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Chapter 7
Atomic Structure and Periodicity
Topics
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Electromagnetic radiation
The nature of matter
The atomic spectrum of hydrogen
The Bohr model
The quantum mechanical model of the atom
Quantum numbers
Orbital shapes and energies
Electron spin and Pauli exclusion principle
Polyelectronic atoms
The history of the periodic Table
The aufbau principle and Periodic Table
Periodic trends in atomic properties
The Wave-like Electron
The electron propagates
through space as an energy
wave. To understand the
atom, one must understand
the behavior of
electromagnetic waves.
Louis deBroglie
7.1 Electromagnetic Radiation

electromagnetic radiation:
 form

of energy that acts as a wave as it
travels
 includes: X rays, Ultraviolet, visible light,
infrared light, microwaves, and radio
waves
 travel at a speed of 2.9979 x 108 m/s in a
vacuum
All forms of EMR are combined to form
electromagnetic spectrum
Electromagnetic Spectrum
High
Energy
The whole range of frequencies
Low
Energy
is called “Spectrum”
Radio
waves
Micro
waves
Infrared
.
Ultra- Xviolet Rays
Low
Frequency
Long
Wavelength
R O Y
Gamma
Rays
High
Frequency
Visible Light
G
B
Short
Wavelength
I V”
Parts of a wave
Crest
Wavelength
Amplitude
Origin
Trough


Wavelength
λ
= Greek letter lambda
 distance between points on adjacent waves
(consicutive peaks or troughs)
 Units used are in nm (109nm = 1m)
Frequency
  = Greek letter nu
 number of wave cycles that passes a point
in a second. 108 cycles/s= 108 s-1
 =108 Hertz = 108 Hz
 in 1/second (Hertz = Hz)
Electromagnetic
radiation
propagates through
space as a wave
moving at the
speed of light.
Equation:
c    
c

c = speed of light, a constant (2.998 x 108 m/s)
 (lambda) = wavelength, in meters
 (nu) = frequency, in units of hertz (hz or sec-1)
7.2 Nature of Matter

Before 1900, scientists thought that matter
and energy were totally different
matter
particles
mass
position
energy
wave
massless
delocalized
In 1900

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

According to the old views, matter could absorb or emit any
quantity (frequency) of energy.
Max Planck found that as the cooling of hot objects
couldn’t be explained by viewing energy as a wave.
Max Planck studied the radiation emitted by solid bodies
heated to incandescence.
Max Planck postulated that energy can be gained or lost
only in whole number multiples of the quantity
h



h =Planck’s constant= 6.626x10-34 J.s
That is change in energy of a system, E is
E  nh
n is an integer;  is the frequency of EMR
emitted or absorbed
Nature of Matter


Mack’s Planck suggested that an object emits
energy in the form of small packets of energy
called quanta. That is the energy is quantized
Quantum- the minimum amount of energy that
can be gained or lost by an atom (energy in each
packet) E  h
Thus energy seems to have particulate properties
Nature of Matter

Einstein proposed that radiation itself is
really a stream of particles called photons

Energy of each photon is :
E photon  hv 

also showed that energy
has mass E  mc 2
E
m 2
c
hc

Nature of Matter
c  v
v
c

E  hv
h

mc
hc

 mc
E
hc

2
E  mc
shows that anything with both mass and velocity
has a corresponding wavelength
2
Calculate the energy of red light vs. blue light.
red light: 700 nm
blue light: 400 nm
red:
hc
E

hc
E
 blue:
hc
E

34
8
(6.62x1034 J  s)( 3.00x108 m / s)
(
6
.
62
x
10
J

s
)(
3
.
00
x
10
m / s)
E
E
700x109 m
400x109 m
E = 2.85 x 10-19 J
E = 4.96 x 10-19 J
What is light?

