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Engineering Chemistry Unit-1, Exams of Engineering Chemistry

Unit 1-Bonds to Bands Sem -1 important questions with answers including long answers

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SCYA1101: Engineering Chemistry UNIT 1: Bonds to Bands
Dr. A. Sheik Mideen, Department of Chemistry, Sathyabama Institute of Science and Technology
UNIT 1
BONDS TO BANDS
Introduction to Quantum Chemistry Motion of a Quantum Mechanical Particle in One
Dimension (Time- Independent) Schrödinger Wave Equation for Hydrogen Atom (No
Derivation) Physical Meaning of Wave Function - Angular and Radial Wave Functions and
Probability Densities Quantum Numbers Principal, Azimuthal, Spin and Magnetic
Quantum Numbers Wave Functions and Orbital Shapes - s, p, d, f - LCAO-MO of H2 Band
Theory of Solids: Conductors, Semi-Conductors and Superconductors Role of As and Ga
Doping on Band Structures.
INTORDUCTION TO QUANTUM CHEMISTRY
1. Compare Classical Mechanics with Quantum Mechanics
S. No.
Classical Mechanics
Quantum Mechanics
1.
It deals with macroscopic particles.
It deals with microscopic particles.
2.
It is based upon Newton’s laws of
motion.
It takes into account Heisenberg’s
uncertainty principle and de Broglie
concept of dual nature of matter.
3.
It is based on Maxwell’s
electromagnetic wave theory according
to which any amount of energy may be
emitted or absorbed continuously.
It is based on Planck’s quantum
theory according to which only
discrete values of energy are
emitted or absorbed.
2. Tell de Broglies hypothesis.
According to de-Broglie, the microscopic particle like electron has dual character. It
can behave as a wave and as a particle.
3. Define Heisenbergs uncertainty principle.
For any microscopic particles like electron that has a dual character of wave and particle,
it is not possible to determine the position and momentum simultaneously”.
4. Write time independent Schrodinger wave equation.
𝝏𝟐𝜳
𝝏𝒙𝟐=−𝟖𝝅𝟐[𝑬−𝑽]
𝒉𝟐 𝜳
5. Write Schrodinger wave equation in Hamiltonian form.
𝑯
𝜳=𝑬𝜳
𝒘𝒉𝒆𝒓𝒆, 𝑯
=[−𝜵𝟐𝒉𝟐
𝟖𝝅𝟐𝒎+𝑽]𝒊𝒔 𝒌𝒏𝒐𝒘𝒏 𝒂𝒔 𝑯𝒂𝒎𝒊𝒍𝒕𝒐𝒏𝒊𝒂𝒏 𝒐𝒑𝒆𝒓𝒂𝒕𝒐𝒓.
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SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

UNIT 1

BONDS TO BANDS

Introduction to Quantum Chemistry – Motion of a Quantum Mechanical Particle in One

Dimension (Time- Independent) – Schrödinger Wave Equation for Hydrogen Atom (No

Derivation) – Physical Meaning of Wave Function - Angular and Radial Wave Functions and

Probability Densities – Quantum Numbers – Principal, Azimuthal, Spin and Magnetic

Quantum Numbers – Wave Functions and Orbital Shapes - s, p, d, f - LCAO-MO of H 2

  • Band

Theory of Solids: Conductors, Semi-Conductors and Superconductors – Role of As and Ga

Doping on Band Structures.

INTORDUCTION TO QUANTUM CHEMISTRY

1. Compare Classical Mechanics with Quantum Mechanics

S. No. Classical Mechanics Quantum Mechanics

  1. It deals with macroscopic particles. It deals with microscopic particles.
  2. It is based upon Newton’s laws of

motion.

It takes into account Heisenberg’s

uncertainty principle and de Broglie

concept of dual nature of matter.

  1. It is based on Maxwell’s

electromagnetic wave theory according

to which any amount of energy may be

emitted or absorbed continuously.

