
The origin of the elements
1.1 The nucleosynthesis of light elements
1.2 The nucleosynthesis of heavy elements
1.3 The classification of the elements
The structures of hydrogenic atoms
1.4 Spectroscopic information
1.5 Some principles of quantum mechanics
1.6 Atomic orbitals
Many-electron atoms
1.7 Penetration and shielding
1.8 The building-up principle
1.9 Atomic parameters
Chemistry 281, Winter 2014, LA Tech
3
3
5
6
8
10
10
11
12
18
18
20
Chapter-1-2
Origin of Elements in the Universe
Scientists have long based the origin of our
Universe on the Big Bang Theory. According to this
theory, our universe was simply an expanding fairly
cold entity consisting of only Hydrogen and Helium
during it's incipient stages. Over the expanse of many
years, and through a continuing process of fusion
and fission, our universe has come to consist of
numerous chemical elements, four terrestrial planets
(Earth, Mars, Venus, and Mercury), and five giant
gas planets (Saturn, Jupiter, Neptune, Pluto, and
Uranus).
Chemistry 281, Winter 2014, LA Tech
Chapter-1-3
Eight Steps in the History of the Earth
1. The Big Bang
2. Star Formation
3. Supernova Explosion
4. Solar Nebula Condenses
5. Sun & Planetary Rings Form
6. Earth Forms
7. Earth's Core Forms
8. Oceans & Atmosphere Forms
Chemistry 281, Winter 2014, LA Tech
Chapter-1-4
Nuclear Chemistry
• Fusion is lighter nuclei coming together to form
•
•
•
•
•
heavier.
Fission is heavier nuclei breaking in to lighter
nuclei.
Mass is not conserved E=mc2
Nuclear reactions are balanced by A (mass) and
Z (atomic) number.
Energy released is E=mc2, m is mass defect in
amu mutiplied by the conversion factor (931.5
MeV/amu)
Binding energy of nuclei expressed in
Mev/nucleons
Chemistry 281, Winter 2014, LA Tech
Chapter-1-5
Balancing Nuclear Equations
Chemistry 281, Winter 2014, LA Tech
Chapter-1-6
Chemistry 281, Winter 2014, LA Tech
Chapter-1-7
Nuclear Binding Energy
The binding energy of a nucleus is a measure of how
tightly its protons and neutrons are held
together by the nuclear forces. The binding energy
per nucleon, the energy required to remove
one neutron or proton from a nucleus, is a function
of the mass number A. (Dm) –mass defect
(Dm) = Mass of Nuclide - mass of (p + n +e )
Proton mass: 1.00728 amu
Neutron mass: 1.00867 amu931.5 MeV/amu
Electron mass: 0.00055 amu
Massdefect (Dm), then multiply by
Chemistry 281, Winter 2014, LA Tech
Chapter-1-8
Bonding Energy Curve
Chemistry 281, Winter 2014, LA Tech
Chapter-1-9
Nuclear Fusion Reactions
• Nuclear energy, measured in millions of electron
volts (MeV), is released by the fusion of two light
nuclei, as when two heavy hydrogen nuclei,
deuterons (2H), combine in the reaction
Chemistry 281, Winter 2014, LA Tech
Chapter-1-10
Nuclear Fission Reactions
• Nuclear energy is also released when the fission
(breaking up of ) of a heavy nucleus such as U is
induced by the absorption of a neutron as in
Chemistry 281, Winter 2014, LA Tech
Chapter-1-11
Origin of the Elements: Nucleosynthesis
•Elements formed in the universe's original stars
were made from hydrogen gas condensing due to
gravity. These young stars "burned" hydrogen in
fusion reactions to produce helium and the
hydrogen was depleted. Reactions such as those
below built up all the heavier elements up to atomic
number 56 in the periodic table.
•When the stars got old they exploded in a super
nova, spreading the new elements into space with
high flux of neutrons to produce heavy elements by
neutron capture.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-12
Nuclear
Burning
Chemistry 281, Winter 2014, LA Tech
Chapter-1-13
Supernova Explosion
Chemistry 281, Winter 2014, LA Tech
Chapter-1-14
The nucleosynthesis of light elements
• Stellar nucleosynthesis
• Elements Carbon to Iron is form by nuclear fusion
•
•
•
•
•
in stars after all H is converted to He.
Double star Supernova
White dwarf steals material from another star
And get heated huge energy get stored in the
while dwarf
It goes to nuclear overload and carbon/oxygen
Fuse to iron and it explodes known as type 1a
supernova. Most of the elements up to iron in the
universe
Chemistry 281, Winter 2014, LA Tech
Chapter-1-15
The nucleosynthesis of heavy elements
• Havier elements are formed during Supernova
•
•
•
•
•
explosion.
Giant one star supernova explosions
Heavier star buns all its H and nuclear burning
goes faster and forms layer after layers of new
elements. Core collapses and become denser.
And the star explodes
Iron capture neutrons and all heavier elements
Corps of supernova explosion leaves a core
neutrons. Rotating neutron produces EM pluses
creating a pulsar
• Hypernova explosions:
Chemistry 281, Winter 2014, LA Tech
g ray bursts
Chapter-1-16
Cosmic Abundances
Chemistry 281, Winter 2014, LA Tech
Chapter-1-17
Terrestrial Abundances
Chemistry 281, Winter 2014, LA Tech
Chapter-1-18
Stability of the Elements and Their
Isotopes
P/N Ratio
Why are elements
With Z > 82 are
Unstable?