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
Light has certain characteristics of
particulate matter
Light is a wave - we can measure its
wavelength and it behaves as a wave
If we combine E=mc2 , c=, E = 1/2 mv2
and E = h, then we can get:
 = h/mv


(from Louis de Broglie)
called de Broglie’s equation
This equation allows calculation of the
wavelength of a particle.
Wave-Particle Duality
J.J. Thomson won the Nobel prize for describing the
electron as a particle.
His son, George Thomson won the Nobel prize for
describing the wave-like nature of the electron.
The
electron is
a particle!
The electron
is an energy
wave!
7.3 The Atomic Spectrum of
Hydrogen



Main experiments led to the information related to
atom:
Thompson discovery of electron
Rutherford discovery of nucleus
Study of emission of light by excited hydrogen
atom
When H2 molecules absorb energy, some H-H
bonds are broken and excited H-atoms will be
produced
The excited H-atoms release energy by emitting
light at various wavelengths that is known as
emission spectrum of H-atoms
Spectroscopic analysis of the visible spectrum
White light
• When sunlight is dispersed by rain drops the rainbow is
Produced; that is a continuous spectrum is
produced.
• continuous spectrum contains all colors; that is all
wavelengths of the visible light
The Continuous Spectrum
 ~ 650 nm
 ~ 575 nm
 ~ 500 nm
 ~ 480 nm
 ~ 450 nm
The different
colors of light
correspond to
different
wavelengths and
frequencies
Spectroscopic analysis of the
hydrogen spectrum…
H receives a high energy
spark
H-H bonds
Are broken and H atoms
are excited
Hydrogen emission spectrum is called “line spectrum”
• Line spectrum
• Unique to each
element, like
fingerprints!
• Very useful for
identifying elements
Significance of the line spectrum of H-atom
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Only certain energies are allowed for the electron in
the hydrogen atom
That is, the energy of an electron in a hydrogen atom
is quantized.
Changes in energy between discrete energy levels in
hydrogen will produce only certain wavelengths of
emitted light.
The discrete line spectrum of hydrogen shows that
only certain energies are possible.
The electron energy levels are quantized. If all
energy levels are allowed the spectrum would be
continuous
7.4 The Bohr Model
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Niels Bohr (Danish physicist) 1885-1962
Developed a quantum model
for H atom that explained the emission line
spectrum
Electron moves around the nucleus only in
certain allowed circular orbits, in which it has
a certain amount of energy
The electrons were attracted to the nucleus
because of opposite charges.
But electron does not fall in to the nucleus
because it is moving around.
The Bohr Atom



He didn’t know why but only certain
energies were allowed.
He called these allowed energies
energy levels.
Putting Energy into the atom moved the
electron away from the nucleus.


From ground state to excited state.
When it returns to ground state it gives
off light of a certain energy.
The Model: Summary
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Space around nucleus is divided into
spherical (circualr) paths (orbits) each has a
number called “Principal Quantum
number”
The electron can exist only in one of these
orbitals but not in between
Orbits possess fixed size and energy,
therefore electron has a definite energy
characteristic of its orbit
En  Eorbit 
 RH Z
2
2
 Energy of electron
n
-18
R H  Rydberg constant  2.178x10
J
particle
En  2.178 X 10
18
23
J
6.02 X 10 particles
1kJ
1  1312kJ / mol
X
X
X 2 
2
particle
1mol
1000 J n
n
En 


 1312kJ
2
n mole
An electron can pass only from one orbit to
another. Absorption or emission will occur
Energy of the outermost orbit is zero
The Bohr Atom
n=4
n=3
n=2
n=1
Bohr Model

equation can be used twice to find the ∆E
when an electron moves energy levels
E  2.178 10
E  [2.178 10
18
J(
Zf
2
nf
2
E  2.178 10
18
2
Z
J( 2 )
n
)]  [2.178 10
18
1
1
J( 2  2 )
nf
ni
18
2
Zi
J ( 2 )]
ni
Bohr Model

Wavelength of photon released can be
calculated by using
hc

E

E=0 is set at an distance of ∞ away from the
nucleus and becomes more negative as the
electron comes closer to the nucleus
E  2.178 10
18
1
J( )  0

Example 1
1
1
Calculate the
18
E  2.178 10 J ( 2  2 )
energy required to
nf
ni
move the hydrogen
electron from n=1
1 1
18
E  2.178 10 J ( 2  2 )  1.633 10 18 J
to n=2. Find the
2 1
wavelength of
radiation that had to
m
34
(6.626 10 J  s)( 2.9979 )
hc
s
be absorbed by the


