Module 3.pdf
-
Upload
advait-vaidya -
Category
Documents
-
view
227 -
download
2
description
Transcript of Module 3.pdf
![Page 1: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/1.jpg)
Electrical and Electronic Materials
Module 3
Elementary Quantum PhysicsElementary Quantum Physics(Not in Syllabus, but mandatory for understanding of Chapter-4, For further reading, refer to
chapter-4 of Kasap Textbook)
![Page 2: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/2.jpg)
Atomic Orbitals
• Electrons inhabit regions of space know as orbitals. An orbital is the region
of space in which an electron exists / lives.
• If an electron is in a particular orbit it will have a particular definable
energy.
• In case of hydrogen (one electron) the electron can be found anywhere
within a spherical space surrounding the nucleus.within a spherical space surrounding the nucleus.
• The orbital occupied by hydrogen electron is called as 1s
orbital. 1 represents the fact that the orbital is in the energy
level closest to the nucleus.
• 2s orbital is similar to 1s orbital expect that the region
where there is the greatest chance of finding the
electron is further from the nucleus.
![Page 3: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/3.jpg)
• p orbital is like two identical balloons tied together at the nucleus.
• At any one energy level it is possible to have three absolutely equivalent p
orbitals pointing mutually at right angles to each other. These are given the
symbols px, py and pz. The p orbitals at the second energy level are called
2px, 2py and 2pz. There are similar orbitals at subsequent levels 3px, 3py and
3pz, 4px, 4py and 4pz
• At the third level there is a set of five d orbitals (with shapes) • At the third level there is a set of five d orbitals (with shapes)
as well as 3s and 3p orbitals.
•At the fourth level there are an additional seven f orbitals
![Page 4: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/4.jpg)
Fitting Electrons into Orbitals
• Electrons fill low energy orbitals (closer to the nucleus) before they fill
higher energy ones. Where there is a choice between orbitals of equal energy,
they fill the orbitals singly as far as possible.
• This filling of orbitals singly where possible is known as Hund's rule. It only
applies where the orbitals have exactly the same energies (as with p orbitals,
for example), and helps to minimise the repulsions between electrons and so
makes the atom more stable.makes the atom more stable.
![Page 5: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/5.jpg)
• Notice that the s orbital always has a slightly lower energy than the p orbitals
at the same energy level, so the s orbital always fills with electrons before the
corresponding p orbitals.
•The real oddity is the position of the 3d orbitals. They are at a slightly higher
level than the 4s - and so it is the 4s orbital which will fill first, followed by all
the 3d orbitals and then the 4p orbitals
•A 1s orbital holding 2 electrons would be drawn as shown below, but it can
be written even more quickly as 1s2. This is read as "one s two" - not as
“one’s squared.”
![Page 6: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/6.jpg)
B 1s22s22px1
Relating orbital filling to the Periodic Table
C 1s22s22px12py
1
N 1s22s22px12py
12pz1
O 1s22s22px22py
12pz1
F 1s22s22px22py
22pz1
Ne 1s22s22px22py
22pz2
Mg 1s22s22p63s2
S1s22s22p63s2
3px23py
13pz1
Ar1s22s22p63s2
3px23py
23pz2
![Page 7: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/7.jpg)
Orbital Hybridisation
• Hybridisation is the concept of mixing atomic orbitals to form new hybrid
orbitals suitable for the qualitative description of atomic bonding properties.
• Types of Hybridisation:
(a) sp hybrids: 2s orbital mixes with only one of the three p-orbitals
resulting in two sp orbitals and two remaining unchanged p orbitals.
(b) sp2 hybrids: In sp2 hybridisation the 2s orbital is mixed with only
two of the three available 2p orbitals:two of the three available 2p orbitals:
(c) sp3 hybrids: In sp3 hybridisation the 2s
orbital is mixed with all three of the 2p
orbitals.
![Page 8: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/8.jpg)
• Photons don't have mass, but they do have energy-and as Einstein famously
proved, mass and energy are really the same thing. So photons have
momentum--but what exactly is a photon?
