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GNDU Question Paper-2023
Bachelor of Computer Application (BCA) (Hons.)
1
st
Semester (Batch 2024-28) (CBGS)
CHEMISTRY
(Inorganic ChemistryI)
Time Allowed: Three Hours Max. Marks:50
Note: Attempt Five questions in all, selecting at least One question from each section. The
Fifth question may be attempted from any section. All questions carry equal marks.
SECTIONA
1. (a) Calculate the wavelength associated with an electron that travels with 30% of the
speed of light.
[Given : mass of electron = 9.1 × 10⁻²⁸ Kg].
(b) Derive Schrodinger wave equation for hydrogen atom. Also explain the physical
significance of ψ and ψ². 8
2. (a) An electron is present in 5d orbital. Give possible values of its four quantum
numbers.
(b) Explain :
(i) Why is s-orbital spherical?
(ii) Why a 4s orbital has less energy than 3d-orbital?
(c) Write brief notes on :
(i) Heisenbergs uncertainty principle
(ii) Hunds multiplicity rule.
SECTIONB
3. (a) Why first ionization energy of N is greater than the first ionization energy of O?
(b) Why are the electron affinities of halogens so high?
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(c) Mention Slaters rules for evaluating screening constant. Using Slater rules, calculate
effective nuclear charge for 3p electron and 4s electron of a copper atom.
4. (a) What is electronegativity? Discuss various factors which affect electronegativity.
Also give its variation in a period and a group in the periodic table.
(b) Discuss Pauling Scale and Mulliken concept of electronegativity.
SECTIONC
5. (a) Discuss the VSEPR theory. Account for the geometry of ClO₄⁻ and ClF₃.
(b) Draw MO diagram of CO molecule. Also predict its bond order.
6. (a) Calculate the percentage ionic character in CsF bond in CsF molecule. The
electronegativity values of Cs and F are 0.7 and 4.0, respectively.
(b) What do you understand by hybridization? On the basis of hybridization, predict the
geometry of :
SnCl₆
ClO₄⁻
SECTION-D
7. (a) Briefly discuss Fajan's rules.
(b) Briefly discuss the following types of defects in crystals:
(i) Schottky defect
(ii) Frenkel defect.
8. (a) Draw and explain Born-Haber cycle for the formation of NaCl.
(b) Explain different types of Van der Waals forces.
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GNDU Answer Paper-2023
Bachelor of Computer Application (BCA) (Hons.)
1
st
Semester (Batch 2024-28) (CBGS)
CHEMISTRY
(Inorganic ChemistryI)
Time Allowed: Three Hours Max. Marks:50
Note: Attempt Five questions in all, selecting at least One question from each section. The
Fifth question may be attempted from any section. All questions carry equal marks.
SECTIONA
1. (a) Calculate the wavelength associated with an electron that travels with 30% of the
speed of light.
[Given : mass of electron = 9.1 × 10⁻²⁸ Kg].
(b) Derive Schrodinger wave equation for hydrogen atom. Also explain the physical
significance of ψ and ψ². 8
Ans: Concept: de Broglie Wavelength
According to Louis de Broglie, every moving particle behaves like a wave. This means that
an electron not only acts like a tiny particle but also has wave properties.
The de Broglie wavelength is given by:
Where:
λ = Wavelength of the electron
h = Planck's constant =
J·s
m = Mass of electron =
kg (The question seems to have a typo. The
correct electron mass is
kg.)
v = Velocity of electron
The electron travels at 30% of the speed of light.
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Speed of light,
Therefore,
Now substitute the values:
or
Answer
The wavelength associated with the electron is
(b) Derive Schrödinger Wave Equation for Hydrogen Atom. Also explain the physical
significance of ψ and ψ².
Introduction
One of the greatest discoveries in quantum mechanics was made by Erwin Schrödinger in
1926. Before this, Bohr's model explained only some properties of hydrogen. Schrödinger
introduced a mathematical equation that describes the wave nature of electrons. Instead of
moving in fixed circular paths, electrons are treated as matter waves whose behavior is
described by a wave function.
The Schrödinger wave equation helps us calculate the allowed energy levels and the most
probable locations of electrons around the nucleus.
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Step 1: Total Energy of an Electron
For an electron moving around the nucleus,
Kinetic Energy Potential Energy
Kinetic Energy,
Potential Energy,
Therefore,
where
=Total energy
=Momentum
=Mass of electron
=Potential energy
Step 2: Replace Momentum by Wave Operator
According to quantum mechanics,
Substituting this operator into the energy equation gives the time-independent Schrödinger
equation:
This is the general Schrödinger wave equation.
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Step 3: Schrödinger Equation for Hydrogen Atom
For hydrogen,
Potential energy is
Substituting into the equation,
This equation is solved in spherical coordinates.
Its solutions give:
Principal quantum number (n)
Orbital shapes
Allowed energy levels
Probability distribution of electrons
Thus, Schrödinger's equation successfully explains the electronic structure of hydrogen.
Diagram
Electron Cloud
***************
**** ****
*** ***
** ● Nucleus **
*** ***
**** ****
***************
Electron is not in a fixed orbit.
It is most likely found inside the
electron cloud (orbital).
Physical Significance of ψ (Psi)
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The symbol ψ is called the wave function.
It represents the quantum state of an electron.
However, ψ itself has no direct physical meaning because it can be positive, negative or
even imaginary.
It is only a mathematical function obtained by solving Schrödinger's equation.
Physical Significance of ψ²
The square of the wave function,
(or more accurately
) is extremely important.
It gives the probability density of finding an electron at a particular point around the
nucleus.
Larger ψ² → Higher probability of finding the electron.
Smaller ψ² → Lower probability.
ψ² = 0 → Electron cannot exist there.
This idea explains why electrons form electron clouds (orbitals) instead of moving in fixed
circular orbits.
Diagram Showing Probability
Nucleus
●
High Probability
*************
***************
*****************
***************
*************
Far Away
*
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* *
* *
Low Probability
Importance of Schrödinger Wave Equation
Explains the wave nature of electrons.
Predicts atomic orbitals accurately.
