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GNDU Question Paper-2021
Ba/Bsc
1
st
Semester (Batch 2024-28) (CBGS)
CHEMISTRY
(Inorganic Chemistry-I)
Time Allowed: Three Hours Max. Marks:35
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.
SECTION-A
1. (a) Calculate de-Broglie wavelength of an electron moving at 2% speed of light [Given:
Mass of electron=9.1×10-31 kg;h=6.63×10-34 kg m²s-1].
(b) Write brief notes on:
(i) Pauli exclusion principle.
(ii) Heisenberg's uncertainty principle.
2. Derive Schrodinger wave equation for hydrogen atom. Also explain the significance of y
and w².
SECTION-B
3. What is ionization energy? Give its variation in a period and in a group in the periodic
table. Also discuss various factors in detail which affect ionization energy.
4. Mention Slater's rule. Calculate the effective nuclear charge for outer electron (4s) of:
(i) Potassium atom (At. No. = 19)
(ii) Copper atom (At. No. = 29)
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SECTION-C
5. Explain the main features of VSEPR theory. Using VSEPR theory, describe the shapes of
the following:
(i) SF4
(ii) IC/2.
6. (a) Calculate the percentage ionic character in HBr molecule. Given electronegativity
values of H and Br are 2.1 and 2.8, respectively.
(b) Discuss the limitations of Valence Bond Theory.
(c) Draw MO diagrams of nitrogen molecule. Also calculate its bond order.
SECTION-D
7. (a) Write a brief note on radius ratio rules.
(b) Sketch and explain Born-Haber cycle for NaCl(s).
8. (a) What are Fajan's rules? How do they help in deciding the covalent character in a
bond?
(b) Write a brief note on Van der Waals forces.
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GNDU Answer Paper-2021
Bachelor of Computer Application (BCA) (Hons.)
1
st
Semester (Batch 2024-28) (CBGS)
CHEMISTRY
(Inorganic Chemistry-I)
Time Allowed: Three Hours Max. Marks:35
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.
SECTION-A
1. (a) Calculate de-Broglie wavelength of an electron moving at 2% speed of light [Given:
Mass of electron=9.1×10-31 kg;h=6.63×10-34 kg m²s-1].
(b) Write brief notes on:
(i) Pauli exclusion principle.
(ii) Heisenberg's uncertainty principle.
Ans: 1. (a) Calculate the de-Broglie Wavelength of an Electron Moving at 2% of the Speed
of Light
Understanding the Concept
Imagine you are playing cricket. When you throw a ball, it behaves like a particle. But
scientists discovered something very surprisingvery tiny particles such as electrons can
behave not only like particles but also like waves. This idea was proposed by the French
scientist Louis de Broglie in 1924. According to him, every moving particle has a wave
associated with it. This wave is called the de-Broglie wave, and its wavelength is known as
the de-Broglie wavelength.
The faster a particle moves, the smaller its wavelength becomes. Similarly, a heavier particle
also has a smaller wavelength.
The de-Broglie wavelength is given by the formula:
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Where:
λ (lambda) = de-Broglie wavelength (m)
h = Planck's constant = 6.63 × 10⁻³⁴ J·s
m = Mass of electron = 9.1 × 10⁻³¹ kg
v = Velocity of electron
The speed of the electron is 2% of the speed of light.
Speed of light,
c = 3 × 10⁸ m/s
Therefore,
v = 2% × 3 × 10⁸
v = 0.02 × 3 × 10⁸
v = 6 × 10⁶ m/s
Now substitute the values:
λ = (6.63 × 10⁻³⁴) / [(9.1 × 10⁻³¹) × (6 × 10⁶)]
First calculate the denominator:
= 54.6 × 10⁻²⁵
Now,
λ = (6.63 × 10⁻³⁴) / (54.6 × 10⁻²⁵)
λ ≈ 1.21 × 10⁻¹⁰ m
Final Answer
The de-Broglie wavelength of the electron is approximately:
λ = 1.21 × 10⁻¹⁰ m
or
λ = 0.121 nm
This wavelength is almost equal to the distance between atoms in a crystal. Because of this,
electrons can produce diffraction patterns, proving that they behave like waves.