E
1.633 10 18 J
electron.
9
10
nm
  1.216 107 m 
 121.6nm
1m
Calculate the
energy required
to remove the
electron from the
hydrogen atom
in its ground
state.
Example 2
E  2.178 10
18
E  2.178 10
E  2.178 10
18
1
1
J( 2  2 )
nf
ni
18
1 1
J(  2 )
 1
J (0  1)  2.178 10
18
Energy was absorbed by the electron so the
value of ∆E value is positive.
J
Bohr Model

problems:
 did not work for other atoms
 did not explain chemical
behavior of atoms
Heisenberg’s Uncertainty Principle
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According to de Broglie: Electron behaves like a
wave
Is it possible to specify the position of a wave at a
particular instant?
Energy, wavelength and amplitude can be
determined
But exact position is impossible to be determined
The electron cannot be imagined as :
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
moving particle
In a path of the same radius (well defined orbits)
Thus, location, direction and speed of motion of a
particle cannot be determined
Then Bohr Model had to be “Abandoned
Heissenberg Uncertainty Principle
“It is impossible to determine both the
position and momentum of a subatomic
particle (such as the electron) with
arbitrarily high accuracy”
 The
effect of this principle is to convert the
laws of physics into statements about relative,
instead of absolute, certainties.
Heisenberg Uncertainty Principle
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we cannot know the
exact position and
momentum (motion)
of the electron
as more is known
about position, less is
known about
momentum
uncertainties are
inversely proportional
h
 x   ( m ) 
4
where
∆x: uncertainty in
position
∆m : uncertainty in
mometum
minimum uncertainty
is h/4
7.5 The Quantum Mechanical Model

Exact position of electron can not be
defined
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Exact bath of electron about nucleus can not be
defined
Werner Heisenberg, Louis de Broglie and
Erwin Schrodinger made the approach
called “Quantum Mechanics”
They assumed that the electron is a standing
wave
The Quantum Mechanical Model
Waves are associated with electrons
 Information about energies of
electrons and their positions are
obtained from studying the associated
waves
 Description of electron is based upon
“ Probability of finding a particle
within a given region of space” “ but
not on the exact position”

Schrödinger Equation
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
Wave equation describing electron as being
a wave
The amplitudes (height), , of electron
wave at various points of space are
calculated
 commonly called “wave function”
 provides information about the allowable
energies for an electron in H atom.
 corresponds to a certain energy and
describes a region around nucleus “Orbital”
where the electron having that energy may
be found
Orbital: Region around the nucleus
where the electron can be expected to
be found
 The Function 2
2 describes the probability of the
position of the electron at a particular
point
 2  Probability of finding a particle
in a given region of space
 2  Electric charge density at a given
region of space

Thus,



The charge can be assumed to be spread out
as a charge cloud by rapid motion of
electron
The cloud is denser in some regions than
others
The probability of finding electron in a
given region in space is proportional to the
density of the cloud
Meaning of Wave Function

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
the wave function itself does not have
concrete meaning
the square of the wave function represents
the probability of finding an electron at a
certain point
easily represented as probability distribution
where the deepness of color indicates the
probability
Meaning of Wave Function

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
(a) electron density map
probability of finding an
electron is highest at short
distances from nucleus
(b) calculated probability of
finding an electron at
certain distances from
nucleus in the 1s orbital
7.6 Quantum Numbers

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There are many solutions to Schroedinger’s
equation for H atom
Each solution is a wave function called
Orbital.
Each orbital can be described with
quantum numbers that describe
properties of the orbital


Quantum numbers specify the properties of
atomic orbitals and of electrons in orbitals
the first three quantum numbers come from
the Schrödinger equation and describe:
main energy level
 shape
 orientation


4th describes state of electron
Principal Quantum Number, n

Main energy level occupied by electron.
They are called atomic orbitals
regions where there is a high probability of
finding an electron.
n is related to the size and energy of the orbital
values are all positive integers >0 (1,2,3,…)
As n increases
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size of orbital is larger and electron is less tightly
bound to nucleus
The electron spends more time further from
nucleus
electron has higher energy
the electron’s average distance from the nucleus
increases
Principal Quantum Number
Maximum number
of electrons that
can fit in an
energy level:
2n2
Angular Momentum Quantum Number: l
It indicates the shape of the orbital
 The number of possible shapes (or l
values) for an energy level is equal to n
 The possible values of l are 0 and all
positive integers less than or equal to
n-1

 l has integer values from 0 to n-1
 l = 0 is called s
 l = 1 is called p
 l =2 is called d
 l =3 is called f
 l =4 is called g
Magnetic Quantum Number, ml
 ml indicates the orientation of the orbital in
space relative to the other orbitals in the
atom
 ml has integer values from +
including 0