Chemistry 281, Winter 2014, LA Tech
Chapter-1-19
Terrestrial Abundances
Chemistry 281, Winter 2014, LA Tech
Chapter-1-20
Magic Numbers
• Nuclei with either numbers of protons or
neutrons equal to Z, N =2, 8, 20, 28, 50, 82,
or 126
• exhibit certain properties which are
analogous to closed shell properties in
atoms, including
• anomalously low masses, high natural
abundances and high energy first excited
states.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-21
The classification of the elements
• Dobereiner Triads
• Newlands called the Law of Octaves
• Lothar Mayer’s atomic volume curves
• Mendeleyev’s periodic table
Chemistry 281, Winter 2014, LA Tech
Chapter-1-22
Dobereiner Triads
Cl 35.5
Li
7
S
32
Br 79
Na
23
Se
79
I
K
39
Te 128
127
Chemistry 281, Winter 2014, LA Tech
Chapter-1-23
Newlands’ Law of octaves
Octaves 1
Li
Be B C
N
O
F
Octaves 2
Na
Mg Al Si
P
S
Cl
Chemistry 281, Winter 2014, LA Tech
Chapter-1-24
Lothar Mayer’s atomic volume curves
Chemistry 281, Winter 2014, LA Tech
Chapter-1-25
Mendeleyev’s Periodic Table
Chemistry 281, Winter 2014, LA Tech
Chapter-1-26
Long Form of Periodic Table
Chemistry 281, Winter 2014, LA Tech
Chapter-1-27
What is periodic table?
Describe its use in chemistry?
All elements in a group have similar chemical
properties
Group I- alkali metal:Li, Na, K Rb, Cs, Fr
Common ele.n conn: ns1
Group II- alkaline earth metals:Be, Mg, Ca, Sr, Ba,
Ra: Common ele.n conn: ns2
Group VII- Halogens: Cl, Br, I, At:
Common ele.n conn:ns2 np5
Group VIII- Noble gases:He, Ne, Ar, Kr, Xe, Rn:
Common ele.n conn ns2 np6
Chemistry 281, Winter 2014, LA Tech
Chapter-1-28
Chemical properties and the
periodic table
• Electron configurations help us understand
changes in atomic radii, ionization energies,
and electron affinities.
• Various trends in reactivity can be observed.
• Main group metals become more reactive as
you go down a group.
• Reactivity of nonmetals decreases as you go
down a group.
• Transition metals become less reactive as you
go down a group.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-29
Other ways of numbering groups in
the periodic table
• Several methods are used for numbering periodic
table groups
• American chemists preferred method.
• The IUPAC old system.
• The IUPAC current system.
• The American Chemical Society (ACS) has also
adopted the current IUPAC system.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-30
Other numbering systems
Previous IUPAC
Current IUPAC and ACS
Preferred US
IA
IIA
III B
IVB
VB
VIB
1
2
13
14
15
16
IIIA
IVA
IA
1
2
IIA
IIIA
VIIIB
17
18
VA VIA VIIA
H
Li
0
He
Be
IIIA IVA VA VIA VIIA
3
4
VIIB
3
Na
Mg
K
Ca
4
5
6
7
IIIB IVB V B VIB VIIB
Sc
Ti
V
Chemistry 281, Winter 2014, LA Tech
Cr
Mn
VIIIA
8
IB IIB
B
C
N
O
F
Ne
Al
Si
P
S
Cl
Ar
Ga
Ge
As
Se
Br
Kr
9 10 11 12
VIII B
Fe
Co
IB IIB
Ni
Cu
Zn
Chapter-1-31
The structures of hydrogenic atoms
:Bohr Theory
• The Bohr model is a
‘planetary’ type
model.
• Each principal
quantum represents a
new ‘orbit’ or layer.
• The nucleus is at the
center of the model.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-32
Emission Spectrum of Hydrogen
•
Bohr studied the the spectra produced when atoms were
excited in a gas discharge tube.
He observed that each element produced its
own set of characteristic lines.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-33
Emission Spectrum of Hydrogen
• Line Spectrum
• Energy is absorbed when an electron goes from a
•
•
•
•
•
lower(n) to a higher(n)
Energy is emitted when an electron goes from a
higher(n) to a lower(n) level
Energy changed is given by:DE = Ef - Ei
or DE = -2.178 x 10-18 [1/n2f - 1/n2i] J
DE is negative for an emission and positive for an
absorption
DE can be converted to l or 1/ l by l = hc/E.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-34
Bohr model of the atom
• The Bohr model is
a ‘planetary’ type
model.
• Each principal
quantum
represents a new
‘orbit’ or layer.
• The nucleus is at
the center of the
model.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-35
What is Bohr’s Atomic model?
• explain emission spectrum of hydrogen
•
•
•
•
•
atom
applied the idea of Quantization to
electrons to orbits
energies of these orbits increase with the
distance from nucleus.