It is based on Planck’s quantum

theory according to which only

discrete values of energy are

emitted or absorbed.

2. Tell de Broglie’s hypothesis.

According to de-Broglie, the microscopic particle like electron has dual character. It

can behave as a wave and as a particle.

3. Define Heisenberg’s uncertainty principle.

For any microscopic particles like electron that has a dual character of wave and particle,

it is not possible to determine the position and momentum simultaneously”.

4. Write time independent Schrodinger wave equation.

𝝏

𝟐

𝜳

𝝏𝒙

𝟐

−𝟖𝝅

𝟐

[𝑬−𝑽]

𝒉

𝟐

5. Write Schrodinger wave equation in Hamiltonian form.

𝑯

̂

𝜳 = 𝑬𝜳

𝒘𝒉𝒆𝒓𝒆, 𝑯

̂ = [

−𝜵

𝟐

𝒉

𝟐

𝟖𝝅

𝟐

𝒎

  • 𝑽] 𝒊𝒔 𝒌𝒏𝒐𝒘𝒏 𝒂𝒔 𝑯𝒂𝒎𝒊𝒍𝒕𝒐𝒏𝒊𝒂𝒏 𝒐𝒑𝒆𝒓𝒂𝒕𝒐𝒓.

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

6. Define the term wave function.

In quantum mechanics, there is no distinction between the particle and wave, and hence

the microscopic system (like electron, atom, or molecule) is described by a mathematical

function known as wave function. It is represented by the symbol, Ψ (psi).

7. What are the conditions for acceptable wave function?

✓ Ψ must be a single valued function.

✓ Ψ must be continuous with respect to the change of variables.

✓ Ψ must have finite value.

✓ Ψ must be normalized.

APPLICATION OF SCHRODINGER WAVE EQUATION FOR A PARTICLE IN ONE

DIMENSIONAL BOX

1. Formulate the Schrodinger wave equation for a particle in one dimensional

box and determine the wave function and energy of the particle.

The Concept of 1 - D Box

Let us consider a particle moving along x direction in a confined space between the limits

x = 0 and x = L. As the particle is moving along the x - direction, its potential energy, V =

0 inside the box while the potential energy at the boundaries and outside the box is, V =

∞. The probability of finding the particle inside the box i.e. 𝛹 ≠ 0 while the probability

of finding particle outside the box is zero.

x = 0 x = L

V =

V=

x - axis

V =

oo

oo = 0

= 0

i.e. The boundary conditions may be expressed in mathematical form as:

(i) when

𝑽 = ∞

𝒙 ≤ 𝟎

𝒙 ≥ 𝑳

} → 𝑽 = ∞ 𝒓𝒆𝒑𝒓𝒆𝒔𝒆𝒏𝒕𝒔 𝒕𝒉𝒂𝒕, 𝒏𝒐 𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆 𝒆𝒙𝒊𝒕𝒔 𝒐𝒖𝒕𝒔𝒊𝒅𝒆 𝒕𝒉𝒆 𝒃𝒐𝒙 𝒂𝒏𝒅 𝒉𝒆𝒏𝒄𝒆 𝜳 = 𝟎.

(ii) when

𝑽 = 𝟎

𝟎 < 𝒙 < 𝑳

} → 𝑽 = 𝟎 𝒓𝒆𝒑𝒓𝒆𝒔𝒆𝒏𝒕𝒔 𝒕𝒉𝒂𝒕 𝒕𝒉𝒆 𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆 𝒆𝒙𝒊𝒕𝒔 𝒊𝒏𝒔𝒊𝒅𝒆 𝒕𝒉𝒆 𝒃𝒐𝒙 𝒂𝒏𝒅 𝒉𝒆𝒏𝒄𝒆 𝜳 ≠ 𝟎.