• Photon is a “pocket of energy” it is an elementary particle, despite the fact
that it has no mass. It cannot decay on its own, although the energy of the
photon can transfer (or be created) upon interaction with other particles.
PHOTONS
• In some experiments, like Young's double slit experiment, light clearly
showed itself to be a wave, but other phenomena, such as the photoelectric
effect and Compton effect demonstrated equally clearly that light was a
particle.
• Sometimes light displays particle-like behavior, and sometimes it acts like a
wave; it all depends on what sort of experiment you're doing. This is known
as wave/particle duality
![Page 9: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/9.jpg)
Light as a Wave
• The classical view of light as an electromagnetic wave.
• An electromagnetic wave is a traveling wave with time-varying electric (Ey)
and magnetic fields (Bz) that are perpendicular to each other and to the
direction of propagation.
![Page 10: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/10.jpg)
Concept of In-Phase and
Out of Phase
![Page 11: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/11.jpg)
Young’s Double Slit Experiment
• Young’s double-slit experiment indicating that light has a wave
form
![Page 12: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/12.jpg)
X-ray diffraction
• X-ray diffraction indicating the wave nature of X-rays.
Braggs law
![Page 13: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/13.jpg)
The Photoelectric Effect
“Work function is the minimum energy (usually measured in electron volts)
needed to remove an electron from a solid to a point immediately outside
the solid surface”
![Page 14: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/14.jpg)
Results from the photoelectric experiment…….
(a) Photoelectric current vs. voltage when
the cathode is illuminated with light of
identical wavelength but different
intensities (I). The saturation current is
proportional to the light intensity
(b) The stopping voltage and therefore
the maximum kinetic energy of the
emitted electron increases with the
frequency of light υ. (Note: The light
intensity is not the same)
![Page 15: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/15.jpg)
Compton Scattering
![Page 16: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/16.jpg)
![Page 17: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/17.jpg)
The ELECTRON AS A WAVE
De Broglie Relationship
Where λ = wavelength
h = constant
P = momentum
m = mass
ʋ = velocity
![Page 18: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/18.jpg)
• When diffraction and interference experiments are repeated with
electron beam, similar results are found to those obtainable with light
or x-rays.
• De Broglie suggest electrons to have a wave nature which earlier was
considered to have a particle nature as suggested by Bohr.
• If we begin to think of electrons as waves, we'll have to change our• If we begin to think of electrons as waves, we'll have to change our
whole concept of what an "orbit" is. Instead of having a little particle
whizzing around the nucleus in a circular path, we'd have a wave sort of
strung out around the whole circle. Now, the only way such a wave could
exist is if a whole number of its wavelengths fit exactly around the circle.
If the circumference is exactly as long as two wavelengths, say, or three
or four or five, that's great, but two and a half won't cut it. So there could
only be orbits of certain sizes, depending on the electrons' wavelengths --
which depend on their momentum.
![Page 19: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/19.jpg)
Only way a wave could exist is if a whole number of its
wavelengths fit exactly around the circle…….
![Page 20: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/20.jpg)
Heisenberg’s Uncertainty Principle
• The principle means that it is impossible to determine simultaneously
both the position and momentum (or velocity) of an electron or any
other particle with any great degree of accuracy or certainty.
![Page 21: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/21.jpg)
Bonding electrons
Bonding electrons
Bonding, Non-bonding and Anti bonding
Hydrogen(Z = 1)
Bonding electrons
Non-bonding electrons
Anti bonding electrons
Oxygen(Z = 8)
Helium(Z = 2)
![Page 22: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/22.jpg)
Wave function (ψ):
• A wavefunction is a scalar function that is used to describe the properties of a wave
in terms of its position at a given time ψ(x,t).
• It is commonly applied as a property of particles relating to their wave-particle
duality, where it is denoted ψ(position,time) and where | ψ | 2 is equal to the chance
of finding the subject at a certain time and position. For example, in an atom with a
single electron, such as hydrogen or ionized helium, the wave function of the
electron provides a complete description of how the electron behaves.electron provides a complete description of how the electron behaves.