Energy of the electron in orbit n (En):
En = -2.178 x 10-18 J (Z2/n2)
En = -2.178 x 10-18 J 1/n2; Z=1 for H
Chemistry 281, Winter 2014, LA Tech
Chapter-1-36
Bohr model of the atom
Balmer later determined an empirical
relationship that described the spectral lines
for hydrogen.
DE
= - 2.178 x 10
-18
m
-1
(
12
nf
-
12
ni
)
nf = 2 ni = 3,4, 5, . . . Blamer series
Spectra of many other atoms can be described by
similar relationships.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-37
Paschen, Blamer and Lyman Series
Chemistry 281, Winter 2014, LA Tech
Chapter-1-38
Calculation using the equation:
E = -2.178 x 10-18 (1/nf2 - 1/ni2 ) J, Calculate
the wavelength of light that can excite the
electron in a ground state hydrogen atom to
n = 7 energy level.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-39
Calculation using Bohr eqaution
The energy for the transition from n = 1 to n = 7:
DE = -2.178 x 10-18 J [1/n2f - 1/n2i]; nf = 7, ni = 1
DE = -2.178 x 10-18 [1/72 - 1/12] J
DE = -2.178 x 10-18 [1/49 - 1/1] J
DE = -2.178 x 10-18 [0.02041 - 1] J
DE = -2.178 x 10-18 [-0.97959] J
= 2.134 x 10-18 J (+, absorption)
calculate the l using l = hc/E
6.626 x 10-34 Js x 3.00 x 108 m/s
l = ---------------------2.13 x 10-18 J
l=
9.31 x 10-8 m
Chemistry 281, Winter 2014, LA Tech
Chapter-1-40
Wave- Particle Duality of Matter
and Energy
• Wave theory applies to electromagnetic radiation
• EMR can also be described as particles
• quanta :A particles of light energy.
• Quantum: One particle of light with a certain
energy.
• Photon: A stream of Quanta
• Wave theory could be applied to electrons
Chemistry 281, Winter 2014, LA Tech
Chapter-1-41
Wave theory of the electron
• 1924: De Broglie suggested that electrons
have wave properties to account for why
their energy was quantized.
• He reasoned that the electron in the
hydrogen atom was fixed in the space
around the nucleus.
• He felt that the electron would best be
represented as a standing wave.
• As a standing wave, each electron’s
path must equal a whole number times
the wavelength.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-42
De Broglie waves
De Broglie proposed that all particles have a
wavelength as related by:
l =
l
h
m
v
=
=
=
=
Chemistry 281, Winter 2014, LA Tech
h
mv
wavelength, meters
Plank’s constant
mass, kg
frequency, m/s
Chapter-1-43
Wave Character of Electrons
Chemistry 281, Winter 2014, LA Tech
Chapter-1-44
What is a wave-mechanical model?
• motions of a vibrating string shows one dimensional
•
•
•
•
motion.
Energy of the vibrating string is quantized
Energy of the waves increased with the nodes.
Nodes are places were string is stationary.
Number of nodes gives the quantum number. One
dimensional motion gives one quantum number.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-45
Constructively Interfered 2D-Wave
Chemistry 281, Winter 2014, LA Tech
Chapter-1-46
destructively Interfered 2D-Wave
Chemistry 281, Winter 2014, LA Tech
Chapter-1-47
Two-dimensional wave - Vibrations on a Drumskin
One circular node
(at the drumskin's edge)
Two circular nodes
(one at the drumskin's edge
plus one more)
Three circular nodes
(one at the drumskin's edge
plus two more)
One transverse node
(plus a circular one at the
drumskin's edge)
Two transverse nodes
(plus one at the drumskin's
edge)
Chemistry 281, Winter 2014, LA Tech
Chapter-1-48
How did Schrodinger come up with a equation
started with The “Vibrating String” and the "P
article in a One-dimensional Box“ solutions
Vibrating String : y = sin(npx/l)
d2y/dx2 = -(n2p2/l2)sin(npx/l) = -(n2p2/l2)y
Since l = 2l/n;
d2y/dx2 = -(4m2v2p2/h2)y
l = h/mv
Particle in One-dimensional Box:
d2y/dx2 = -(4m2v2p2/h2)y
E = ½mv2 + V or v2 = (2/m)(E-V)
d2y/dx2 = -(8mp2/h2)(E - V)y
Chemistry 281, Winter 2014, LA Tech
Chapter-1-49
Schrödinger Equation
y = wave function
E = total energy
V = potential energy
Chemistry 281, Winter 2014, LA Tech
Chapter-1-50
Polar Coordinates
Chemistry 281, Winter 2014, LA Tech
Chapter-1-51
Chemistry 281, Winter 2014, LA Tech
Chapter-1-52
Components of y
Mathematical expression of hydrogen like orbitals
in polar coordinates:
y n, l, ml, ms (r,,) = R n, l, (r) Y l, ml, (,)
R n, l, (r )
Y l, ml, (,)
Chemistry 281, Winter 2014, LA Tech
= Radial Wave Function
=Angular Wave Function
Chapter-1-53
Quantum model of the atom
• Schrödinger developed an equation to
describe the behavior and energies of
electrons in atoms.
• His equation ( Wave function y ) is similar to
one used to describe electromagnetic waves.
