Download quantum number

PHYSICS FOR
ENGINEERING
Sub-topics
1
Structure of atom
Bonding in materials
Bonding and properties
WHY TO STUDY ATOMIC STRUCTURE?
The structure of atoms is important to
engineers because it influences the way atoms
are bonded together which helps us to categorize
the materials that they form.
The atomic structure and bonding also allows us
to formulate some general conclusions on the
mechanical and physical properties of the
material.
2
WHY STUDY BONDING?
Because the properties of materials (strength,
hardness, conductivity, etc..) are determined
by the manner in which atoms are
connected.
What determines the nature of the chemical bond
between atoms?
Electronic structure (distribution of electrons in
atomic orbitals)
Number of electrons and electronegativity
(tendency for an atom to attract an electron)
3
INTERATOMIC BONDING
All of the mechanisms which cause bonding between the atoms
derive from electrostatic interaction between nuclei and electrons.
The differing strengths and differing types of bond are determined
by the particular electronic structures of the atoms involved.
The existence of a stable bonding arrangement implies that the
spatial configuration of positive ion cores and outer electrons has
less total energy than any other configuration (including infinite
separation of the respective atoms).
The energy deficience of the configuration compared with isolated
atoms is known as a cohesive energy, and ranges in value from
0.1 eV/atom for solids which can muster only the weak van der
Waals to 7ev/atom or more in some covalent and ionic compounds
and some metals.
4
WHAT IS THE STRUCTURE OF ATOM?
It well known that the material properties are structure-sensitive.
neutron
Subatomic
<1A
●
●
●
●
●
nucleus
●
proton
●
●
electron
●
●
●
●
Atoms are made by massive, point-like
nuclei (protons + neutrons)
- Electron structure dictates how •Surrounded by tightly bound, rigid
shells of core electrons
bonding occurs
- The nature of the bond, in turn,
dictates many material properties •Bound together by a glue of valence
electrons (gas vs. atomic orbitals)
5
STRUCTURE OF ATOM
A normal atom has equal numbers of
protons and electrons.
The Atomic Number of an atom is the
number of protons it has in it’s nucleus.
6
ATOMIC MASS
7
BOHR ATOM
The energies of electrons
are quantized;
electrons are permitted to
have only specific
values of energy.
May e change its energy?
The simplified Bohr atomic model, in
which electrons are assumed to revolve
around the atomic nucleus in
discrete orbitals, and the position of any
particular electron is more or less well
defined in terms of its orbital.
8
ELECTRON ENERGY STAGES
n – principal
quantum number
Pauli exclusion principal states that no two identical
9
fermions may occupy the same quantum state
simultaneously.
QUANTUM PHYSICS MILESTONES
Between 1900 and 1925 Quantum Physics
was developed by a number of physicists,
including Planck, Einstein, Bohr and de
Broglie.
From 1925 onwards a more mathematical
approach was developed by Schrödinger
(wave mechanics), Heisenberg (matrix
mechanics) and Dirac (who developed a
more general formulation).
10
If you are not confused by Quantum Physics then you haven't really
understood it.
N.Bohr
WHAT IS QUANTUM MECHANICS GOOD FOR?
Quantum mechanics does not explain how a quantum
particle behaves.
Instead, it gives a recipe for determining the probability
of the measurement of the value of a physical variable
(e.g. energy, position or momentum).
This information enables us to calculate the average
value of the measurement of a physical variable.
Quantum mechanics
is the study of mechanical systems whose dimensions are close to the
atomic scale. Quantum mechanics is a fundamental branch of physics
with wide applications. Quantum theory generalizes classical
mechanics to provide accurate descriptions for many previously
unexplained phenomena such as black body radiation and stable
electron orbits. The effects of quantum mechanics become evident at
the atomic and subatomic level, and they are typically not observable
on macroscopic scales. - Wikipedia
11
WAVE-PARTICLE DUALITY
In physics and chemistry,
wave–particle duality
is the concept that all matter
and energy exhibits both
wave-like and particle-like
properties.
Particles are waves,
waves are particles.
