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)

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.

• 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

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.

• 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.”

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

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.

• 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

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.

Concept of In-Phase and

Out of Phase

Young’s Double Slit Experiment

• Young’s double-slit experiment indicating that light has a wave

form

X-ray diffraction

• X-ray diffraction indicating the wave nature of X-rays.

Braggs law

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”

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)

Compton Scattering

The ELECTRON AS A WAVE

De Broglie Relationship

Where λ = wavelength

h = constant

P = momentum

m = mass

ʋ = velocity

• 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.

Only way a wave could exist is if a whole number of its

wavelengths fit exactly around the circle…….

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.

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)

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.

General Bonding Principles

Force vs. interatomic separation

ro = bond length

Eo = bond energy

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

Release and absorption of energy during bond formation

and breaking

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.

Interaction of orbitals

Isolated atom having

discrete energy levels

Molecule having separate molecular

orbitals each with separate energy

• 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.

• 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.

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.

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.

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.