Each electron can be described in terms of
Wave function y its quantum numbers. y n, l,
ml, ms),
• y2 is proportional probablity of finding the
electron in a given volume. Max Born
Interpretation: y2 = atomic orbital
Chemistry 281, Winter 2014, LA Tech
Chapter-1-54
Quantum Model of atom
• Electrons travel in three dimensions
• Four quantum numbers are needed
• three to describe, x, y, z, and four for the spin
• four quantum numbers describe an orbital
currently used to explain the arrangement,
bonding and spectra of atoms.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-55
Quantum numbers
• Principal quantum number, n
• Tells the size of an orbital and largely
•
•
•
•
determines its energy.
n = 1, 2, 3, ……
Angular momentum, l
The number of subshells (s, p, d, f) that a
principal level contains. It tells the shape
of the orbitals.
l = 0 to n - 1
Chemistry 281, Winter 2014, LA Tech
Chapter-1-56
Quantum numbers
• Magnetic quantum number, ml
• Describes the direction that the orbital
projects in space.
• ml = l to +l (all integers, including zero)
• For example, if l = 2, then ml would have
values of -2, -1, 0, 1 and 2.
• Knowing all three ml numbers provide us
with a picture of all of the orbitals.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-57
Four Quantum Numbers of the Atom
• n
value could be 1, 2, 3, 4, 5, 6. 7. . . etc.
• l values depend on n value: can have
0..
. (n - 1) values
• ml values depends on l value: can have -l . , 0 .
. . +l values of ml
• ms values should always be -1/2 or +1/2
Chemistry 281, Winter 2014, LA Tech
Chapter-1-58
Radial Distribution Function, Pnl(r).
This is defined as the probability that an electron in
the orbital with quantum numbers n and l will be
found at a distance r from the nucleus. It is
related to the radial wave function by the
following relationship:
; normalized by
Chemistry 281, Winter 2014, LA Tech
Chapter-1-59
s-Atomic orbitals
R n, l, (r) only no Y l, ml, (,)
s orbitals
Chemistry 281, Winter 2014, LA Tech
Chapter-1-60
s-Atomic orbitals
2s
3s
Chemistry 281, Winter 2014, LA Tech
Chapter-1-61
p-Atomic orbitals
2p
3p
Chemistry 281, Winter 2014, LA Tech
Chapter-1-62
Nodes in the y
Total nodes = n -1
Radial nodes = n -1- l
Angular nodes = l
Eg 4d orbital:
Total nodes = 4 -1 = 3
Radial nodes = n -1- l = 4-1-2 = 1
Angular nodes = l = 2
Chemistry 281, Winter 2014, LA Tech
Chapter-1-63
.
Radial wavefunctions, Rnl(r), and the radial distribution functions, Pnl(r)
Rnl(r)
Pnl(r)
n
l
1s
1s
1
0
2s
2s
2
0
2p
2p
2
1
3s
3s
3
0
3p
3p
3
1
3d
3d
3
2
Chemistry 281, Winter 2014, LA Tech
Chapter-1-64
d-orbitals
Chemistry 281, Winter 2014, LA Tech
Chapter-1-65
Representative d orbitals
Chemistry 281, Winter 2014, LA Tech
Chapter-1-66
f-orbitals
Chemistry 281, Winter 2014, LA Tech
Chapter-1-67
Classification by sublevels
s
p
H
He
d
Li
Be
Na
Mg
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Cs
Ba
Lu
Hf
Ta
W
Re
Os
Ir
Pt
Fr
Ra
Lr
f
Chemistry 281, Winter 2014, LA Tech
B
C
N
O
F
Ne
Al
Si
P
S
Cl
Ar
Zn
Ga
Ge
As
Se
Br
Kr
Ag
Cd
In
Sn
Sb
Te
I
Xe
Au
Hg
Tl
Pb
Bi
Po
At
Rn
La Ce
Pr Nd Pm Sm Eu Gd Tb
Dy Ho
Ac Th
Pa
Cf
U
Np Pu Am Cm Bk
Er
Tm Yb
Es Fm Md No
Chapter-1-68
Atomic Orbitals of Multi-Electrnon Atoms
• Unlike a hydrogen-like atom multi-electron atoms
there are electron-electron repulsions.
• Schrodinger equation cannot be solved
analytically for multi-electron atoms.
• However, it is possible to obtain a crude solution
for a multi-electron atom by employing a relatively
simple construct.
• The "effective" nuclear charge for each electron is
used in place of nuclear charge in the equations
for a hydrogen-like atom
Chemistry 281, Winter 2014, LA Tech
Chapter-1-69
Screening (shielding) constant (σ)
• Screening (shielding) constant (σ) for each
•
•
•
•
electron is calculated based on:
the principle quantum number
orbital type and penetration and of all
other electrons in an atom.
σ gives Zeff .
Zeff = Z - σ; Z is the atomic number.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-70
Effective nuclear charge (Zeff)
Zeff is the nuclear charge felt by an electron in a
multielectron atom:
• Each electron in an atom has different Zeff.
• Each Zeff is less than atomic number (Z) since
electrons screen each other from the nucleus.
• Zeff depends on the n and l quantum number of an
electron.