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Simple Diagram
Electron Moving
● ───────────────►
Wave Associated with Electron
~~~~~~~ ~~~~~~~ ~~~~~~~ ~~~~~~~
Distance between two crests = λ
(b) (i) Pauli Exclusion Principle
Simple Explanation
Imagine there is a hostel room with only two beds. No matter how many students arrive,
only two students can stay in that room, and even those two must be different in one
important way (their spin).
Similarly, in an atom, electrons occupy different orbitals. The Pauli Exclusion Principle,
proposed by the Austrian physicist Wolfgang Pauli in 1925, states that:
No two electrons in the same atom can have the same set of all four quantum numbers.
In simpler words:
One orbital can hold a maximum of two electrons.
Those two electrons must have opposite spins.
If one electron has spin ↑, the other must have spin ↓.
Diagram
Orbital
+----------------+
| ↑ ↓ |
+----------------+
✔ Allowed
+----------------+
| ↑ ↑ |
+----------------+
✘ Not Allowed
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Why is it Important?
Explains why electrons are arranged in different shells and orbitals.
Helps us understand the structure of atoms.
Explains the periodic table.
Determines the chemical properties of elements.
Responsible for the stability of matter.
Everyday Example
Think of a cinema seat. Only one person can occupy one seat. Similarly, only two electrons
with opposite spins can occupy one orbital.
(b) (ii) Heisenberg's Uncertainty Principle
Simple Explanation
Suppose you are trying to photograph a very fast-moving fan with your mobile phone. If you
use a slow camera, you cannot know its exact position clearly. If you use a very fast shutter
speed, you can capture its position, but measuring its exact motion at the same instant
becomes difficult.
The same thing happens with tiny particles like electrons.
The German physicist Werner Heisenberg stated that:
It is impossible to know both the exact position and the exact momentum (or velocity) of
an electron at the same time.
If we measure one quantity very accurately, the other automatically becomes uncertain.
The mathematical form is:
Where:
Δx = Uncertainty in position
Δp = Uncertainty in momentum
h = Planck's constant
This equation shows that the product of the uncertainties can never be smaller than a fixed
minimum value.
Simple Diagram
Trying to Measure an Electron
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●
Position Measured Very Accurately
↓
Momentum becomes Uncertain
OR
Momentum Measured Accurately
↓
Position becomes Uncertain
Everyday Analogy
Imagine trying to catch a tiny mosquito in a dark room. If you focus on exactly where it is, it
quickly changes its motion. If you focus on how fast it is moving, you lose track of its exact
position. Although this is only an analogy (electrons follow quantum laws), it helps explain
why both quantities cannot be measured perfectly at the same time.
Importance of the Principle
Forms the foundation of Quantum Mechanics.
Explains why electrons cannot have fixed paths like planets around the Sun.
Helps scientists understand the behavior of atoms and molecules.
Essential in modern technologies such as electron microscopes, semiconductors,
lasers, and quantum computing.
Conclusion
The de-Broglie hypothesis introduced the revolutionary idea that every moving particle has
wave-like properties, and the calculated wavelength of an electron moving at 2% of the
speed of light is approximately 1.21 × 10⁻¹⁰ m. The Pauli Exclusion Principle explains how
electrons are arranged inside atoms by stating that no two electrons can have the same set
of quantum numbers, allowing only two electrons with opposite spins in one orbital. The
Heisenberg Uncertainty Principle further transformed our understanding of the microscopic
world by showing that the exact position and momentum of an electron cannot both be
known simultaneously. Together, these three concepts form the basis of modern quantum
mechanics and help explain the structure and behavior of atoms, which is fundamental to
physics, chemistry, electronics, and many advanced technologies.
2. Derive Schrodinger wave equation for hydrogen atom. Also explain the significance of y
and w².
Ans: 2. Derive Schrödinger Wave Equation for Hydrogen Atom. Also explain the
significance of ψ and ψ².
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The Schrödinger Wave Equation is one of the most important equations in quantum
mechanics. It was developed by the Austrian physicist Erwin Schrödinger in 1926 to explain
the behavior of very tiny particles such as electrons. Unlike classical physics, where we can
predict the exact position of an object, quantum mechanics tells us that the exact position
of an electron cannot be known. Instead, we can only calculate the probability of finding it
in a particular region.
What is the Hydrogen Atom?
The hydrogen atom is the simplest atom. It consists of:
One proton at the center (nucleus)
One electron moving around the nucleus
Simple Diagram
Electron (e)
●
.-''-.
.-' '-.