![Page 23: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/23.jpg)
General Bonding Principles
Force vs. interatomic separation
ro = bond length
Eo = bond energy
![Page 24: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/24.jpg)
As two atoms approach each
other a molecule will be formed
if the energy of the two atoms
attain a minimum energy
This energy is called the bond
energy and the corresponding
Potential energy versus interatomic separation
ro = bond length
Eo = bond energy
energy and the corresponding
length between the atoms the
bond length
![Page 25: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/25.jpg)
Release and absorption of energy during bond formation
and breaking
![Page 26: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/26.jpg)
Band Theory of Solids
• The electronic band structure (or simply band structure) of a solid
describes those ranges of energy, called energy bands, that an electron
within the solid may have ("allowed bands"), and ranges of energy
called band gaps ("forbidden bands"), which it may not have.
• Band theory models the behavior of electrons in solids by postulating
the existence of energy bands. It successfully uses a material's band the existence of energy bands. It successfully uses a material's band
structure to explain many physical properties of solids, such as electrical
resistivity and optical absorption. Bands may also be viewed as the large-
scale limit ofmolecular orbital theory. A solid creates a large number of
closely spaced molecular orbitals, which appear as a band.
• The electrons of a single isolated atom occupy atomic orbitals, which form
a discrete set of energy levels. If several atoms are brought together into a
molecule, their atomic orbitals split into separate molecular orbitals each
with a different energy.
![Page 27: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/27.jpg)
Interaction of orbitals
Isolated atom having
discrete energy levels
Molecule having separate molecular
orbitals each with separate energy
![Page 28: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/28.jpg)
• This produces a number of molecular orbitals proportional to the number of
valence electrons. When a large number of atoms (of order ×1020 or more) are
brought together to form a solid, the number of orbitals becomes exceedingly
large.
• Consequently, the difference in energy between them becomes very small.
Thus, in solids the levels form continuous bands of energy rather than the
discrete energy levels of the atoms in isolation. However, some intervals of
energy contain no orbitals, no matter how many atoms are aggregated,
forming band gapsforming band gaps
• When solids made of an infinite number of atoms are formed, it is a
common misconception to consider each atom individually. Rather, we must
consider the structure of the solid as a whole. This provides the basis for the
description of metals and other types of solids to account for their unique
chemical and physical properties.
![Page 29: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/29.jpg)
• In the basic theory, it was assumed that if atoms were brought together,
they would form bonding, non-bonding and antibonding orbitals of
different energies. These molecular orbitals are described by wave
functions.
• The most important point to come out of the theory is that for N atomic
orbitals in a molecule, N molecular orbitals must be the outcome.
For example, consider a molecule with two atomic orbitals. The result
must be that two molecular orbitals will be formed from these atomic
orbitals: one bonding and one antibonding, separated by a certain energy.orbitals: one bonding and one antibonding, separated by a certain energy.
![Page 30: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/30.jpg)
If this is expanded to a molecule with three atoms, assuming 1 atomic
orbital for each, then the result must be that 3 molecular orbitals will be
formed: one bonding, one non-bonding and one anti-bonding.
![Page 31: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/31.jpg)
Now , let's take it to 10 atoms. This will produce 10 molecular orbitals:
5 bonding and 5 anti-bonding. Now lets take a close look at the
separation between each set of orbitals. As the number of molecular
orbitals increases, the energy difference between the lowest bonding and
the highest antibondig increases, while the space between each
individual orbital decreases. As the number of molecular orbitals
increses with the number of atoms in a molecule, it will be observed that
the spacing between the lowest bonding and highest antibonding orbital
will reach a maximum.
![Page 32: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/32.jpg)
Now consider a metal with an infinite number of atoms. This will form an
infinite number of molecular orbitals so close together they blur into one
another forming a band. This whole process is shown below.
![Page 33: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/33.jpg)
![Page 34: Module 3.pdf](https://reader035.fdocuments.in/reader035/viewer/2022062407/55cf92b1550346f57b98cbe2/html5/thumbnails/34.jpg)