• Zeff Depends on orbital type the electron is in: Zeff
of 4s > 4p > 4d > 4f.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-71
Radial Distribution Functions, Penetration and Shielding
Chemistry 281, Winter 2014, LA Tech
Chapter-1-72
Penetration & Shielding of an Electron in
Multi-electron Atom
Penetration of an electron:
• Greater the penetration there is more chance of
electrons being located close to the nucleus.
• Comparing s, p, d, or f orbitals within same shell (or
principle QN), penetration of an electrons are in the
order: s > p> d > f
Shielding power of an electron:
• Shields of other electrons depends penetration and the
orbital type. Shielding power of electrons in orbitals of
that same shell are: s > p > d > f
Chemistry 281, Winter 2014, LA Tech
Chapter-1-73
Slater Rules of Obtaining Zeff
Group electron configuration in the following form:
[1s][2s 2p][3s 3p][3d][4s 4p][4d][4f][5s 5p][5d][5f] etc
Orbitals within a bracket are said to belong to the same group.
• [1s] group where they contribute .30.
• [ns np] group, other electrons in the same group contribute .35
• [ns np] group, each electron in the n-2 or lower group
contributes 1.0.
• [nd] or [nf] group, rules 1 and 2 remain the same and all
electrons in groups to the left contribute 1.0
Chemistry 281, Winter 2014, LA Tech
Chapter-1-74
Slater Rules of Obtaining Zeff
Consider the outer electron in K. Assume the configuration is
[1s2][2s2 2p6][3s2 3p6)[3d1] s is then (18 x 1) since the outer electron is
in a [nd] group. Thus Zeff is (19-18)= 1
If we assume that the configuration is [1s2][2s2 2p6][3s2 3p6][3d°][4s1],
the value of s is (8 x 0.85) + (10 x 1)= 16.8 and Zeff is 2.2.
Therefore Zeff is greater and the outer electron experiences more
nuclear attraction when it is in the 4s orbital.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-75
Slater Rules of Obtaining Zeff
Slater's rule states S = 0.35*x + 0.85*y +z
x,y and z refer to the electron configuration of the atom.
This is for Cl: 1s²2s²2p⁶3s²3p⁵ and for
K: 1s²2s²2p⁶3s²3p⁶4s¹
x is the number of valence electrons, the electrons in the highest
energy level, 7 for Cl and 1 for K.
y is the number of electrons in the energy level below the
valence level, 8 for Cl and 8 for K.
z is the remaining number of electrons, 2 for Cl and 10 for K.
So we get for Cl S = 0,35*7 + 0,85*8 +2 = 11,25 and for K S =
0,35*1 +0,85*8 + 10 = 17,15
Chemistry 281, Winter 2014, LA Tech
Chapter-1-76
Effective nuclear charge (Zeff) of Atomic
Orbitals vs. Z (atomic number)
Chemistry 281, Winter 2014, LA Tech
Chapter-1-77
How do you get the electronic
configuration of an atom?
• Use periodic table
• Periodic table is divided into orbital blocks
• Each period:
• represents a shell or n
• Start writing electron configuration
• Using following order
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d…
(building up (Auf Bau) principle:)
Chemistry 281, Winter 2014, LA Tech
Chapter-1-78
What is Building Up (Auf Bau) Principle
• Scheme
used by chemist to obtain
electronic configuration of a multi-electron
atom in the ground state by filling hydrogen
like atomic orbital starting with lowest
energy.
• 1s 2s 2p3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s
• 5f 6d… (building up principle)
•
If two or more orbitals exist at the same
energy level, they are degenerate. Do not
pair the electrons until you have to.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-79
What is Pauli Exclusion Principle:
Electrons in an atom cannot have all four of
their quantum numbers equal.
Eg. He: 1s2
electron orbital n l
ml
ms
________________________________
1s1
1
0
0
+½()
1s2
1
0
0
-½()
Chemistry 281, Winter 2014, LA Tech
Chapter-1-80
Filling order of orbitals
Chemistry 281, Winter 2014, LA Tech