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

Determination of Energy of a Moving Particle in 1 - D Box

Squaring the equation (5) on both the sides, we have:

2

2

2

2

From equation (3), we have:

2

2

2

Comparing equation (3) and equation (7), we have:

2

2

2

2

2

2

2

2

Therefore, the energy of particle depends upon ‘ n ’ value, so we have:

𝒏

𝟐

𝟐

𝟐

Where n is the principal quantum number and can have the values 1, 2, 3, ….; h is the

Planck’s constant; m is the mass of particle (electron) and L is the length of box (space

between two quantum numbers).

When n = 1, then 𝐸

1

2

8 𝑚𝐿

2

; this is the minimum energy possessed by the particle.

When n = 2, then 𝐸

2

4ℎ

2

8 𝑚𝐿

2

; energy level of particle increases by four times.

When n = 3, then 𝐸

3

9ℎ

2

8 𝑚𝐿

2

When n = 4, then 𝐸

4

16ℎ

2

8 𝑚𝐿

2

and so on ….

As the principle quantum number increases, the spacing between two energy level

increases. Further, the spacing between two energy level decreases when length of one-

dimensional box increases.

Zero Point Energy: It the minimum amount of energy possessed by a particle in one

dimensional box, and it is given by:

𝟏

𝟐

𝟐

Where h is Planck’s constant (6.626 × 10

kg m

2

s

and m is mass of electron (9.1 ×

kg).

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

x = 0 x = L

n = 1

n = 2

n = 3

E

3

=

E

2

=

E

1

=

9h

2

8mL

2

4h

2

h

2

E

n

e

r

g

y

8mL

2

8mL

2

2. Determine the value of “A” in the wave function of particle in one

dimensional box by normalization method.

The wave function Ψ can have a positive real value and a negative imaginary value and

hence it has no significance.

The wave function for a particle in one dimensional box is given by:

On squaring both the sides, we get Ψ

2

, which will have always a positive value.

Integrating Ψ

2

with the limits 0 → L can be used for finding the particle in one

dimensional box, which is equal to unity (100%).

2

2

2

𝐿

0

𝐿

0

2

[

] 𝑑𝑥 = 1

𝐿

0

2

[∫ 𝑑𝑥

𝐿

0

𝐿

0

] = 1

2

[𝐿] = 1 (𝑜𝑟) 𝐴

2

Therefore, the wave function for particle in one dimensional box is given by:

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

2. Explain the physical significance of Ψ and Ψ

2

The Ψ is known as wave function while Ψ

2

is known as probability density function of

the particle in 1-D box.

The Ψ can have a positive value and a negative value while Ψ

2

always will have a positive

value.

The Ψ

2

can be used: (i) to find out the probability density of particle in 1-D box and (ii)

to calculate the number of nodes of a system in 1-D box.

3. What is probability density?

Probability density (function) refers to the probability of finding particle like electron in

a given region of space.

APPLICATION OF SWE FOR HYDROGEN ATOM

1. Outline the time-independent Schrodinger equation of hydrogen atom

using φ and θ****.

The hydrogen atom is an example of two particle system (electron and proton).

The proton has a mass of M with a charge of + Ze and the electron has a mass of m with

a charge of – e.

Since the proton has heavier mass than the electron, the electron revolves around the

nucleus with its reduced mass along the distance r.

The potential energy of electron moving at a distance of r due to electrostatic attraction

with proton is given as:

𝑍𝑒

2

( 4 𝜋𝜀

𝑜

)𝑟

𝑒

2

( 4 𝜋𝜀

𝑜

)𝑟

Where Z is the atomic number, e is the electronic charge in Coulomb, and 𝜀

𝑜

is the

absolute permittivity of the medium, vacuum, in this case (𝜀

𝑜

= 8.85×

Now there are two types of motions are involved in hydrogen atom and they are:

i) Translation motion of electron

ii) Internal motion of electron and proton

The Schrodinger wave equation for these two types motions is given by:

𝑇

𝑇

𝑇

Where Ĥ is Hamiltonian operator; Ψ T

is complete (or total) wave function and E T

is the

total energy of hydrogen atom.