In quantum mechanics,
the motion of particles is described with
probabilities.
Probability distribution of the Bohr atom –
Wikipedia
12
HOW MANY QUANTUM NUMBERS?
Using wave mechanics, every electron in an atom is characterized by four
parameters called quantum numbers.
The Bohr model was a one-dimensional model
that used one quantum number to describe the
distribution of electrons in the atom.
The only information that was important was the
size of the orbit, which was described by the n
quantum number.
Schrödinger's model allowed the electron to
occupy three-dimensional space.
It therefore required three coordinates, or three
quantum numbers, to describe the orbitals in
which electrons can be found.
The three coordinates that come from Schrödinger's wave equations are the
principal (n), angular (l), and magnetic (m) quantum numbers.
13
These quantum numbers describe the size, shape, and orientation in
space of the orbitals on an atom.
QUANTUM NUMBERS
The principal quantum number (n) describes the size (distance of an
electron from the nucleus) of the orbital.
Orbitals for which n = 2 are larger than those for which n = 1.
The principal quantum number therefore indirectly describes the energy
of an orbital.
The angular quantum number (l) describes the shape of the orbital.
Orbitals have shapes that are best described as spherical (l = 0), polar (l
= 1), or cloverleaf (l = 2). They can even take on more complex shapes as
the value of the angular quantum number becomes larger.
A third quantum number, known as the magnetic quantum number (m),
describes the orientation in space of a particular orbital and shows the
energy states in sub-shells.
14
SHELLS AND SUB-SHELLS OF ORBITALS
Orbitals that have the same value of the
principal quantum number form a shell.
Orbitals within a shell are divided into
subshells that have the same value of the
angular quantum number.
Bohr and (b)
wavemechanical
atom models in
terms of electron
distribution.
15
SUB-SHELLS
•s, p, d and f signify
the subshells which the
electrons occupy.
• Different types of
subshells have
different
numbers of energy
states
•Within each energy
state there are two
possible spin
orientations
Schematic
representation of the relative
energies of the electrons for the
various shells and subshells
16
ELECTRON STATES
What is electron configuration for C?
Na and Cl (is it easy to create sodium chloride molecule?)
17
ELECTRON CONFIGURATIONS
18
CHEMICAL BONDING BETWEEN ATOMS
• Electron states is controlling factor for atomic
bonding
• Types of primary (strong) bonds: ionic, covalent,
metallic
• Types of secondary (weak) bonds: van der Waals,
hydrogen
• Properties that are controlled by interatomic
potentials: melting point, bond stiffness, thermal
expansion coefficient
19
BONDING FORCES
Many properties of materials are determined by the interatomic forces
that bind the atoms together.
Equilibrium spacing
These forces are of two types, attractive and repulsive, and the magnitude
20
of each is a function of the separation or interatomic
distance.
ENERGY OF BONDING
Bonding energy
Once in this position, the
two atoms will counteract
any attempt to separate
them by an attractive force,
or to push them together by21
a repulsive action.
This typical curve has a
minimum at equilibrium
distance R0
R > R0 ;
the potential increases
gradually, approaching 0
as R ∞
the force is attractive
R < R0;
the potential increases
very rapidly, approaching
∞ at small separation.
the force is repulsive
V(R)
Repulsive
0
R0
R
Attractive
r
R
Force between the atoms is the negative of the slope of this curve. At
equlibrium, repulsive force becomes equals to the attractive part.
22
IS IT DIFFICULT TO SEPARATE ATOMS?
represents the energy that
would be required to separate
The magnitude of this bonding energy and the
these two atoms to an infinite
shape of the energy versus interatomic separation distance
23
curve vary from material to material, and they
both depend on the type of atomic bonding.