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
l-l
each orbital holds maximum of 2
electrons
total number of orbitals is equal to n2 for an
energy level
number of possible ml values for a
certain subshell is equal to 2l + 1
Quantum Numbers for the first four levels of
orbitals in the hydrogen atom
7.7 Orbital shapes and Energies
s orbitals: 1: s
 spherical
 l value of 0
Representations of the Hydrogen 1s, 2s, and 3s Orbitals
A. The Electron
Probability Distribution
B. The surface
contains 90% of the
total electron
probability
p-orbitals
- +
+
-
+
-
p orbitals: 3
2px, 2py, 2pz
 dumbbellshaped
 l value = 1
 No 1p orbitals
 1st occur at
n=2
 for n>2,
shape is same
but size
increases
d- orbitals
-+
+ d orbitals: 5: 3dxz, 3dyz, 3dxy, 3dx2-y2, dz2
 mostly cloverleaf
 l value of 2


1st occur at n=3; no d-orbitals for n=1 or n=2
for n>3, same shape but larger size
f-orbitals

f orbitals: 7 types
various shapes
 l value of 3

begin in n=4

Other shapes can exist in energy levels as long as
they follow the rules

g (l =4) starts in 5 with 9 orbitals

h (l =5) starts in 6 with 11 orbitals, etc


but no known elements have electrons in them at
ground state
Remember that all orbitals of the same n has the
same energy; they are called “degenerate”
7.8 Electron spin and the Pauli Principle
Spin Quantum Number: ms





Electron has a magnetic moment with two possible
orientations when the atom is placed in an external
magnetic field
The electron could have two spin states
only 2 possible directions
ms can have two possible values: +½ and -½
paired electrons must
have opposite spins

Pauli Exclusion Principle:

In a given atom, no two electrons can have the
same set of four quantum numbers (n, l, ml , ms )
An orbital can hold only two electrons and they
must have opposite spins.

7.9 Polyelectronic Atoms
Three energy contributions must be considered
in the description of polyelectronic atom:
 Kinetic energy of electrons - as the electrons
move around the nucleus
 Potential energy - from attraction between
electrons and nucleus
 Potential energy of repulsion between two
electrons
Electron Correlation Problem



can’t find the exact location of electrons
can’t find the specific repulsions between
electrons
so we must treat each electron as if it has an
average amount of attraction to nucleus and
repulsion to other electrons
Electron Shielding


occurs when an electron is not attracted to the
nucleus
because of electrons in lower energy levels
repelling it.
Penetration Effect





all orbitals in the same energy level do NOT have
the same amount of energy ( are not degenerate)
same as the case in H-atom
Ens < Enp < End < Enf
the amount of energy in each sublevel is determined
by its average distance from the nucleus
For example, in He atom, 2p orbital has its
maximum probability closer to the nucleus than 2s
orbital, thus we would predict 2p would have less
energy than 2s.
However, 2s electron spends more time closer to
nucleus and usually has less energy.
That is 2s electron penetrates to the nucleus more
than an electron in a 2p orbital
7.10 The history of the Periodic Table




Developed independently by German
Julius Lothar Meyer and Russian Dmitri
Mendeleev (1870’s).
They didn’t know much about atom.
Elements were arranged in columns by
similar properties.
Properties of missing elements were
predicted.
Mendeleev's Early Periodic Table, Published in 1872
7.11 The aufbau Principle and Periodic Table
Electron Arrangement in Atoms