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

We know that, 𝐻

= [

−𝛻

2

2

8 𝜋

2

𝑚

+ 𝑉] 𝑤ℎ𝑒𝑟𝑒 𝛻

2

= [

𝜕

2

𝜕𝑥

2

𝜕

2

𝜕𝑦

2

𝜕

2

𝜕𝑧

2

]

2

2

[

2

2

2

2

2

2

] + 𝑉} … ( 2 )

When Ĥ is substituted in equation (1), we get:

2

2

[

2

2

2

2

2

2

] + 𝑉} 𝛹 = 𝐸𝛹

𝑒

2

( 4 𝜋𝜀 𝑜

) 𝑟

Therefore, {

𝟐

𝟐

[

𝟐

𝟐

𝟐

𝟐

𝟐

𝟐

] −

𝟐

𝒐

Conversion of Cartesian Coordinate into Spherical Polar Coordinate

In order to solve the equation (3) to express the cartesian coordinate (x, y, z) into

spherical polar coordinate (r, θ, φ) for hydrogen like atom, ( i.e .: for the spatial rotation

of an electron around the nucleus with the angular variables θ (Zenith angle) and φ

(Azimuthal angle) and radial distance r ), we have:

x

y

z

x

r

y

z

P'

P

Q

O

R

S

Replacing ( x, y, z) with ( r , θ , φ ) in equation (3), we get Schrodinger wave equation for

hydrogen atom as:

{

−𝒉

𝟐

𝟖𝝅

𝟐

𝒎

[

𝟏

𝒓

𝟐

𝝏

𝝏𝒓

(𝒓

𝟐

𝝏

𝝏𝒓

) +

𝟏

𝒓

𝟐

𝒔𝒊𝒏𝜽

𝝏

𝝏𝜽

(𝒔𝒊𝒏𝜽

𝝏

𝝏𝜽

) +

𝟏

𝒓

𝟐

𝒔𝒊𝒏

𝟐

𝜽

(

𝝏

𝟐

𝝏𝝋

𝟐

)] −

𝒁𝒆

𝟐

𝒓

} 𝜳 ( 𝒓,𝜽,𝝋

)

= 𝑬𝜳 ( 𝒓,𝜽,𝝋

)

… (𝟒)

Equation (4) gives the complete wave function for hydrogen like atom.

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

2. Summarize the significance of four quantum numbers.

The location, the energy and the spin of an electron, the size of orbits, the shape and

orientation of orbitals in an atom can be described by quantum numbers.

They are: principal quantum number (n), azimuthal quantum number (l), magnetic

quantum number (m) and spin quantum number (s).

1. Principle Quantum Number (n)

The principal quantum number gives the address of an electron in a shell or orbit.

It can have the values of 1, 2, 3, 4 … and here, n = 1 denotes K-shell, n =2 denotes L-

shell, n = 3 denotes M-shell and so on …

It also gives the information about radial distance of electron revolving around the

nucleus, in turn used to determine the radius, velocity and the energy level of electron in

various orbits.

According to Bohr’s atomic theory, the radius of orbits, velocity and the energy of

electron in an atom can be calculated by using the following expressions:

𝑛

2

× 0. 53 × 10

− 10

𝑛

  1. 18 × 10

10

𝑛

𝑛

− 1313. 31

𝑛

2

As the principal quantum number increases, the energy of electron also increases.

The maximum number of electrons that can be accommodated in each shell can be

calculated by using the expression 2 n

2

  1. n = 1 represents K-shell, which can accommodate, 2 n

2

2

= 2 electrons

  1. n = 2 represents L-shell, which can accommodate, 2 n

2

2

= 8 electrons

  1. n = 3 represents M-shell, which can accommodate, 2 n

2

2

= 18 electrons

  1. n = 3 represents N-shell, which can accommodate, 2 n

2

2

= 32 electrons

2. Azimuthal Quantum Number (l)

It gives the address of an electron in various sub-shells or sub-orbits.