ATOMIC INTERACTIONS
24
THE POTENTIAL ENERGY OF ATOM
V=
decrease in potential energy+increase in potential energy
(due to attraction)
(due to repulsion)
−a b
V (r ) = m + n
r
r
V(r): the net potential energy of interaction as function of r
r : the distance between atoms, ions, or molecules
a,b: proportionality constant of attraction and repulsion,
respectively
m, n: constant characteristics of each type of bond and type of
structure
25
MODULUS AND BONDING ENERGY
The magnitude of the modulus of
elasticity is proportional to
the slope of each curve at the
equilibrium interatomic separation r0
26
ELASTIC MODULUS
27
COHESIVE ENERGY
Atoms are held together by bonds
that behave like springs
Cohesive energy is a measure of
the strength of the bonds
Bond Stiffness
28
TYPES OF BONDING
It is conventional to classify the bonds between
atoms into different types as
Ionic,
Covalent,
Metallic,
Van der Waals,
Hydrogen.
All bonding is a consequence of the electrostatic
interaction between nuclei and electrons obeying
Schrödinger’s equation.
29
IONIC BONDING
• Occurs between strongly electronegative and strongly
electropositive atoms
• Electron(s) are transferred from electropostive atom to
electronegative atom, thereby forming a cation (positively
charged) and an anion (negatively charged)
30
NACL
When sodium loses its one valence electron it gets smaller in
size,
while chlorine grows larger when it gains an additional valance
electron.
After the reaction takes place, the charged Na+ and Cl- ions are
held together by electrostatic forces, thus forming an ionic
bond.
31
IONIC BONDING
When the Na+ and Cl- ions approach each other closely
enough so that the orbits of the electron in the ions begin
the overlap each other,
then the electron begins to repel each other by virtue of the
repulsive electrostatic coulomb force.
The closer together the ions are, the grater the repulsive
force.
Pauli exclusion principle has an important role in
repulsive force.
To prevent a violation of the exclusion principle, the
potential energy of the system increases very rapidly.
32
Property
Explanation
Melting point
and boiling point
The melting and boiling points of ionic
compounds are high because a large amount of
thermal energy is required to separate the ions
which are bound by strong electrical forces.
Electrical
conductivity
Solid ionic compounds do not conduct electricity
when a potential is applied because there are no
mobile charged particles.
No free electrons causes the ions to be firmly
bound and cannot carry charge by moving.
Hardness
Most ionic compounds are hard; the surfaces of
their crystals are not easily scratches. This is
because the ions are bound strongly to the
lattice and aren't easily displaced.
Brittleness
Most ionic compounds are brittle; a crystal will
shatter if we try to distort it. This happens
because distortion cause ions of like charges to
33
come close together then sharply repel.
EXAMPLES OF IONIC BONDING
34
COVALENT BONDING
35
COVALENT BONDING
Covalent bonding takes place between atoms with
small differences in electronegativity which are
close to each other in periodic table (between nonmetals and non-metals).
The covalent bonding is formed by sharing of
outer shell electrons (i.e., s and p electrons)
between atoms rather than by electron transfer.
This bonding can be attained if the two atoms
each share one of the other’s electrons.
So the noble gas electron configuration can be
attained.
36
COVALENT BONDING
Atoms form stable electron structures, i.e. those of inert gases, by
sharing of electrons with other atoms
• Resulting bonds are strongly directional
37
Property
Melting point
and boiling point
Electrical
conductivity
Hardness
Brittleness
Explanation
Very high melting points because each atom is
bound by strong covalent bonds. Many covalent
bonds must be broken if the solid is to be melted
and a large amount of thermal energy is
required for this.
Poor conductors because electrons are held
either on the atoms or within covalent bonds.
They cannot move through the lattice.
They are hard because the atoms are strongly
bound in the lattice, and are not easily
displaced.
Covalent network substances are brittle.If
sufficient force is applied to a crystal, covalent
bond are broken as the lattice is distorted.
Shattering occurs rather than deformation of a38
shape.
COMPARISON OF IONIC AND COVALENT
BONDING
39
METAL BONDING
Valence electrons ( in outer
shell) leave atoms and form a
“sea” of free electrons
Positively charged ion cores
are shielded from one another
by the free electrons
Free electron acts as the
“glue” that hold positive cores
together
Non-directional
High thermal and electrical conductivity
40
HOW STRONG IS METAL BONDING?
Valance electrons are relatively bound to the nucleus
and therefore they move freely through the metal and they
are spread out among the atoms in the form of a lowdensity electron cloud.