Chapter-1-81
Filling order of orbitals
Chemistry 281, Winter 2014, LA Tech
Chapter-1-82
Electronic Configuration of elements (core format)
Li1
2s
2s
H1
1s
Na1
Mg
2
K1
Ca2
Rb1
Sr2
3s
4s
4s
Sc1
Ti2
N2
2s 3
2p
O2
2s 4
2p
F2
2s 5
2p
Ne2
Al2
3s 1
3p
Si2
3s 2
3p
P2
3s 3
3p
S2
3s 4
3p
Cl2
3s 5
3p
Ar2
3s 6
3p
Zn
10
Ga
10
3d 2
4s 1
4p
Ge
10
3d 2
4s 2
4p
As
10
3d 2
4s 3
4p
Se
10
3d 2
4s 4
4p
Br
10
3d 2
4s 5
4p
Kr
10
3d 2
4s 6
4p
He2
Mn5
3d2
4s
Fe6
3d2
4s
Co7
Ni8
Cu
10
3d2
4s
3d2
4s
3d 1
4s
3d 2
4s
Tc5
Ru7
Rh8
4d1
5s
Pd
10
4d
Ag
10
4d 1
5s
Cd
10
4d 2
5s
In10
4d 2
5s 1
5p
Sn
10
4d 2
5s 2
5p
Sb
10
4d 2
5s 3
5p
Te
10
4d 2
5s 4
5p
I10
4d 2
5s 5
5p
Xe
10
4d 2
5s 6
5p
Ir14
4f 7
5d2
6s
Pt
14
4f 9
5d1
6s
Au
14
4f 10
5d 1
6s
Hg
14
4f 10
5d 2
6s
Tl10
5d 2
6s 1
6p
Pb
10
5d 2
6s 2
6p
Bi10
5d 2
6s 3
6p
Po
10
5d 2
6s 4
6p
At
10
5d 2
6s 5
6p
Rn
10
5d 2
6s 6
6p
3d2
4s
3d1
4s
Y1
Zr2
Nb3
Mo5
4d1
5s
4d2
5s
Ta
14
4f 3
5d2
6s
W
14
4f 4
5d2
6s
Re
14
4f 5
5d2
6s
Os
14
4f 6
5d2
6s
La1
Ce
1
5d2
6s
4f 1
5d2
6s
Pr3
Nd
4
Pm
Sm
5
6
Eu
7
Ac1
Th2
Pa2
U3
5f 1
6d2
7s
Np
4
Cm
7
Am
7
5f
4d2
5s
Cs1
Ba2
Lu
14
4f 1
5d2
6s
Hf
14
4f 2
5d2
6s
Fr1
Ra2
Lr1
6d2
7s
7s
Cr5
3d2
4s
4d2
5s
6s
V3
4d2
5s
6d2
7s
Chemistry 281, Winter 2014, LA Tech
6f 2
7s
2s 6
2p
1s
3d2
4s
5s
7s
C2
2s 2
2p
3s
5s
6s
B2
2s 1
2p
Be2
4f 2
6s
5f 1
6d2
7s
4d1
5s
4f 2
6s
4f 2
6s
5f 1
6d2
7s
4f 2
6s
Pu
6
5f 2
7s
4f 2
6s
5f 2
7s
Gd
7
4f 1
5d2
6s
1
6d2
7s
Tb
9
Dy
10
4f 2
6s
Ho
11
4f 2
6s
Er
12
4f 2
6s
Tm
13
4f 2
6s
Yb
14
4f 2
6s
Bk
9
Cf
10
5f 2
7s
Es
11
5f 2
7s
Fm
12 Md
13
No
14
5f 2
7s
4f 2
6s
5f 2
7s
5f 2
7s
5f 2
7s
Chapter-1-83
Using the periodic table
To write the ground-state electron configuration of an
element:
Starting with hydrogen, go through the elements in
order of increasing atomic number
As you move across a period
• Add electrons to the ns orbital as you pass through groups
IA (1) and IIA (2).
• Add electrons to the np orbital as you pass through
Groups IIIA (13) to 0 (18).
• Add electrons to (n-1) d orbitals as you pass through IIIB
(3) to IIB(12) and add electrons to (n-2) f orbitals as you
pass through the f -block.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-84
Writing electron configurations
• Examples
O
•
Ti
•
Br
• Core format
1s2 2s2 2p4
1s2 2s2 2p6 3s2 3p6 3d2 4s2
1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p5
•
[He] 2s2 2p4
[Ar] 3d2 4s2
[Ar] 3d10 4s2 4p5
•
•
•
O
Ti
Br
Chemistry 281, Winter 2014, LA Tech
Chapter-1-85
Writing electron configurations
Example - Cl• First, write the electron configuration for chlorine:
• Cl [Ne] 3s2 3p5
• Because the charge is 1-, add one electron. Cl-
[Ne] 3s2 3p6
Chemistry 281, Winter 2014, LA Tech
or
[Ar]
Chapter-1-86
Writing electron configurations
• Electron configurations can also be written
for ions.
• Start with the ground-state configuration for
the atom.
• For cations, remove a number of the
outermost electrons equal to the charge.
• For anions, add a number of outermost
electrons equal to the charge.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-87
Writing electron configurations
Example - Ba2+
• First, write the electron configuration for barium.
Ba
[Xe] 6s2
• Because the charge is 2+, remove two electrons.
Ba2+
[Xe] or [Kr] 3d10 4s2 4p6
Chemistry 281, Winter 2014, LA Tech
Chapter-1-88
Hund’s Rule
• Rule to fill electrons into p,d,f orbitals containing
•
•
•
•
more than one sublevel of the same energy.
filling p, d, f orbitals: Put electrons into separate
orbitals of the subshell with parallel spins before
pairing electrons.
The existence of unpaired electrons can be tested
for since each acts like a tiny electromagnet.
Paramagnetic - attracted to magnetic field.
Indicates the presence of unpaired electrons.
Diamagnetic - pushed out of a magnetic field.
