Chapter 7 Atomic Structure and Periodicity by 8kP90aF2

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```									             Chapter 7
Atomic Structure and Periodicity

behavior and travels through space at the
speed of light in a vacuum.
• Example: The sun light, energy used in
microwave oven, the x-rays used by doctors.
Waves
Waves have 3 primary characteristics:
1. Wavelength (): distance between two
consecutive peaks in a wave.
2. Frequency (): number of waves (cycles)
per second that pass a given point in space.
3. Speed: speed of light is 2.9979  108
m/s. We will use 3.00 x108 m/s.
The Nature of Waves
Wavelength and frequency can be interconverted
and they have an inverse relationship
 = c/
 = frequency (s1)
 = wavelength (m)
c = speed of light (m s1)
• Wavelength is also given in nm (1 nm = 10-9 m)
and Angstroms (Å) (1 Å = 10-10 m).
• The frequency value of s1 or 1/s is also called
“hertz (Hz)” like KHz on the radio.
Example: When green light is emitted from an
oxygen atom it has a wavelength of 558 nm.
What is the frequency?
We know,
 = c/           where, c = speed of light
= 3.00 x 108m/s
3.00  10m / s
8

                         = wavelength
558  10m
.          7
= 558 nm
14 1
 5.38  10s            (need to 9convert in m)
14                 
7
 5.38  10 Hz       558nm 
10m
 558  10m
.
1nm
Planck’s Constant
• Transfer of energy is quantized, and can only
occur in discrete units, called quanta.

hc
E = h =

E = change in energy, in J
h = Planck’s constant, 6.626  1034 J s
 = frequency, in s1
 = wavelength, in m
• Example: The Blue color in fireworks is often achieved by
heating copper (I) chloride (CuCl) to about 1200oC. Then the
compound emits blue light having a wavelength of 450 nm. What
is the increment of energy (the quantum) that is emitted at 4.50 x
102 nm by CuCl?
The quantum of energy can be calculate from the equation
E = h
The frequency  for this case can be calculated as follows:
8
c2.9979  10m / s           14
                    6.66  10s1
So,                  4.50  10m
7

E = h = (6.626 x 10-34J.s)(6.66 x 1014 s-1)
= 4.41 x 10-19J
A sample of CuCl emitting light at 450 nm can only lose energy
in increments of 4.41 x 10-19J, the size of the quantum in this
case.
Energy and Mass
• According to Einstein theory of relativity-
Energy has mass; Einstein equation,
E = mc2 where, E = energy, m = mass
c = speed of light
• After rearrangement of the equation,
E
m 2
c
Now we can calculate the mass associated
with a given quantity of energy
• Einstein suggested that electromagnetic radiation
can be viewed as a stream of “particles” called
photons. The energy of each photon is given by,
hc
E photon   = h =

E hc /    h
mphoton   = 2=      =
c   c 2
c
• It was Einstein who realized that light could not
be explained completely as waves but had to
have particle properties. This is called the dual
nature of light.
Wavelength and Mass
• de Broglie thought if waves like light could have
particle properties that particles like electrons could
have wave properties. We have,

  velocity
h        h
m     m
c      
de Broglie’s equation,             h
 =
m
 = wavelength (m); m = mass (kg);  = velocity (m/s)
h = Planck’s constant, 6.626  1034 J s = kg m2 s1

• This equation allows us to calculate the wavelength of a
particle. Matter exhibits both particulate and wave
properties.
• Example: Compare the wavelength for an electron
(mass = 9.11 x 10-31 kg) traveling at a speed of 1.0 x
107 m/s with that for a ball (mass = 0.10 kg) traveling at
35 m/s.
We use the equation  = h/m, where
h = 6.626  1034 J.s or 6.626  1034 kg m2 /s
since, 1 J = 1 kg. m2 /s2
For the electron,            34   kg. m. m
6.626  10                             11
e                         s          7.27  10 m
9.11  10 kg 10  10
31
.       7m / s

For the ball,                    34 kg. m. m
6.626  10                   34
b                s      19  10 m
010 kg 35 m / s
.
.
Atomic Spectrum of Hydrogen
• When H2 molecules absorb energy, some of the H-H
bonds are broken and resulting hydrogen atoms are
excited. The excess energy is released by emitting light of
various wavelengths to produce the emission spectrum of
hydrogen atom.
• Continuous spectrum: Contains all the wavelengths of
light.
Line (discrete) spectrum: Contains only some of the
wavelengths of light. Only certain energies are allowed,
i.e., the energy of the electron in the hydrogen atom is
quantized.                       hc
 E = h =

A Continuous Spectrum (a) and A Hydrogen Line Spectrum (b)
A Change between Two Discrete Energy Levels
The Bohr Model
• The electron in a hydrogen atom moves around the
nucleus only in certain allowed circular orbits. The
energy levels available to the hydrogen atom:
18
E =  2.178  10 J (z / n )
2 2