Explains hydrogen spectrum.
Gives energy levels of atoms.
Forms the foundation of modern quantum mechanics.
Helps explain chemical bonding and electronic configuration.
Conclusion
Schrödinger's wave equation revolutionized atomic physics by treating electrons as matter
waves rather than tiny particles moving in fixed paths. The wave function ψ is a
mathematical description of the electron's state, while ψ² gives the probability of finding
the electron at a particular location. This concept led to the modern understanding of
atomic orbitals and forms the basis of quantum mechanics and chemistry.
(c) Explain the term Magnetic Intensity and give its units.
Introduction
When a magnet or an electric current creates a magnetic field, it exerts a force on magnetic
materials placed nearby. The strength of this magnetic field is called magnetic intensity,
also known as the magnetizing field.
It is represented by the symbol H.
Magnetic intensity tells us how strong the applied magnetic field is, independent of the
material placed in it.
Definition
Magnetic intensity (H) is defined as the magnetic field strength produced by an electric
current or magnet at a point.
It represents the magnetizing force responsible for producing magnetization in a material.
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Mathematically,
Where:
N = Number of turns of the coil
I = Current (A)
l = Length of the magnetic path (m)
Relationship with Magnetic Flux Density
Magnetic intensity is related to magnetic flux density by:
Where:
B = Magnetic flux density (Tesla)
μ = Permeability of the material
H = Magnetic intensity
Diagram
Battery
│
│ Current
▼
((((((( Coil )))))))
----------------------
| Iron Core |
----------------------
↑
H
Magnetic Intensity
SI Unit
The SI unit of magnetic intensity is:
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Ampere per metre (A/m)
Importance
Measures the strength of the applied magnetic field.
Determines how strongly a material becomes magnetized.
Used in transformers, motors, generators, and electromagnets.
Helps compare the magnetic behavior of different materials.
Conclusion
Magnetic intensity is the strength of the magnetic field produced by a magnet or electric
current. It is denoted by H and measured in ampere per metre (A/m). It plays a vital role in
understanding magnetic materials and designing electrical devices such as transformers,
motors, and generators.
2. (a) An electron is present in 5d orbital. Give possible values of its four quantum
numbers.
(b) Explain :
(i) Why is s-orbital spherical?
(ii) Why a 4s orbital has less energy than 3d-orbital?
(c) Write brief notes on :
(i) Heisenbergs uncertainty principle
(ii) Hunds multiplicity rule.
Ans: Every electron in an atom is described by four quantum numbers. These quantum
numbers tell us the exact "address" of the electron inside an atom.
1. Principal Quantum Number (n)
It tells the main energy level or shell of the electron.
Since the electron is in the 5d orbital, the value is:
n = 5
2. Azimuthal Quantum Number (l)
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It tells the shape of the orbital.
Different orbitals have different values:
Orbital
l
s
0
p
1
d
2
f
3
Since the electron is in a d-orbital,
l = 2
3. Magnetic Quantum Number (mₗ)
It tells the orientation of the orbital in space.
For a d-orbital (l = 2), possible values are:
mₗ = 2, 1, 0, +1, +2
So the electron may occupy any one of these five d-orbitals.
4. Spin Quantum Number (mₛ)
It tells the direction of the electron's spin.
There are only two possibilities:
mₛ = +½ or ½
Therefore, the possible quantum numbers are:
n = 5
l = 2
mₗ = 2, 1, 0, +1, +2
mₛ = +½ or ½
Diagram of 5d Orbitals
5d Orbitals
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m = -2 -1 0 +1 +2
[ ] [ ] [ ] [ ] [ ]
Each orbital can hold two electrons:
↑↓
(b) Explain:
(i) Why is the s-orbital spherical?
The s-orbital is spherical because its azimuthal quantum number (l) is zero.
When l = 0, the wave function of the electron does not depend on any direction. This means
the probability of finding the electron is the same in every direction around the nucleus.
Imagine placing a small lamp in the center of a room. If the light spreads equally in all
directions, it forms a sphere. Similarly, the electron cloud in an s-orbital spreads equally
around the nucleus.
Diagram
*********
**** ****
*** ● ***
**** ****
*********
● = Nucleus
Electron probability is equal in all directions.
Key Points
l = 0
Equal probability in every direction
Therefore, the shape is spherical.
(ii) Why does the 4s orbital have less energy than the 3d orbital?
Although the principal quantum number of 4s is higher than that of 3d, the 4s orbital
penetrates closer to the nucleus.
Because it comes closer to the nucleus:
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It experiences a stronger attraction.
It becomes more stable.
Hence its energy is lower.
This follows the (n + l) rule.
Orbital
n
l
n+l
4s
4
0
4
3d
3
2
5
The orbital with the smaller (n+l) value has lower energy.
Since:
4 < 5
Therefore,
Energy of 4s < Energy of 3d
This is why electrons fill the 4s orbital before the 3d orbital.
(c) Write brief notes on:
(i) Heisenberg's Uncertainty Principle
The Heisenberg Uncertainty Principle was proposed by the German physicist Werner
Heisenberg.
It states that:
It is impossible to determine both the exact position and the exact momentum (or
velocity) of an electron at the same time.
This is because electrons are extremely tiny particles. Whenever scientists try to observe an
electron, the measuring instrument itself disturbs its motion.
Mathematical Expression
Where:
Δx = uncertainty in position
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Δp = uncertainty in momentum
h = Planck's constant
Simple Example
Suppose a butterfly is flying in a dark room. If you switch on a bright torch to see its exact
position, the light may disturb its flight. Similarly, observing an electron changes its motion.
Importance
Electrons do not move in fixed circular paths.
They exist in regions called orbitals where the probability of finding them is highest.
This principle is the basis of quantum mechanics.
(ii) Hund's Multiplicity Rule
Hund's rule explains how electrons fill orbitals of the same energy (degenerate orbitals).
It states:
Electrons occupy all degenerate orbitals singly with parallel spins before pairing begins.
For example, the three p-orbitals have the same energy.
Correct filling:
↑ ↑ ↑
Not:
↑↓ ↑ _
The first arrangement is more stable because electrons remain farther apart, reducing
repulsion.