It can have the values of 0, 1, 2, 3, 4 …, and here l = 0 denotes s - sub-shell, l = 1 denotes

p - sub-shell, l = 2 denotes d - sub-shell and so on …

The l value depends upon principal quantum number ( n ), and its value varies from 0 to

( n ‒1).

When n= 1, l can have the values: 0 to ( n ‒1) = 0; and l = 0 represents 1 s sub-shell and

the prefix 1 represents s sub-shell belongs to K shell.

When n= 2, l can have the values: 0 to ( 2 ‒1) = 0 to 1; i.e .: l = 0, 1; in which 0 represents

2 s sub-shell and 1 represents 2 p sub-shell.

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

When n= 3, l can have the value of 0 to ( 3 ‒1) = 0 to 2; i.e .: l = 0, 1, 2; in which 0 represents

3 s sub-shell, 1 represents 3 p sub-shell, and 2 represents 3 d sub-shell.

The maximum number of electrons that can be accommodated in each sub-shell = 4( l ) +

l = 0 represents s - sub-shell, which can accommodate [4(0) +2] = 2 electrons.

l = 1 represents p - sub-shell, which can accommodate [4(1) +2] = 6 electrons.

l = 2 represents d - sub-shell, which can accommodate [4(2) +2] = 10 electrons.

l = 3 represents f - sub-shell, which can accommodate [4(3) +2] = 14 electrons.

3. Magnetic Quantum Number (m)

It gives the number of orbitals present in various sub-shells.

It also gives the information about the shape and orientation of orbitals in various sub-

shells.

The magnetic quantum number ( m) depends upon azimuthal quantum number ( l ) and,

the m value explains the possible orientations of orbitals and the m values vary from ‒ l

to + l through 0, which can be calculated using the expression = 2( l ) + 1.

For l = 0 (denotes s sub-shell), magnetic quantum number, m = 2( l ) + 1 = 2( 0 ) + 1 = 1

(represents s orbital)

Since, m = 1 depends only on radial wave function and, hence the s orbital exhibits

spherically symmetrical in shape and the probability of finding electron is equal in all the

directions.

For l = 1, (denotes p sub-shell), m = 2( 1 ) + 1 = 3, m = 3.

m = 3 represents three p - orbitals and hence they exhibit three possible orientations (‒ l to

  • l through 0): ‒1, 0, +1 and are designated as p x

, p y

and p z

orbitals.

For l = 2, (denotes d sub-shell), m = 2( 2 ) + 1 = 5, m = 5

m = 5 represents five d - orbitals and hence they exhibit five possible orientations (‒ l to + l

through 0): ‒2, ‒1, 0, +1, +2.

4. Spin Quantum Number (s)

It gives the direction of spin of electron along its axes. If an electron has spin in clock-

wise direction, it is designated as s = + ½ (↑). If an electron has spin in clock-wise

direction, it is designated as s = ‒ ½ (↓).

The total spin of electron in an atom is given by ½ ( n ), where n is the number of unpaired

electrons.

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

3. Shapes of d-orbitals

✓ The angular wave function for d - orbitals l = 2 and hence m has five values (orbitals)

( m =2 l +1) through ‒2, ‒1, 0, +1, +2 and are designated as d z

2

, d x

2

‒y

2

, d xy

, d yz

, d xz

✓ The d xy

, d yz

and d xz

orbitals are similar in shape and size consisting of four lobes,

arranged between x & y , y & z and x & z respectively.

✓ The d x

2

‒y

2

orbital has also four lobes, arranged along x - axis and y - axis.

✓ The d z

2

orbital consisting of two lobes along z - axis and a ring of electron density

around the nucleus.