E = energy of the levels in the H-atom
z = nuclear charge (for H, z = 1)
n = an integer, the large the value, the larger is the
• Bohr was able to calculate hydrogen atom energy levels
that exactly matched the experimental value. The
energy of the electron bound to the nucleus is lower than
it would be if the electron were at an infinite distance.
Electronic Transitions in the Bohr Model for the Hydrogen Atom
• Ground State: The lowest possible energy
state for an atom (n = 1).
• Energy Changes in the Hydrogen Atom
E = Efinal state  Einitial state

 1          1 
= -2.178 x 10-18J  2       2        
 n final n initial 
• The wavelength of absorbed or emitted photon
can be calculated from the equation,
 c                  hc
 E  h                 =
                   E
Example: Calculate the energy required to excite
the hydrogen electron from level n = 1 to level n =
2. Also calculate the wavelength of light that must
be absorbed by a hydrogen atom in its ground state
to reach this excited state.
18 2 2
Using Equation, E =  2.178  10 J (z / n ) with Z = 1
we have

E1 = -2.178 x 10-18 J(12/12) = -2.178 x 10-18 J
E2 = -2.178 x 10-18 J(12/22) = -5.445 x 10-19 J

E = E2 - E1 = (-5.445 x 10-19 J) – (-2.178 x 10-18 J)
= 1.633 x 10-18 J
The positive value for E indicates that the
system has gained energy. The wavelength of
light that must be absorbed to produce this
change is

hc (6.626 x 10-34 J.s)(2.9979 x 108 m/s)
     
E          1.633 x 10-18 J

= 1.216 x 10-7 m
Example: Calculate the energy required to remove
the electron from a hydrogen atom in its ground
state.
Removing the electron from a hydrogen atom in its
ground state corresponds to taking the electron
from ninitial = 1 to nfinal = . Thus,

 1         1 
E = -2.178 x      J  2  2
10-18
 n final n initial 

1         1
= -2.178 x 10-18 J          1
2
            
The energy required to remove the electron from a
hydrogen atom in its ground state is 2.178 x 10-18 J.
Quantum Mechanics
Based on the wave properties of the atom
Schrodinger’s equation is (too complicated to be
detailed here),

H = E
 = wave function

H = mathematical operator
E = total energy of the atom
A specific wave function is often called an orbital.
This equation is based on operators – not simple
algebra. This is a mathematical concept you will not
have dealt with yet.
Heisenberg Uncertainty Principle
h
 x    mv 
x = position                    4
mv = momentum
h = Planck’s constant
The more accurately we know a particle’s
position, the less accurately we can know its
momentum. Both the position and momentum
of a particle can not be determined precisely at a
given time. The uncertainty principle implies
that we cannot know the exact motion of the
electron as it moves around the nucleus.
Quantum Numbers (QN)
When we solve the Schrodinger equation, we find many
wave functions (orbitals) that satisfy it. Each of these
orbitals is characterized by a series of numbers called
quantum numbers, which describe various properties of
the orbital.
1. Principal QN (n = 1, 2, 3, . . .) - related to size and
energy of the orbital.
2. Angular Momentum QN (l = 0 to n  1) - relates to
shape of the orbital. l = 0 is called s; l = 1 is called p; l = 2
is called d; l = 3 is called f.
3. Magnetic QN (ml = l to l including 0) - relates to
orientation of the orbital in space relative to other orbitals.
4. Electron Spin QN (ms = +1/2, 1/2) - relates to the
spin states of the electrons.
Example: For principal quantum level n = 5,
determine the number of allowed subshells
(different values of l), and give the designation of
each.
For n = 5, the allowed values of l run from 0 to 4
(n – 1 = 5 – 1). Thus the subshells and their
designations are

l=0      l=1      l=2     l=3      l=4
5s       5p       5d      5f        5g
Orbital Shapes and Energies
Two types of representations for the hydrogen 1s,
2s and 3s orbitals are shown below. The s orbitals
are spherical shape.

Two Representations of the
Hydrogen 1s, 2s, and 3s Orbitals
Representation of p orbitals
The p orbitals are not spherical like s orbital but have two
loves separated by a node at the nucleus. The p orbitals are
labeled according the axis of the xyz coordinate system.

The Boundary Surface Representations of All Three 2p Orbitals
Representation d orbitals

The five d orbital shapes are shown below. The d
orbitals have two different fundamental shapes.

The Boundary Surfaces of All of the 3d Orbitals
Energy Diagram for Hydrogen Atom
The energy of a particular orbital is determined by its value
of n. All orbitals with the same value of n have the same
energy and are said to be degenerate. Hydrogen single
electron occupy the lowest energy state, the ground state.
If energy is put into the system, the electron can be
transferred to higher energy orbital called excited state.