Example: Nitrogen (1s² 2s² 2p³)
2p Orbitals
↑ ↑ ↑
All three electrons occupy different orbitals with parallel spins.
Importance
Minimizes electron-electron repulsion.
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Increases stability.
Helps determine the electronic configuration of atoms.
Additional Magnetic Questions
(b) A magnetic flux of 0.004 Wb is produced in a bar of cross-section 0.2 cm². Find the
permeability and magnetic susceptibility of the bar.
Given
Magnetic Flux, Φ = 0.004 Wb
Cross-sectional Area, A = 0.2 cm² = 2 × 10⁻⁵ m²
The complete numerical solution cannot be determined from the given data alone. To
calculate permeability (μ) and magnetic susceptibility (χ), the magnetic field strength (H)
or the current and number of turns of the magnetizing coil must also be provided.
From the available data, we can only calculate the magnetic flux density (B):
T
Then, if H were given:
and
where
H/m.
Therefore, the question is incomplete because the value of H (or equivalent information)
is missing.
(c) Explain the term Magnetic Intensity and give its units.
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Magnetic intensity (H) is the strength of the magnetic field produced by an electric current
or a magnetizing force. It indicates how strongly a magnetic field can magnetize a material.
It depends on the current flowing through a coil and the number of turns of the coil, but it is
independent of the material placed inside the field.
For a long solenoid:
Where:
N = Number of turns
I = Current (A)
L = Length of the solenoid (m)
SI Unit
Ampere per metre (A/m)
Importance
Measures the magnetizing force.
Helps compare magnetic fields.
Used in designing electromagnets, transformers, electric motors, and generators.
Quick Revision
Topic
Key Point
5d Quantum
Numbers
n = 5, l = 2, mₗ = 2 to +2, mₛ = ±½
s-orbital
Spherical because l = 0
4s vs 3d
4s has lower energy due to greater penetration and lower (n+l) value
Heisenberg
Principle
Exact position and momentum cannot be known simultaneously
Hund's Rule
Electrons fill equal-energy orbitals singly before pairing
Magnetic
Intensity
Magnetizing force; SI unit = A/m
Magnetic
Calculation
Given data is insufficient to find permeability and susceptibility; only
Tcan be calculated.
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SECTIONB
3. (a) Why first ionization energy of N is greater than the first ionization energy of O?
(b) Why are the electron affinities of halogens so high?
(c) Mention Slaters rules for evaluating screening constant. Using Slater rules, calculate
effective nuclear charge for 3p electron and 4s electron of a copper atom.
Ans: Introduction
To understand this question, imagine an atom as a tiny solar system. The nucleus is like the
Sun, and the electrons are like planets revolving around it. The closer an electron is to the
nucleus, the more strongly it is attracted. However, the inner electrons act like bodyguards,
reducing the attraction between the nucleus and the outer electrons. This effect is called
screening (shielding).
The concepts of ionization energy, electron affinity, and effective nuclear charge are all
connected to how strongly the nucleus attracts electrons.
(a) Why is the first ionization energy of Nitrogen greater than that of Oxygen?
What is Ionization Energy?
Ionization energy is the minimum amount of energy required to remove the outermost
electron from an isolated gaseous atom.
Simple Definition
More tightly held electron = Higher ionization energy
Electronic Configurations
Nitrogen (Atomic Number = 7)
1s² 2s² 2p³
2p orbitals:
↑ ↑ ↑
Each orbital contains one electron.
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Oxygen (Atomic Number = 8)
1s² 2s² 2p⁴
2p orbitals:
↑↓ ↑ ↑
One orbital contains two paired electrons.
Why is Nitrogen's Ionization Energy Higher?
Nitrogen has a half-filled 2p subshell (2p³).
Half-filled orbitals are especially stable because:
Electrons remain unpaired.
Repulsion between electrons is minimum.
The arrangement has extra stability (exchange energy).
Removing one electron from nitrogen destroys this stable arrangement, so more energy is
needed.
In oxygen, one orbital already contains two electrons. These paired electrons repel each
other.
Because of this repulsion:
One electron is easier to remove.
Less energy is required.
Therefore,
First Ionization Energy: Nitrogen > Oxygen
Diagram
Nitrogen (2p³)
↑ ↑ ↑
Stable Half-filled
Difficult to remove electron
Higher Ionization Energy
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Oxygen (2p⁴)
↑↓ ↑ ↑
Electron-Electron Repulsion
Easy to remove one paired electron
Lower Ionization Energy
Conclusion
Nitrogen has a stable half-filled electronic configuration, while oxygen contains a paired
electron that experiences repulsion. Hence, nitrogen requires more energy to remove its
first electron.
(b) Why are the Electron Affinities of Halogens So High?
What is Electron Affinity?
Electron affinity is the energy released when an isolated gaseous atom gains one electron.
The more energy released, the higher the electron affinity.
Electronic Configuration of Halogens
Example: Chlorine
1s² 2s² 2p⁶ 3s² 3p⁵
Outer shell:
↑↓ ↑↓ ↑
Only one electron is needed to complete the octet.
After gaining one electron:
↑↓ ↑↓ ↑↓
Complete Octet
Why is Electron Affinity High?
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Halogens:
Have seven valence electrons.
Need only one more electron to become stable.
Strongly attract an incoming electron.
Release a large amount of energy after gaining it.
Hence, halogens possess very high electron affinity.
Trend
F → Cl → Br → I
Electron Affinity decreases down the group
(Although chlorine has a slightly higher electron affinity than fluorine because fluorine's very
small size causes greater electron-electron repulsion.)
Diagram
Halogen
7 Electrons
● ● ● ● ● ● ●
Needs only one more electron
↓
● ● ● ● ● ● ● ●
Stable Noble Gas Configuration
Conclusion
Halogens have very high electron affinity because they require only one electron to
complete their outermost shell and achieve a stable noble gas configuration.
(c) Slater's Rules for Evaluating Screening Constant
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What is Screening (Shielding)?
Inner electrons reduce the attractive force of the nucleus on outer electrons.