✓ Since, all the five-d orbital have same energy and are known as degenerate orbitals.

d

xy

Z

Y

X

d

yz

Z

Y

X

d

xz

Z

Y

X

d

Z

Y

X

x

2

-y

2 d

Z

Y

X

z

2

LCAO-MO TREATMENT OF HYDROGEN MOLECULE

**1. Define atomic orbital.

  1. Elaborate the LCAO-MO method in the formation of hydrogen molecule.**

Atomic orbital: The single electron wave function is known as atomic orbital.

According to linear combination of atomic orbitals (LCAO) theory, the atomic orbital of

one atom linearly combines with the atomic orbital of similar energy atom (overlap each

other) to give two types of molecular orbitals namely a bonding molecular orbital [BMO]

and an antibonding molecular orbital [ABMO].

Usually a wave function of a wave possesses a crust portion and a trough portion, and

are arbitrarily assigned the sign + and ‒ respectively.

Formation of bonding molecular orbital

If a crust of one wave overlaps with the crest of other wave, they interact to give a

constructive reinforcement wave.

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

Let us consider, there are two hydrogen atoms H A

and H B

in which each atom has one

electron in 1s atomic orbital in the ground state.

When the crust one hydrogen atom (+Ψ A

) overlaps with the crest of other hydrogen atom

B

), they interact to give a more stable, less energy bonding molecular orbital. The

combination of two atomic orbitals of hydrogen atoms is Ψ b

A

B

The formation of more stable bonding molecular orbital is due to the force of attraction

of high electron density with the nuclei.

Constructive wave

+

Crust

Trough

+ +

Formation of antibonding molecular orbital

If a crust of one wave overlaps with the trough of another wave, they interact to give a

destructive wave.

When the crust one hydrogen atom (+Ψ A

) overlaps with the trough of other hydrogen

atom (‒Ψ B

), they interact to give an unstable stable, higher energy antibonding molecular

orbital. The combination of two atomic orbitals of hydrogen atoms is Ψ b

A

B

The formation of unstable antibonding molecular orbital is due to the force of attraction

of less electron density with the nuclei.

Destructive wave

+

+

Crust

Trough

Determination of Energy of Molecular Orbitals for Hydrogen Molecule

According to wave mechanics, the atomic orbitals can be represented by wave functions.

The energy of molecular orbitals for hydrogen system can be determined by using the

Schrodinger wave equation, and it is given as:

Since the wave functions of two atomic orbitals are in involved in overlapping to form

molecular orbitals, the equation (1) is multiplied by another Ψ on both the sides, and we

obtain:

2

Integrating the equation (2) over the spatial configuration, we get:

2

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

The energy level diagram of hydrogen atom through LCAO is given in the following diagram.

Higher energy ABMO

1s

1

H

A

of atom

Lower energy BMO

E

a

=(Q )

1s

1

H

B

of atom

E

b

=(Q + )

E

N

E

R

G

Y

BAND THEORY OF SOLIDS

**1. Explain the band theory of solids.

  1. Explain conductors, semiconductors and insulators with a neat diagram.**

It is based on molecular orbital (MO) theory.

Overlapping of atomic orbitals gives rise to two types of bonding orbitals namely:

bonding molecular orbital (BMO) and antibonding molecular orbital (ABMO).

In order to understand band theory of solids, let us consider, the element sodium atom.

Sodium atom has an atomic number of 11 and it has the electronic configuration 1 s

2

2 s

2

3 p

6

3 s

1

When two sodium atoms are brought together, the valence electron of 3 s orbital starts

overlapping with the other 3 s orbital of sodium atom to form one bonding molecular

orbital (BMO) with two electrons and one antibonding molecular orbital (ABMO) with

no electrons.