Orbital Energy
Levels for the
Hydrogen Atom
Pauli Exclusion Principle

• In a given atom, no two electrons can have the
same set of four quantum numbers (n, l, ml, ms).

• Therefore, an orbital can hold only two electrons,
and they must have opposite spins.
Polyelectronic Atoms
• For polyelectronic atoms in a given principal
quantum level all orbital are not in same energy
(degenerate). For a given principal quantum level
the orbitals vary in energy as follows:

Ens< Enp < End < Enf

• In other words, when electrons are placed in a
particular quantum level, they prefer the orbital in
the order s, p, d and then f.
Aufbau Principle

As protons are added one by one to the nucleus
to build up the elements, electrons are similarly

H : 1s1, He : 1s2, Li : 1s2 2s1, Be : 1s2 2s2
B : 1s2 2s2 2p1, C : 1s2 2s2 2p2.
Hund’s Rule
The lowest energy configuration for an atom is
the one having the maximum number of
unpaired electrons allowed by the Pauli principle
in a particular set of degenerate orbitals.

N : 1s2 2s2 2p3, O : 1s2 2s2 2p4,
F : 1s2 2s2 2p5, Ne : 1s2 2s2 2p6,
Na : 1s2 2s2 2p63s1 OR [Ne] 3s1
The Electron Configurations in the Type of
Orbital Occupied Last for the First 18 Elements
Valence Electrons
The electrons in the outermost principle quantum
level of an atom.
Atom            Valence Electrons
Ca                   2
N                    5
Br                     7
Valence electron is the most important electrons
to us because they are involved in bonding.
Elements with the same valence electron
configuration show similar chemical behavior.
Inner electrons are called core electrons.
Electron Configurations for Potassium Through Krypton
The Orbitals Being Filled for Elements in Various Parts of the Periodic Table
The Periodic Table With Atomic Symbols, Atomic
Numbers, and Partial Electron Configurations

• Representative Elements (main group): filling s
and p orbitals (Na, Al, Ne, O)
• Transition Elements: filling d orbitals (Fe, Co, Ni)
• Lanthanide and Actinide Series (inner transition
elements): filling 4f and 5f orbitals (Eu, Am, Es)
The Order in which the Orbitals Fill in Polyelectronic Atoms
Ionization Energy
The quantity of energy required to remove an
electron from the gaseous atom or ion.

X(g)       X+ (g) + e-
where, the atom or ion is assumed to be in its
ground state.
Periodic Trends

First ionization energy:
increases from left to right across a
period;
decreases going down a group.
The Values of First Ionization Energy for
The Elements in the First Six Periods
Trends in Ionization Energies
for the Representative Elements
Electron Affinity

The energy change associated with the addition
of an electron to a gaseous atom.
X(g) + e  X(g)
These values tend to be exothermic (energy
released). Adding an electron to an atom causes it
to give off energy. So the value for electron
affinity will carry a negative sign.
The Electronic Affinity Values for Atoms Among the
First 20 Elements that Form Stable, Isolated X- Ions
Periodic Trends
measuring the distances between atoms in chemical
compounds and atomic radius is assumed to be half
this distance.
• Decrease going from left to right across a period.
This decrease can be explained in terms of the
increasing effective nuclear charge in going from
left to right. The valence electron are drawn closer
to the nucleus, decreasing the size of the atom.
• Increase going down a group, because of the
increase in orbital sizes in successive principal
quantum levels.
Information Contained
in the Periodic Table
1. Each group member has the same valence electron
configuration. Group elements exhibit similar chemical
properties.
2. The electron configuration of any representative element can
be obtained from periodic table. Transition metals – two
exceptions, chromium and copper.
3. Certain groups have special names (alkali metals, halogens,
etc).
4. Metals and nonmetals are characterized by their chemical
and physical properties. Many elements along the division
line exhibit both metallic and non metallic properties which
are called metalloids or semimetals.
Special Names for Groups in the Periodic Table
Summary
behavior.
• Frequency,  = c/ ( = wavelength, c = speed of
light).
• Energy Transfer, E = h = hc/
• de Broglie’s Equation:  = h/m
• The Bohr Model: electron in a hydrogen atom moves
around the nucleus only in certain allowed circular
orbits.
• Quantum Mechanics: H= E
• Heisenberg Uncertainty Principle: Position and
momentum cannot be determined precisely at a
given time.
• Quantum Numbers: Principal QN, Angular
momentum QN, Magnetic QN, an Electron Spin
QN.
• Orbital Shapes and Energies: s, p, and d orbitals.
• Pauli Exclusion Principle:
• Aufbau Principle:
• Hund’s Rule:
• Periodic Table:
• Ionization Energy:
• Electron Affinity:
• Periodic Trends:

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