The way electrons are arranged in various
orbitals around the nuclei of atoms.
Aufbau is a German word means “Building up”
Aufbau principle - electrons enter the lowest
energy first.
•
Orbitals of different energies overlap
•
Electron Configurations
• Electron configuration describes the distribution of
electrons among the various orbitals in the atom
The spdf notation uses
numbers to designate a
principal shell and the
letters to identify a subshell;
a superscript number
indicates the number of
electrons in a designated
subshell
Orbital Diagram
An orbital diagram uses boxes to represent
orbitals within subshells and arrows to represent
electrons:
Each box has arrows representing electron spins;
opposing spins are paired together
EOS
Rules for Electron Configurations
Electrons occupy the lowest available energy orbitals
Pauli exclusion principle – no two electrons in the
same atom may have the same four quantum
numbers
•Orbitals hold a maximum of two electrons
with opposed spins
Rules for Electron Configurations
For orbitals of identical energy, electrons enter empty
orbitals whenever possible – Hund’s rule
When electrons occupy orbitals of equal energy,
they don’t pair up until they have to.
Electrons in half-filled orbitals have parallel spins
EOS
Rules for Electron Configurations
Capacities of shells (n) and subshells (l)
EOS
Rules for Electron Configurations
Subshell filling order :
Each subshell must
be filled before
moving to the next
level
Electron Configurations
Let’s write the electron configuration for
Phosphorus


We need to account for all 15
electrons in phosphorus
Increasing energy
7s
6s
5s
7p
6p
6d
5d
5p
4d
4p
3d
4s
3p
3s
2s
1s
5f
4f
15P
The first two
electrons go into the
2p 1s orbital
Notice the opposite
direction of the spins
 only 13 more to go

Increasing energy
7s
6s
5s
7p
6p
6d
5d
5p
4d
4p
5f
4f
3d
4s
3p
3s
2p

The next electrons
go into the 2s orbital

only 11 more
2s
1s
Increasing energy
7s
6s
5s
7p
6p
5p
4p
4s
6d
5d
4d
5f
4f
3d
3p
3s
2p
2s
• The next electrons go
into the 2p orbital
• only 5 more
1s
Increasing energy
7s
6s
5s
7p
6p
5p
4p
4s
6d
5d
4d
5f
4f
3d
3p
3s
2p
2s
1s
• The next electrons go
into the 3s orbital
• only 3 more
Increasing energy
7s
6s
5s
4s
3s
2s
1s
7p
6p
5p
4p
6d
5d
4d
5f
4f
3d
3p • The last three electrons
go into the 3p orbitals.
2p
They each go into
separate orbitas (Hund’s)
• 3 unpaired electrons
• = 1s22s22p63s23p3
The Aufbau Principle
A hypothetical building up of an atom from the one that
precedes it in atomic number
(Z = 1) H 1s1
(Z = 3) Li 1s22s1  [He]2s1
(Z = 2) He 1s2
Abbreviated electron configuration
(Z = 3) Li 1s22s1
EOS
The Aufbau Principle
[He]2p2
[He]2p3
[He]2p4
[He]2p5
[He]2p6
EOS
Orbital Diagram for A Nitrogen Atom
7N

1s

2s

2p


3s
Orbital Diagram for A Fluorine Atom
9F

1s

2s

2p


3s
Orbital Diagram for A Magnesium Atom
12Mg

1s

2s

2p


3s

8O

1s

2s

2p


3s
Write the orbital diagram for the electrons in
an iron atom 26Fe
 
1s 2s
  

2p
3s
   
3d

  
3p
Orbitals fill in an order



Lowest energy to higher energy.
Adding electrons can change the energy of
the orbital. Full orbitals are the absolute
best situation.
However, half filled orbitals have a lower
energy, and are next best
• Makes them more stable.
• Changes the filling order
Write the electron configurations for these
elements:
 Titanium - 22 electrons
 1s22s22p63s23p64s23d2

Vanadium - 23 electrons
 1s22s22p63s23p64s23d3

Chromium - 24 electrons
 1s22s22p63s23p64s23d4 (expected)
But this is not what happens!!
Chromium is actually:
 1s22s22p63s23p64s13d5
 Why?
 This
gives us two half filled
orbitals (the others are all still full)
 Half full is slightly lower in energy.
 The same principal applies to
copper.
Copper’s electron configuration





Copper has 29 electrons so we expect:
1s22s22p63s23p64s23d9
But the actual configuration is:
1s22s22p63s23p64s13d10
This change gives one more filled orbital
and one that is half filled.
Remember these exceptions: d4, d9
Irregular configurations of Cr and Cu
Chromium steals a 4s electron to
make its 3d sublevel HALF FULL
Copper steals a 4s electron
to FILL its 3d sublevel
Electron Configurations of Ions
Cations: lose e– to attain a complete valence
shell
Example:
(Z = 11) Na
(Z = 11) Na+
Details of the Periodic Table




Elements in the same column have the
same electron configuration.
Elements in columns have similar
properties.
Noble gases have filled energy levels.
Transition metals are filling the d orbitals

Valence electrons- the electrons in the
outermost energy levels (not d).
Core electrons- the inner electrons.