3s

1

Filled valence bond

Empty conduction bond

E

n

e

r

g

y

3s

1

BMO

ABMO

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

When four sodium atoms are brought together, the valence electron of 3 s orbital starts

overlapping to form two bonding molecular orbitals (BMO) with two electrons each and

two antibonding molecular orbitals (ABMO) with no electrons.

3s

1

Filled valence bond

Empty conduction bond

E

n

e

r

g

y

3s

1

BMO

ABMO

3s

1

3s

1

Na-atom 2 Na-atom 3

Na-atom 4 Na-atom 1

We know that one-gram equivalent of sodium will have 6.023× 10

23

atoms (i.e., n number

of Na-atoms).

When n number of sodium atoms overlap each other, they form N/2 number of BMO

with 2e

each and N/2 number of ABMO with no electron.

The n number of closely spaced filled valence bonds appears like a band known as filled

valence band, VB), while n number of closely spaced empty conduction bonds appears

like a band known as empty conduction band, CB.

The energy gap present between filled VB and empty CB is called as forbidden gap or

energy gap ( E g

Energy gap, E

g

3s

1

of n number

of atoms

Filled

valence band

Empty

conduction band

Energy

Classification of Solids on the Basis of Band Theory

Based on E g

values, the solids are classified into three types namely: insulator,

semiconductors and conductors.

(i) Insulators:

Solids in which the valence band and conduction band are largely separated [> 5 eV] in

such a way that, there is no electronic conduction takes place between them are known

as insulators (Examples: Rubbers, Mica, Quartz).

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

Role of Arsenic Doping (n-type Doping)

The process of adding impure metal atom directly into a pure semiconductor is known as

doping and the added impure metal atom is known as dopant.

The arsenic metal atom is an example of pentavalent impurity. When an arsenic atom is

added into a silicon crystal, it replaces one of the silicon atoms and thereby forming four

covalent bonds with nearby four silicon atoms.

Further, the fifth electron of arsenic atom remains totally free and can move

independently in the crystal lattice in turn can act as charge carrier when subjected to an

electric field and is responsible for maximum conductance of semiconductor.

Si Si

Si

Si

As

Si

Si Si

Si

Excess

Free

electron

Role of Gallium Doping (p-type Doping)

The gallium metal atom is an example of trivalent impurity.

When a gallium atom is added into a silicon crystal, it replaces one of the silicon atoms

and thereby forming three covalent bonds with nearby three silicon atoms. Since gallium

is an electron deficient atom, it creates a positive hole with respect to the fourth silicon

atom in the crystal lattice.

Further, this positive hole of gallium atom can move independently in the crystal lattice

in turn can act as charge carrier when subjected to an electric field and is responsible for

maximum conductance of semiconductor.

Si Si

Si

Si

Ga Si

Si Si

Si

Positive

hole

SCYA 1101 : Engineering Chemistry UNIT 1: Bonds to Bands

SUPERCONDUCTORS

**1. What are superconductors? Give examples.

  1. Define Meissner effect.
  2. Mention any two applications of superconductors.
  3. Mention some important properties of superconductors.**

Definition: Metals/ alloys, which conduct electricity with zero resistance when cooled

below to its critical (threshold) temperature are known as super conductors.

Examples:

S. No. Superconductor Critical Temperature

  1. He 4K
  2. Hg 4.2K
  3. Pb 7.2K
  4. Alloy of Pu, Ga and Co 18.5K
  5. Alloy of Cu, Ba, Ce, and Tl 125K

Meissner Effect: The expulsion of magnetic lines of forces during the change from

normal conducting state to superconducting state when cooled below to the critical

temperature is known as Meissner effect.

Properties:

✓ They possess greater resistivity than other elements at room temperature

✓ On adding impurity to super conducting element, the critical temperature can be

lowered

✓ In superconducting state, all electromagnetic effects disappear

✓ Superconductors can exhibit Meissner effect

Applications:

✓ Quantum computing

✓ Sensors

✓ Magnetic Resonance Imaging (MRI)

✓ Military and marine transportations