This reduction is called the screening effect.
The amount of shielding is represented by the screening constant (S).
The effective nuclear charge is:
eff
Where:
Z = Atomic number
S = Screening constant
Slater's Rules
For calculating the screening constant:
1. Arrange electrons into groups:
(1s)
(2s,2p)
(3s,3p)
(3d)
(4s,4p)
(4d)
(4f)
2. Electrons to the right contribute 0
They do not shield.
3. Electrons in the same group
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Each contributes:
0.35
(Except 1s, where each contributes 0.30.)
4. Electrons in the shell immediately below
Each contributes:
0.85
(for s and p electrons)
5. Electrons two or more shells below
Each contributes:
1.00
6. For d and f electrons
Electrons in the same d/f group contribute 0.35 each.
All electrons in groups to the left contribute 1.00 each.
Copper Configuration
Copper
Atomic Number
Z = 29
Electronic configuration
1s²
2s²2p⁶
3s²3p⁶
3d¹⁰
4s¹
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Effective Nuclear Charge for 3p Electron
Configuration relative to a 3p electron:
(1s²)
(2s²2p⁶)
(3s²3p⁶)
Screening Constant
Same group (3s²3p⁶):
Other electrons = 7
Contribution
7 × 0.35 = 2.45
Second shell
8 × 0.85 = 6.80
First shell
2 × 1.00 = 2.00
Total
S = 2.45 + 6.80 + 2.00
S = 11.25
Effective Nuclear Charge
Zeff = Z − S
= 29 − 11.25
= 17.75
Effective nuclear charge on a 3p electron ≈ 17.75
Effective Nuclear Charge for 4s Electron
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Configuration relative to a 4s electron:
1s²
2s²2p⁶
3s²3p⁶
3d¹⁰
4s¹
Screening contributions:
Same group (4s):
No other electron
0
3d electrons
10 × 1.00 = 10
3s and 3p electrons
8 × 0.85 = 6.80
1st and 2nd shell electrons
10 × 1.00 = 10
Total
S = 10 + 6.80 + 10
= 26.80
Effective Nuclear Charge
Zeff = 29 − 26.80
= 2.20
Effective nuclear charge on a 4s electron ≈ 2.20
Final Summary
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(a) Nitrogen has a stable half-filled 2p³ configuration, so removing an electron
requires more energy than in oxygen, where paired-electron repulsion makes
electron removal easier.
(b) Halogens have very high electron affinity because they need only one electron to
complete their octet and achieve a stable noble gas configuration.
(c) According to Slater's rules, the effective nuclear charge is calculated using the
screening constant:
o For a 3p electron in Cu:
eff
o For a 4s electron in Cu:
eff
These concepts explain how the arrangement of electrons and the shielding effect influence
important atomic properties such as ionization energy, electron affinity, and the attraction
between the nucleus and electrons.
4. (a) What is electronegativity? Discuss various factors which affect electronegativity.
Also give its variation in a period and a group in the periodic table.
(b) Discuss Pauling Scale and Mulliken concept of electronegativity.
Ans: Electronegativity A Simple and Easy Explanation
Imagine two children sharing a rope in a game of tug-of-war. One child pulls the rope more
strongly than the other. In a chemical bond, atoms behave in a similar way. They "pull" the
shared electrons toward themselves. The ability of an atom to attract the shared electrons
in a chemical bond is called electronegativity.
In simple words:
Electronegativity is the tendency of an atom to attract the bonding (shared) electrons
toward itself.
It is not the same for every element. Some atoms attract electrons very strongly, while
others attract them only weakly.
For example:
Fluorine (F) attracts electrons very strongly, so it has the highest electronegativity.
Cesium (Cs) and Francium (Fr) attract electrons very weakly, so they have very low
electronegativity.
Simple Diagram
Hydrogen Fluorine
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H ---------> F
Shared electrons move closer to Fluorine
because Fluorine has higher electronegativity.
The arrow shows that fluorine pulls the shared electrons more strongly than hydrogen.
Factors Affecting Electronegativity
Several factors determine how strongly an atom attracts electrons.
1. Atomic Size
The smaller the atom, the closer its nucleus is to the shared electrons.
When electrons are closer to the nucleus, they experience a stronger attractive force.
Small atom → High electronegativity
Large atom → Low electronegativity
Example:
Fluorine is much smaller than iodine.
Therefore,
Fluorine > Iodine in electronegativity.
2. Nuclear Charge
The nucleus contains positively charged protons.
More protons mean a stronger positive charge.
A stronger positive charge pulls electrons more effectively.
Therefore,
Higher nuclear charge → Higher electronegativity.
3. Shielding Effect (Screening Effect)
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Inner electrons block some of the attraction between the nucleus and the outer electrons.
This is called the shielding effect.
If shielding is high,
The nucleus cannot attract bonding electrons strongly.
Electronegativity decreases.
If shielding is low,
Electronegativity increases.
4. Distance Between Nucleus and Bonding Electrons
The farther the bonding electrons are from the nucleus, the weaker the attraction.
Therefore,
Greater distance → Lower electronegativity
Shorter distance → Higher electronegativity
5. Oxidation State (Charge on Atom)
A positively charged ion attracts electrons more strongly than a neutral atom because it has
fewer electrons and a stronger pull from the nucleus.
Example:
Fe³⁺ has higher electronegativity than Fe²⁺.
Variation of Electronegativity in the Periodic Table
Electronegativity follows a regular trend.
(A) Across a Period (Left to Right)
As we move from left to right,
Atomic size decreases.
Nuclear charge increases.
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Therefore,
Electronegativity increases.
Example:
Li → Be → B → C → N → O → F
Increasing Electronegativity →
Fluorine has the highest value.
(B) Down a Group (Top to Bottom)
As we move downward,
Atomic size increases.
Shielding effect increases.
Therefore,
Electronegativity decreases.
Example:
F
↓
Cl
↓
Br
↓
I
Electronegativity decreases
Easy Memory Trick
Across a Period → Electronegativity Increases
Down a Group → Electronegativity Decreases
Remember:
Across = Increase
Down = Decrease
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(b) Pauling Scale of Electronegativity
The Pauling Scale was introduced by the American scientist Linus Pauling.