Indicates that all electrons are paired.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-89
Orbital Box Diagrams
Valence Shell Electron configuration shown in
box or circle form.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-90
Exception to Building Up Principle
a) Electronic Configuration of d-block and f-
block elements
d5 or d10 and f7 or f14 are stable
Cr :[Ar] 3d4 4s2 wrong
Cr :[Ar] 3d5 4s1 correct
Cu :[Ar] 3d9 4s2 wrong
Cu :[Ar] 3d10 4s1 correct
Chemistry 281, Winter 2014, LA Tech
Chapter-1-91
Lanthanoids
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb
1
1 4f
3
1 4f
5d2
2
5d2
6s
6s
6s
4
5
6
4f 2 4f 2 4f 2
6s
6s
6s
Chemistry 281, Winter 2014, LA Tech
7
9
10
11
12
13
14
7 4f
1
4f
4f
4f
4f
4f
4f
4f 2
2
2
2
2
2
2
5d2
6s
6s
6s
6s
6s
6s
6s
6s
Chapter-1-92
Actinoids
Ac Th Pa
1
6d2
7s
U
Np Pu Am Cm Bk Cf Es Fm Md No
4
2
3
2 5f
6
5f 1 5f 1
1
6f 2
5f 2
6d2 6d2 6d2
7s
7s
7s
7s
7s
Chemistry 281, Winter 2014, LA Tech
7
7 5f
9
10
11
12
13
14
1
5f 2
5f 2 5f 2 5f 2 5f 2 5f 2 5f 2
6d2
7s
7s
7s
7s
7s
7s
7s
7s
Chapter-1-93
Exception to Building Up Principle
Electronic Configuration of Transition Metal cations
d-block and f-block elements
d orbitals are lower in energy than s orbitals
f orbitals are lower in energy than d orbitals
E.g. Neutral atom Fe :[Ar] 3d
3+
5
Cation, Fe :[Ar] 3d
Chemistry 281, Winter 2014, LA Tech
6
2
4s
Chapter-1-94
Magnetic Properties of Atoms
a) Paramagnetism?
attracted to magnetic field due to un-paired
electrons.
b) Ferromagnetism?
attracted very strongly to magnetic field due to
un-paired electrons.
c) Diamagnetism?
Repelled by a magnetic field due to paired
electrons.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-95
Periodic trends
• Many trends in physical and chemical properties
can be explained by electron configuration.
• We’ll look at some of the more important
examples.
Atomic radii
Ionic radii
First ionization energies
Electron affinities
Chemistry 281, Winter 2014, LA Tech
Chapter-1-96
How does Zeff vary across a period
and down a group?
• Zeff increase going across a
period
• Zeff decrease going down a
group
Chemistry 281, Winter 2014, LA Tech
Chapter-1-97
Types of Atomic Radii
1 Covalent Radii: Radii based on covalently liked
atoms in covalently bonded molecules.
2 Van der Waals Radii: Radii based on non
bonded atoms in solids.
3 Metallic Radii (12-coordinate):Radii based on
metallic solids.
4 Ionic Radii: Radii basesd on bond distances in
ionic solids.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-98
How does Atomic radii of atoms vary going
across a period?
•
•
•
Atomic radii depend on the distance from the nucleus to the
outermost electron in the valence shell.
Going across protons are added to nucleus This
increase the Zeff decreasing radii
Atomic radii decrease going across a period
Chemistry 281, Winter 2014, LA Tech
Chapter-1-99
How does Atomic radii of elements vary
going down a group?
•
•
•
Atomic radii depend on the distance from the nucleus
to the outermost electron in the valence shell.
Going down the group outer most shell increases radii
hence the distance from the nucleus
The atomic radii increase going down a group
Chemistry 281, Winter 2014, LA Tech
Chapter-1-100
How does Ionic radii of elements vary?
•
•
•
Cations have smaller radii than neutral
atoms.
Anions have larger radii than neutral atoms
The more charge on the ion more effect on
the radii.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-101
Atomic radii of elements going down a group?
Chemistry 281, Winter 2014, LA Tech
Chapter-1-102
Atomic radii for the main group (s,p block)
elements
H
Li
Be
B
C
N
O
F
Na
Mg
Al
Si
P
S
Cl
K
Ca
Ga
Ge
As
Se
Br
Rb
Sr
In
Sn
Sb
Te
I
Cs
Ba
Tl
Pb
Bi
Chemistry 281, Winter 2014, LA Tech
Chapter-1-103
Atomic radii of the representativemain group elements
• Atoms get larger as you go down a group.
A new shell is being added.
• Atoms get smaller as you go across a
period.
The nucleus contains more protons.
The higher charge attracts the electrons
more strongly, making the atom smaller.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-104
Lanthanoide Contration
• Filling of the 4f orbitals in the lanthanides,
which occur within the third series of transition
elements, causes these transition metals to be
smaller than expected because the 4f orbitals
are very poor nuclear shielders and Zeff of 6s2
obitals increase and the atomic radii decrease.
• 3rd-series elements have nearly the same
effective nuclear charge as the 2nd-series
elements, and thus, nearly the same size
Ce [Xe]
Chemistry 281, Winter 2014, LA Tech
1
1
2
4f 5d 6s
Chapter-1-105
Ionic radii
• Cations
• These are smaller than the atoms from
which they are formed.
• For main group elements, the outer shell of
electrons is removed.
• The positively charged ion can also do a
better job of holding on to the electrons
that remain.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-106
Ionic radii
• Anions
• These are larger than the atoms from which
there are formed..
• Adding electrons increases the repulsion
between electrons.