A metallic bond result from the
sharing of a variable number of
electrons by a variable number of
atoms. A metal may be described
as a cloud of free electrons.
Therefore, metals have high
electrical and thermal
conductivity.
+
+
+
+
+
+
+
+
+
41
METAL BONDING - SUMMARY
All valence electrons in a metal combine to form a “sea”
of electrons that move freely between the atom cores.
The more electrons, the stronger the attraction.
This means the melting and boiling points are higher,
and the metal is stronger and harder.
The positively charged cores are held together by these
negatively charged electrons.
The free electrons act as the bond (or as a “glue”)
between the positively charged ions.
This type of bonding is non-directional and is rather
insensitive to structure.
As a result we have a high ductility of metals - the
“bonds” do not “break” when atoms are rearranged –
metals can experience a significant degree of plastic
deformation.
42
VAN DER WAALS BONDING
It is a weak bond, with a typical strength of 0.2
eV/atom.
It occurs between neutral atoms and molecules.
The explanation of these weak forces of attraction is
that there are natural fluctuation in the electron
density of all molecules and these cause small
temporary dipoles within the molecules. It is these
temporary dipoles that attract one molecule to another.
They are called van der Waals' forces.
The bigger a molecule is, the easier it is to polarize (to
form a dipole), and so the van der Waal's forces get
stronger, so bigger molecules exist as liquids or solids
rather than gases.
43
THE WAY TO CREATE VAN DER WAALS BOND (1)
The shape of a molecule influences its ability to form
temporary dipoles. Long thin molecules can pack closer to
each other than molecules that are more spherical. The
bigger the 'surface area' of a molecule, the greater the van
der Waal's forces will be and the higher the melting and
boiling points of the compound will be.
Van der Waal's forces are of the order of 1% of the strength
of a covalent bond.
Homonuclear molecules,
such as iodine, develop
temporary dipoles due to
natural fluctuations of electron
density within the molecule
Heteronuclear molecules,
such as H-Cl have permanent
dipoles that attract the opposite
pole in other molecules. 44
THE WAY TO CREATE VAN DER WAALS BOND (2)
The dipoles can be formed as a result of
unbalanced distribution of electrons in
asymettrical molecules. This is caused by
the instantaneous location of a few more
electrons on one side of the nucleus than on
the other.
symmetric asymmetric
Therefore atoms or molecules containing dipoles are
attracted to each other by electrostatic forces.
Display a marked
attractive forces
45
No attraction is produced
THE WAY TO CREATE VAN DER WAALS BOND (3)
These forces are due to the electrostatic attraction between
the nucleus of one atom and the electrons of the other.
In polyvinyl chloride (PVC), the chlorine atoms attached to the polymer chain
have a negative charge and the hydrogen atoms are positively charged. The
46
chains are weakly bonded by van der Waals bonds.
This additional bonding makes PVC stiffer.
VAN DER WAALS BONDING
•
Dipole moment produced
by instantaneous
asymmetry of electron
charge distribution
•
Coulombic attraction
occurs between positive
end of one
dipole and negatively
charged end of another
47
SECONDARY BONDING
The bonding results from the coulombic
attraction between the positive end of
one dipole and the negative region of an
adjacent one
48
HYDROGEN BONDING
49
HYDROGEN BONDING
A hydrogen atom, having one electron, can be covalently
bonded to only one atom. However, the hydrogen atom
can involve itself in an additional electrostatic bond
with a second atom of highly electronegative character
such as fluorine or oxygen. This second bond permits a
hydrogen bond between two atoms or strucures.
The strength of hydrogen bonding varies from 0.1 to 0.5
ev/atom.
Hydrogen bonds connect water
molecules in ordinary ice.
Hydrogen bonding is also very
important in proteins and
nucleic acids and therefore in
life processes.
50
BOND STIFFNESS AND MODULUS
Bond stiffness largely determines the value
of the modulus - E
51
SUMMARY
52
MELTING TEMPERATURE
53
BONDING ENERGIES AND
MELTING TEMPERATURES
54