It is the first and most widely used scale for measuring electronegativity.
Pauling found that atoms with different electronegativities form stronger chemical bonds
than expected. Using bond energy data, he assigned numerical values to the
electronegativity of different elements.
Important Points
It is based on bond energies.
Values are relative, not absolute.
Fluorine is assigned the highest value.
Examples
Element
Electronegativity (Pauling Scale)
Fluorine (F)
4.0
Oxygen (O)
3.5
Nitrogen (N)
3.0
Carbon (C)
2.5
Hydrogen (H)
2.1
Sodium (Na)
0.9
Cesium (Cs)
0.7
Advantages
Simple and easy to use.
Most commonly accepted scale.
Helps predict bond polarity and chemical behavior.
Limitation
It gives relative values, not absolute measurements.
Mulliken Concept of Electronegativity
The Mulliken concept was proposed by Robert S. Mulliken.
According to Mulliken:
Electronegativity is the average of an atom's Ionization Energy (IE) and Electron Affinity
(EA).
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Formula
Ionization Energy Electron Affinity
Where:
Ionization Energy (IE): Energy needed to remove an electron from an atom.
Electron Affinity (EA): Energy released when an atom gains an electron.
If both IE and EA are high, the atom strongly attracts electrons, so its electronegativity is
high.
Advantages
Based on measurable physical properties.
Gives a more scientific explanation of electronegativity.
Limitation
Accurate values of electron affinity are not available for every element.
Less commonly used than the Pauling scale.
Difference Between Pauling and Mulliken Concepts
Pauling Scale
Mulliken Concept
Based on bond energies
Based on ionization energy and electron affinity
Relative values
Calculated using measurable properties
Most widely used
More theoretical and scientific
Simple and practical
Requires experimental data
Summary
Electronegativity is the ability of an atom to attract the shared electrons in a
chemical bond.
It depends on atomic size, nuclear charge, shielding effect, distance from the
nucleus, and oxidation state.
Across a period, electronegativity increases because atomic size decreases and
nuclear charge increases.
Down a group, electronegativity decreases because atomic size and shielding
increase.
Pauling Scale measures electronegativity using bond energies and is the most widely
used scale.
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Mulliken Concept defines electronegativity as the average of ionization energy and
electron affinity, giving it a stronger theoretical basis.
SECTIONC
5. (a) Discuss the VSEPR theory. Account for the geometry of ClO₄⁻ and ClF₃.
(b) Draw MO diagram of CO molecule. Also predict its bond order.
Ans: (a) VSEPR Theory (Valence Shell Electron Pair Repulsion Theory)
Imagine you are sitting on a round table with your friends. If everyone wants maximum
personal space, each person will sit as far away from the others as possible. Electron pairs
behave in exactly the same way around the central atom.
The VSEPR Theory states that:
"The electron pairs present around the central atom repel each other and arrange
themselves as far apart as possible to minimize repulsion and make the molecule stable."
The theory was proposed by Sidgwick and Powell and later improved by Gillespie and
Nyholm.
Basic Principles of VSEPR Theory
1. Electron pairs repel each other.
2. The arrangement with the least repulsion is the most stable.
3. Lone pair (LP) repulsion is greater than bond pair (BP) repulsion.
4. The order of repulsion is:
LP LP > LP BP > BP BP
This means lone pairs occupy more space than bonding pairs because they are attracted by
only one nucleus.
Geometry of ClO₄⁻ (Perchlorate Ion)
Step 1: Identify the Central Atom
Central atom = Cl
Four oxygen atoms are attached.
Step 2: Count Electron Pairs
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Chlorine forms four ClO bonds.
No lone pair is present on chlorine.
Therefore,
Bond pairs = 4
Lone pairs = 0
According to VSEPR theory,
4 electron pairs arrange themselves in a tetrahedral shape.
Geometry
O
/
Cl
/ | \
O O O
(Actual arrangement is three-dimensional.)
Shape
Tetrahedral
Bond Angle
109.5°
Reason
Since there are only bonding pairs and no lone pairs, repulsion is equal in all directions,
giving a perfect tetrahedral geometry.
Geometry of ClF₃ (Chlorine Trifluoride)
Step 1: Count Electron Pairs
Chlorine has 7 valence electrons.
It forms:
3 bond pairs
2 lone pairs
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Total electron pairs = 5
Five electron pairs first arrange themselves in a trigonal bipyramidal arrangement.
Step 2: Position of Lone Pairs
Lone pairs always occupy the equatorial positions because they experience less repulsion
there.
After placing two lone pairs, the remaining three fluorine atoms occupy two axial and one
equatorial positions.
Shape
F
|
LP Cl LP
|
F
\
F
(Simplified representation)
Actual Geometry
T-shaped
Bond Angles
Approximately 87° and 180°
Reason
The two lone pairs repel the bonding pairs strongly, forcing the fluorine atoms into a T-
shaped geometry.
Comparison
Molecule
Bond Pairs
Lone Pairs
Electron Geometry
Molecular Shape
ClO₄⁻
4
0
Tetrahedral
Tetrahedral
ClF₃
3
2
Trigonal Bipyramidal
T-shaped
(b) Molecular Orbital (MO) Theory of CO Molecule
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The Carbon Monoxide (CO) molecule contains:
Carbon = 6 electrons
Oxygen = 8 electrons
Total electrons = 14
According to Molecular Orbital Theory, atomic orbitals combine to form:
Bonding Molecular Orbitals (lower energy)
Antibonding Molecular Orbitals (higher energy)
Electrons always fill the lower-energy orbitals first.