C 1s2 2s2 2p2

Valence Electrons and Core Electrons
Valence electrons are those with the highest
principal quantum number
 The electrons in the outermost energy
levels (not d).
Sulfur has six valence electrons
Valence Electrons and Core Electrons
Electrons in inner shells are called core electrons
Sulfur has 10 core electrons
EOS
Periodic Relationships
We can deduce the general form of electron
configurations directly from the periodic table
The Periodic Table
More exceptions
2
1
 Lanthanum La: [Xe] 6s 5d
2 1
1
 Cerium Ce: [Xe] 6s 4f 5d
Promethium Pr: [Xe] 6s2 4f3 5d0
2 7
1
 Gadolinium Gd: [Xe] 6s 4f 5d
2
14
1
 Lutetium Pr: [Xe] 6s 4f
5d
 We’ll just pretend that all except Cu
and Cr follow the rules.

Main Group (Representative) 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
(Representative) elements
“A” group designation on the periodic
table
The first 20 elements are all main group
elements
Transition Elements
In transition elements, the sublevel (shell) being
filled in the aufbau process is in an inner
principal shell (d or f)
d-Block transition elements: Electrons enter the
d-sublevels.
f-Block transition elements: d sublevels are
completely filled. Electrons enter f-sublevels
Lanthanides: electrons fill 4f subleve
Actinides: electrons fill 5f sublevels
The Periodic Table
Periodic Relationships
7.12 Periodic Trends in
Atomic Properties
Ionization Energy

Ionization energy the energy required to remove
an electron completely form a ground state atom
in the gaseous phase
A (g) + energy  A+ (g) + e Highest energy electron removed first.
 First ionization energy (I1) is that required
to remove the first electron.
 Second ionization energy (I2) - the second
electron, etc.
Successive ionization Energies

for Mg
•
•
•


I1 = 735 kJ/mole
I2 = 1445 kJ/mole
I3 = 7730 kJ/mole
The effective nuclear charge increases as
electrons are removed
It takes much more energy to remove a core
electron than a valence electron because
there is less shielding.
Successive ionization Energies
Continual removal of electrons increases ionization
energy greatly
B  B+ + e–
I = 801 kJ mol–1
B+  B+2 + e–
I = 2427 kJ mol–1
B+2  B+3 + e–
I = 3660 kJ mol–1
B+3  B+4 + e–
I = 25,025 kJ mol–1
B+4  B+5 + e–
I = 32,822 kJ mol–1
Core electron
Ionization Energy
First ionization energies across Periods and Groups
The Values of First Ionization Energy for the Elements
in the First Six Periods
For B electrons in 2s provide some shielding
From nucleus charge
E for O < E for N
due to extra
electron repulsion
in the doubly
occupied O 2p
orbitals
Ionization Energy
Ionization Energy
Electron Affinity
Electron Affinity – the energy change when an
electron is added to a gaseous neutral
atom
A + e-  A- + energy
Cl(g) + e-  Cl-(g) E = -349 kJ/mol
• Electron affinities are expressed as negative
because the process is exothermic
Electron affinity values
Electron Affinity
Electron Affinity

Across Period:
releases more
energy so number
increases (gets more
negative)
 because electrons
added in the same
energy level do not
shield electrons
from nuclear charge


Down Group:
 releases less energy
so number
decreases (gets less
negative)
 because the
electrons being
added are farther
away from the
attracting protons
Atomic Radii


Size of orbitals can not be
specified exactly, neither
can the size of atom
Atomic Radii – half the
distance between the
nuclei of identical atoms
that are bonded together
Atomic Radii

Across Period:
 atoms get smaller
 because of the
increased number of
protons attracting the
electrons
 the electrons added in
the same energy level
do not shield electrons
from nuclear charge

Down Group:
 atoms
get larger
 increases
 because the energy
levels being added
to the atom
Atomic Radii Properties
Summary of Periodic Trends