• The ion has a harder time holding on to the
electrons.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-107
Ionic radii (pm)
Li
152
Li+
74
Be
111
Be2+
35
O
74
O2140
F
71
F133
Na
186
Na+
102
Mg
160
Mg2+
72
S
103
S2184
Cl
99
Cl181
K
227
K+
138
Ca
197
Ca2+
100
Br
114
Br195
Rb
248
Rb+
149
Sr
215
Sr2+
116
I
133
I216
Cs
265
Cs+
170
Ba
217
Ba2+
136
Chemistry 281, Winter 2014, LA Tech
Chapter-1-108
Isoelectronic configurations
Species that have the same electron
configurations.
Example
Each of the following has an electron
configuration of 1s2 2s2 2p6
O2- FNe
Na+ Mg2+ Al3+
Chemistry 281, Winter 2014, LA Tech
Chapter-1-109
What is Ionization Potential?
The energy required to remove an electron
from an atom.
First Ionization Energy (DH1 ):
Ca ----> Ca+ + e-; DH1 = positive
Second Ionization Energy (DH2)
Ca+ ----> Ca2+ + e-; DH2 = positive
DH2 > DH1
Chemistry 281, Winter 2014, LA Tech
Chapter-1-110
How does Ionization Potential vary going down a
group?
•
•
•
Ionization Potential depend on Zeff of the nucleus to the outermost
electron in the valence shell.
Going down the group Zeff for the outer most shell decrease
hence the Ionization Potential also decrease
Going across the period Zeff for the outer most shell increase
hence the Ionization Potential also increase
Chemistry 281, Winter 2014, LA Tech
Chapter-1-111
Ionization energy
• First ionization energy
The energy to remove one electron from a
neutral atom in the gas phase.
• A(g) + first ionization energy
A+(g) + e• This indicates how easy it is to form a cation.
Metals tend to have lower first ionization
energies than nonmetals.
• They prefer to become cations.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-112
First
ionization
energy
2500
He
Ne
First ionization energy (kJ/mol)
2000
Ar
1500
Kr
Xe
Rn
1000
500
0
0
20
40
60
80
100
Atomic number
Chemistry 281, Winter 2014, LA Tech
Chapter-1-113
Changes of I.E. Across a period
Chemistry 281, Winter 2014, LA Tech
Chapter-1-114
Electron affinity
• A measure of an atom’s tendency to gain
electrons in the gas phase.
• A(g) + eA-(g) + thermal energy
• Electron affinity is an irregular periodic
function of atomic number. In general, it
increases from left to right.
• Noble gases are not included since they have
little or no tendency to gain electrons.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-115
How does Electron Affinity vary in the
periodic table?
• Electron Affinity depends on Zeff of the nucleus to
the outermost electron in the valence shell.
• Going down the group Zeff for the outer most shell
decrease hence the Electron Affinity also increase
• Going across the period Zeff for the outer most
shell increase hence the Electron Affinity also
decrease
Chemistry 281, Winter 2014, LA Tech
Chapter-1-116
Electron affinity
Chemistry 281, Winter 2014, LA Tech
Atomic number
Chapter-1-117
Electronegativity
Pauling Electronegativity, cP
The ability of an atom that is bonded to another atom or
atoms to attract electrons to itself.
It is related to ionization energy and electron affinity.
It cannot be directly measured.
The values are unitless since they are relative to each
other.
The values vary slightly from compound to compound
but still provide useful qualitative predictions.
Chemistry 281, Winter 2014, LA Tech
Chapter-1-118
Electronegativities
4
3.5
Electronegativity is a
periodic property.
Electronegativity
3
2.5
2
1.5
1
0.5
0
20
Chemistry 281, Winter 2014, LA Tech
40
Atomic number
60
80
100
Chapter-1-119
Electronegativity Scales
• Pauling Electronegativity, cP
• Mulliken Electronegativity, cM
• The Allred-Rochow, cAR
• Sanderson electronegativity
• Allen electronegativity
Chemistry 281, Winter 2014, LA Tech
Chapter-1-120
Pauling Electronegativity, cP
EA-A and EB-B bond-energy of homonuclear A-A & B-B diatomic molecules
EA-B bond-energy of heteronuclear A-B diatomic molecule
cA cB are electronegativity values of A and B
Pauling comments that it is more accurate to use the geometric mean
rather than the arithmetic mean
Chemistry 281, Winter 2014, LA Tech
Chapter-1-121
Mulliken Electronegativity, cM
The Mulliken electronegativity can only be
calculated for an element for which the electron
affinity is known
• For ionization energies and electron affinities in
electronvolts
• For energies in kilojoules per mole
Chemistry 281, Winter 2014, LA Tech
Chapter-1-122
The Allred-Rochow, cAR
The effective nuclear charge, Zeff experienced by
valence electrons can be estimated using Slater's
rules, while the surface area of an atom in a
molecule can be taken to be proportional to the
square of the covalent radius, rcov. When rcov is
expressed in ångströms,
Chemistry 281, Winter 2014, LA Tech
Chapter-1-123
Sanderson, cs
Sanderson has also noted the relationship between
electronegativity and atomic size, and has
proposed a method of calculation based on the
reciprocal of the atomic volume.
Allen, cA
The simplest definition of electronegativity is that
of Allen, bases on average energy of the valence
electrons in a free atom
where εs,p are the one-
Chemistry 281, Winter 2014, LA Tech
electron energies of s- and
p-electrons in the free atom
and ns,p are the number of
s- and p-electrons in the
valence shell. Chapter-1-124