MO Energy Order for CO
Higher Energy
σ*2p
π*2p
π2p
σ2p
π2p
σ2s*
σ2s
σ1s*
σ1s
Lower Energy
Electronic Configuration of CO
The 14 electrons fill the orbitals as follows:
(σ1s)²
(σ1s*)²
(σ2s)²
(σ2s*)²
(π2p)⁴
(σ2p)²
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Simple MO Diagram
Antibonding Orbitals
σ*2p
-------------
π*2p
-------------------
σ2p ↑↓
π2p ↑↓ ↑↓
σ*2s ↑↓
σ2s ↑↓
σ*1s ↑↓
σ1s ↑↓
Bonding Orbitals
Bond Order
The bond order is calculated using the formula:
Bond Order
Bonding Electrons Antibonding Electrons
Bonding electrons
σ1s = 2
σ2s = 2
π2p = 4
σ2p = 2
Total = 10
Antibonding electrons
σ1s* = 2
σ2s* = 2
Total = 4
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Therefore,
Bond Order
Bond Order = 3
This means CO has a triple bond (C≡O), which makes it a very strong and stable molecule.
Key Points for Exams
VSEPR Theory
Electron pairs repel each other.
Molecules adopt shapes that minimize repulsion.
Repulsion order: LPLP > LPBP > BPBP.
ClO₄⁻
Bond pairs = 4
Lone pairs = 0
Shape = Tetrahedral
Bond angle = 109.5°
ClF₃
Bond pairs = 3
Lone pairs = 2
Electron geometry = Trigonal Bipyramidal
Molecular shape = T-shaped
Bond angles ≈ 87° and 180°
CO Molecule (MO Theory)
Total electrons = 14
Molecular orbital bond order = 3
Contains a strong triple bond (C≡O)
High bond order indicates high stability and short bond length.
Conclusion
The VSEPR theory helps us predict molecular shapes by considering the repulsion between
electron pairs around the central atom. Using this theory, ClO₄⁻ is found to have a
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tetrahedral shape because it contains four bonding pairs and no lone pairs, while ClF₃ has a
T-shaped geometry because two lone pairs occupy equatorial positions in a trigonal
bipyramidal arrangement. The Molecular Orbital (MO) theory explains bonding in the CO
molecule by showing how atomic orbitals combine to form molecular orbitals. Filling these
orbitals with 14 electrons gives a bond order of 3, confirming the presence of a strong triple
bond and the exceptional stability of carbon monoxide. These concepts together provide a
clear understanding of how molecular geometry and chemical bonding determine the
properties of molecules.
6. (a) Calculate the percentage ionic character in CsF bond in CsF molecule. The
electronegativity values of Cs and F are 0.7 and 4.0, respectively.
(b) What do you understand by hybridization? On the basis of hybridization, predict the
geometry of :
SnCl₆
ClO₄⁻
Ans: (b) Explain Hybridization and Predict the Geometry of SnCl₆ and ClO₄⁻
Chemistry is all about understanding how atoms join together and why molecules have
different shapes. Some atoms share electrons equally, while others transfer electrons
completely. Similarly, atoms arrange themselves in different directions to make stable
molecules. Let us understand both parts of this question in a simple and interesting way.
(a) Percentage Ionic Character in CsF
What is Ionic Character?
When two atoms form a bond, they may either:
Share electrons → Covalent bond
Transfer electrons → Ionic bond
Most bonds are partly ionic and partly covalent. The greater the difference in
electronegativity between two atoms, the greater is the ionic character.
What is Electronegativity?
Electronegativity is the ability of an atom to attract shared electrons toward itself.
Fluorine (F) has very high electronegativity = 4.0
Cesium (Cs) has very low electronegativity = 0.7
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Therefore, fluorine pulls the electron strongly from cesium, making the bond highly ionic.
Step 1: Find the Electronegativity Difference
Step 2: Use the Formula
Percentage ionic character is calculated by:
Ionic Character
Substitute the values:
Since,
Therefore,
Final Answer
Percentage ionic character of CsF ≈ 93.4%
This means the bond is almost completely ionic, which is expected because fluorine is the
most electronegative element and cesium is one of the least electronegative metals.
(b) Hybridization
What is Hybridization?
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Hybridization is the mixing of atomic orbitals of similar energy (such as s, p, and d orbitals)
to form new equivalent orbitals called hybrid orbitals.
These hybrid orbitals:
Have equal energy
Point in specific directions
Help atoms form strong and stable chemical bonds
Decide the shape (geometry) of molecules
Simple Example
Imagine mixing different colors of clay.
One red clay
Three blue clay
After mixing, all pieces become the same purple color.
Similarly, orbitals mix to form identical hybrid orbitals.
Types of Hybridization
Hybridization
Number of Orbitals
Geometry
sp
2
Linear
sp²
3
Trigonal Planar
sp³
4
Tetrahedral
sp³d
5
Trigonal Bipyramidal
sp³d²
6
Octahedral
Geometry of SnCl₆
The compound is usually considered as the octahedral complex [SnCl₆]²⁻.
Step 1
Tin (Sn) is the central atom.
It is surrounded by 6 chlorine atoms.
Therefore,
Bond pairs = 6
Lone pairs = 0
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Total electron pairs = 6
Step 2
Six electron pairs require
hybridization.
Geometry
The six chlorine atoms arrange themselves equally around tin.
Cl
|
Cl Sn Cl
/ \
Cl Cl
|
Cl
This arrangement is called an Octahedral Geometry.
Final Answer
Hybridization = sp³d²
Shape = Octahedral
Geometry of ClO₄⁻ (Perchlorate Ion)
Step 1
Chlorine is the central atom.
It is bonded with four oxygen atoms.
There are:
Four bond pairs
No lone pair on chlorine (in the ideal VSEPR description)
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Total electron groups = 4
Step 2
Four electron groups require
hybridization.
Geometry
The four oxygen atoms move as far apart as possible.
O
|
O Cl O
\
O
(The actual molecule is tetrahedral, with the four oxygen atoms pointing toward the corners
of a tetrahedron.)
Final Answer
Hybridization = sp³
Shape = Tetrahedral
Why Does Hybridization Decide Shape?
Atoms try to keep their electron pairs as far apart as possible because electrons repel each
other.
Hybrid orbitals point in directions where this repulsion is minimum, giving each molecule its
characteristic shape.
For example:
2 orbitals → Linear
3 orbitals → Trigonal planar
4 orbitals → Tetrahedral
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6 orbitals → Octahedral
Summary
Part
Answer
Electronegativity
Difference
3.3
Percentage Ionic
Character of CsF
≈ 93.4%
Definition of
Hybridization
Mixing of atomic orbitals to form equivalent hybrid orbitals
for stronger bonding and definite molecular shapes
SnCl₆ / [SnCl₆]²⁻
Hybridization
sp³d²
SnCl₆ / [SnCl₆]²⁻
Geometry
Octahedral
ClO₄⁻ Hybridization
sp³
ClO₄⁻ Geometry
Tetrahedral
Exam Points to Remember
Electronegativity difference increases → Ionic character increases.
CsF has a very high ionic character (≈93.4%) because Cs easily loses an electron and
F strongly attracts it.
Hybridization is the mixing of atomic orbitals to form equivalent hybrid orbitals.
Six electron groups (SnCl₆/[SnCl₆]²⁻) → sp³d² → Octahedral shape.
Four electron groups (ClO₄⁻) → sp³ → Tetrahedral shape.
The geometry of a molecule is determined by the arrangement of electron pairs
around the central atom to minimize repulsion.
SECTION-D
7. (a) Briefly discuss Fajan's rules.
(b) Briefly discuss the following types of defects in crystals:
(i) Schottky defect
(ii) Frenkel defect.
Ans: (a) Fajan's Rules
Introduction
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When a metal reacts with a non-metal, we usually expect the bond to be ionic. However,
not all ionic compounds are completely ionic. Some of them show covalent character. To
explain this behavior, the Polish scientist Kazimierz Fajans proposed a set of rules called
Fajan's Rules.
Definition:
Fajan's Rules state that the greater the polarization of an anion by a cation, the greater
will be the covalent character of the ionic bond.
What is Polarization?
Imagine the anion (negative ion) as a soft rubber ball and the cation (positive ion) as a hand
pressing the ball.
If the hand presses very hard, the ball changes its shape.
Similarly, when a cation pulls the electron cloud of an anion toward itself, the anion
gets distorted.
This distortion is called polarization.
Greater polarization means the bond behaves more like a covalent bond.
Fajan's Rules
1. Small cation → Greater covalent character
A small positive ion has a strong attractive force because its positive charge is concentrated
in a small space.
Example:
LiCl has more covalent character than NaCl because Li⁺ is smaller than Na⁺.
2. Highly charged cation → Greater covalent character
A cation with a higher positive charge attracts electrons more strongly.
Example:
AlCl₃ is more covalent than NaCl because Al³⁺ has a +3 charge.
3. Large anion → Greater covalent character
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Large anions hold their outer electrons less tightly.
They are easily distorted.
Example:
LiI is more covalent than LiF because I⁻ is much larger than F⁻.
4. Cations with 18-electron configuration polarize more
Transition metal ions with an 18-electron configuration have stronger polarizing power than
ions with noble gas configurations.
Example:
AgCl shows more covalent character than NaCl.
Simple Diagram of Polarization
Before Polarization
(-)
( O O )
Anion
+
Cation
After Polarization
+
Cation
( OOO )
Electron cloud pulled
towards cation
Importance of Fajan's Rules
Explains why some ionic compounds dissolve poorly in water.
Helps predict ionic or covalent nature.
Explains melting and boiling points.
Useful in chemistry, metallurgy, and material science.
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(b) Defects in Crystals
Introduction
An ideal crystal has atoms or ions arranged in a perfect repeating pattern.
However, in reality, no crystal is completely perfect.
Sometimes ions are missing or occupy incorrect positions. These imperfections are called
crystal defects.
Crystal defects affect:
Density
Electrical conductivity
Strength
Diffusion
Optical properties
The two most common defects are:
1. Schottky Defect
2. Frenkel Defect
(i) Schottky Defect
Definition
A Schottky defect occurs when equal numbers of cations and anions are missing from their
normal lattice positions.
Since both ions are missing, the crystal remains electrically neutral.
How does it happen?
Imagine a classroom where one boy and one girl both leave their seats.
The classroom still has equal numbers of boys and girls, but there are now empty seats.
Similarly, in a crystal:
One positive ion leaves.
One negative ion also leaves.
Empty spaces called vacancies are created.
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Diagram
Normal Crystal
+ - + -
- + - +
+ - + -
Schottky Defect
+ - □ -
- + - +
+ □ + -
□ = Missing ion
Characteristics
Equal number of ions are absent.
Electrical neutrality remains.
Density decreases because ions are missing.
Common in highly ionic compounds.
Examples
NaCl
KCl
KBr
CsCl
(ii) Frenkel Defect
Definition
A Frenkel defect occurs when a small cation leaves its normal position and occupies an
interstitial (empty) position within the crystal.
No ion leaves the crystal.
Easy Understanding
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Imagine a student leaves his bench but sits on the classroom floor.
The total number of students remains the same.
Only the position changes.
Similarly,
Positive ion moves.
Vacancy is created.
Another position becomes occupied.
Diagram
Normal Crystal
+ - + -
- + - +
+ - + -
Frenkel Defect
+ - □ -
- + - +
+ - + -
+
Small cation moves
to an interstitial site
Characteristics
Cation changes position.
No ions are lost.
Density remains unchanged.
Common when cation is much smaller than anion.
Examples
AgCl
AgBr
ZnS
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Difference Between Schottky and Frenkel Defect
Schottky Defect
Frenkel Defect
Equal numbers of cations and anions are
missing.
A cation moves to an interstitial site.
Vacancies are created.
Vacancy and interstitial ion are created.
Density decreases.
Density remains unchanged.
Common in NaCl, KCl, KBr.
Common in AgCl, AgBr, ZnS.
Both positive and negative ions leave lattice
sites.
Only a small positive ion changes its
position.
Conclusion
Fajan's Rules help us understand why some ionic compounds develop covalent character
due to the polarization of ions. A small, highly charged cation and a large anion increase
polarization, making the bond more covalent.
On the other hand, crystal defects explain why real crystals are not perfectly arranged. In a
Schottky defect, equal numbers of positive and negative ions are missing, reducing the
crystal's density while maintaining electrical neutrality. In a Frenkel defect, a small cation
shifts from its normal lattice site to an interstitial position, creating a vacancy without
changing the crystal's density.
Together, these concepts are essential for understanding the structure, bonding, and
physical properties of ionic solids and are widely applied in chemistry, materials science, and
solid-state physics.
8. (a) Draw and explain Born-Haber cycle for the formation of NaCl.
(b) Explain different types of Van der Waals forces.
Ans: (a) BornHaber Cycle for the Formation of NaCl
The BornHaber Cycle is a special energy cycle used to explain how an ionic compound is
formed from its elements. It is based on Hess's Law, which states that the total energy
change of a reaction is the same, no matter how many steps are involved.
Think of building a house. Instead of constructing it all at once, workers complete it step by
steplaying the foundation, building walls, adding the roof, and painting. Similarly, sodium
chloride (NaCl) is formed through several energy changes instead of one direct step.
Formation of Sodium Chloride (NaCl)
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The overall reaction is:
Na(s) + ½Cl₂(g) → NaCl(s)
This reaction occurs through the following stages:
Step 1: Sublimation of Sodium
Solid sodium is converted into gaseous sodium atoms.
Na(s) → Na(g)
Energy is absorbed.
This energy is called Sublimation Energy (ΔHsub).
Step 2: Ionization of Sodium
A gaseous sodium atom loses one electron to form a sodium ion.
Na(g) → Na⁺(g) + e⁻
Energy is required.
This is called the First Ionization Energy (IE).
Step 3: Dissociation of Chlorine
Chlorine exists as Cl₂ molecules. One-half molecule breaks into one chlorine atom.
½Cl₂(g) → Cl(g)
Energy is absorbed.
This is called Bond Dissociation Energy.
Step 4: Electron Gain by Chlorine
A chlorine atom gains one electron to become a chloride ion.
Cl(g) + e⁻ → Cl⁻(g)
Energy is released.
This released energy is called Electron Affinity (EA).
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Step 5: Formation of NaCl Crystal
The gaseous sodium ion and chloride ion combine to form solid sodium chloride.
Na⁺(g) + Cl⁻(g) → NaCl(s)
A large amount of energy is released.
This energy is called Lattice Energy.
BornHaber Cycle Diagram
Na(g) + Cl(g)
│
Ionization │ Electron Affinity
│
Na(g) + Cl(g)
│
Lattice Energy
↓
NaCl(s)
↑
Na(s) + ½Cl(g)
│ │
Sublimation Bond Dissociation
Important Terms
Term
Meaning
Sublimation Energy
Converts solid sodium into gaseous sodium.
Ionization Energy
Removes an electron from sodium atom.
Bond Dissociation Energy
Breaks chlorine molecule into atoms.
Electron Affinity
Energy released when chlorine gains an electron.
Lattice Energy
Energy released when Na⁺ and Cl⁻ form solid NaCl crystal.
Why is the BornHaber Cycle Important?
It helps calculate lattice energy, which cannot be measured directly.
It explains why ionic compounds are stable.
It shows how energy is absorbed and released during ionic bond formation.
It helps compare the stability of different ionic compounds.
(b) Different Types of Van der Waals Forces
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Van der Waals forces are weak attractive forces between atoms or molecules. They are
much weaker than ionic or covalent bonds but play an important role in determining the
boiling point, melting point, solubility, and physical properties of substances.
Imagine two small pieces of paper lying close together. They are not glued, but they can still
stick slightly due to a tiny attraction. Similarly, molecules attract each other through Van der
Waals forces.
These forces are mainly of three types.
1. DipoleDipole Forces
These forces occur between polar molecules.
Polar molecules have one end slightly positive (δ⁺) and the other end slightly negative (δ⁻).
Example:
HCl
SO₂
CH₃Cl
δH Clδ δH Clδ
Positive end attracts negative end.
Characteristics
Occur only in polar molecules.
Stronger than London forces.
Increase boiling and melting points.
2. DipoleInduced Dipole Forces
A polar molecule can temporarily induce a dipole in a nearby non-polar molecule.
Example:
H₂O with O₂
HCl with Ar
Polar Molecule → Non-polar Molecule
δ⁺ δ⁻ (+) (-)
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Characteristics
Attraction between one polar and one non-polar molecule.
Weaker than dipoledipole forces.
Temporary in nature.
3. London Dispersion Forces (Induced DipoleInduced Dipole)
These are the weakest but most common Van der Waals forces.
Electrons continuously move around atoms. Sometimes, electrons gather more on one side
of an atom, creating a temporary dipole. This temporary dipole induces another temporary
dipole in a nearby atom or molecule, causing attraction.
These forces are present in all molecules, especially non-polar molecules.
Examples:
Helium (He)
Neon (Ne)
Nitrogen (N₂)
Oxygen (O₂)
Methane (CH₄)
Temporary Dipole
(+ ) ( - ) attracts (+ ) ( - )
Temporary and constantly changing
Characteristics
Present in every atom and molecule.
Increase with molecular size and number of electrons.
Responsible for the liquefaction of noble gases.
Comparison of Van der Waals Forces
Type
Occurs Between
Relative Strength
Example
DipoleDipole
Polar molecules
Strongest among Van der
Waals forces
HCl, SO₂
DipoleInduced
Dipole
Polar + Non-polar
molecules
Moderate
H₂OO₂
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London
Dispersion
All molecules (especially
non-polar)
Weakest
He, Ne, N₂,
CH₄
Key Points to Remember
The BornHaber Cycle explains the stepwise formation of ionic compounds such as
NaCl using energy changes and helps calculate lattice energy.
The formation of NaCl involves sublimation, ionization, bond dissociation, electron
affinity, and lattice energy.
Van der Waals forces are weak intermolecular attractions that hold molecules
together.
There are three main types: DipoleDipole, DipoleInduced Dipole, and London
Dispersion Forces.
Although weak, these forces strongly influence boiling point, melting point,
solubility, and the physical state of substances.
This paper has been carefully prepared for educational purposes. If you notice any mistakes or
have suggestions, feel free to share your feedback.