/ \
| + |
| Proton |
\ /
'-.______.-'
Hydrogen Atom
The electron does not move in a fixed circular orbit like a planet. Instead, it exists in a cloud
of probability, where some regions have a higher chance of containing the electron than
others.
Schrödinger Wave Equation
The motion of an electron is described by the wave function (ψ).
The general time-independent Schrödinger equation is:
Where:
ψ (Psi) = Wave function of the electron
ħ = Reduced Planck's constant
m = Mass of the electron
² = Laplacian operator (describes change of the wave)
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V = Potential energy
E = Total energy of the electron
Derivation for the Hydrogen Atom (Simple Explanation)
For the hydrogen atom, the electron is attracted to the positively charged nucleus by the
electrostatic (Coulomb) force.
The potential energy is:
Substituting this potential into the Schrödinger equation gives the hydrogen atom equation:
This equation is solved using spherical polar coordinates because the electron can move in
every direction around the nucleus.
After solving the equation mathematically, we obtain:
Allowed energy levels of the hydrogen atom
Shape and size of electron orbitals
Quantum numbers
Electron probability distribution
Thus, Schrödinger's equation successfully explains why electrons occupy only certain energy
levels instead of moving randomly.
Meaning of the Wave Function (ψ)
The symbol ψ (Psi) is called the wave function.
It is a mathematical function that describes the wave nature and quantum state of an
electron.
Important points:
ψ itself cannot be directly measured.
It may have positive, negative, or even complex values.
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It contains all the information about the electron.
Think of ψ like a weather forecast model. The model itself is not the weather, but it contains
all the information needed to predict it.
Significance of ψ² (Psi Square)
The square of the wave function, written as ψ² (more precisely, |ψ|²), has real physical
meaning.
It represents the probability density of finding the electron at a particular point.
Probability Illustration
Probability of Finding Electron
Nucleus
+
High Probability
███████████
Medium Probability
██████
Low Probability
██
Very Low Probability
█
Large value of ψ² → High probability of finding the electron.
Small value of ψ² → Low probability.
ψ² = 0 → The electron cannot exist at that point (called a node).
This concept completely changed our understanding of atoms. Instead of saying "the
electron is here," quantum mechanics says "there is a certain probability of finding the
electron here."
Importance of Schrödinger Wave Equation
The Schrödinger equation is important because it:
Explains the behavior of electrons in atoms.
Predicts the allowed energy levels of hydrogen accurately.
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Introduces the concept of atomic orbitals (s, p, d, and f orbitals).
Explains electron probability instead of fixed orbits.
Forms the foundation of modern quantum mechanics.
Helps explain chemical bonding, spectroscopy, semiconductors, lasers, and many
modern technologies.
Conclusion
The Schrödinger wave equation is the basic equation of quantum mechanics used to
describe the motion of electrons. For the hydrogen atom, the equation includes the
attractive force between the electron and the nucleus. Solving it gives the allowed energy
levels and the shapes of atomic orbitals. The wave function (ψ) describes the quantum state
of the electron, while ψ² represents the probability of finding the electron at a particular
position. Thus, Schrödinger's theory replaced the idea of fixed electron orbits with the
modern concept of electron probability clouds, making it one of the greatest achievements
in modern physics.
SECTION-B
3. What is ionization energy? Give its variation in a period and in a group in the periodic
table. Also discuss various factors in detail which affect ionization energy.
Ans: Ionization Energy Definition, Trend in the Periodic Table, and Factors Affecting It
Ionization energy is one of the most important concepts in chemistry because it explains
how strongly an atom holds its electrons.
Imagine that every atom is like a house, and the electrons are like children living inside it.
The nucleus (which contains protons) acts like the parent holding the children close. If the
parent is very strong, it is difficult for a child to leave the house. Similarly, if the nucleus
attracts the electrons strongly, more energy is required to remove an electron. This required
energy is called ionization energy.
Definition of Ionization Energy
Ionization energy is the minimum amount of energy required to remove the outermost
(most loosely held) electron from an isolated gaseous atom, forming a positive ion
(cation).
For example:
Na(g) + Energy → Na⁺(g) + e⁻
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Here, energy is supplied to remove one electron from a sodium atom.
Simple Diagram
Before Ionization
e
●
-------------
| |
| Nucleus |
| (+ Protons) |
-------------
↑
Electron is attracted to the nucleus.
+ Energy
After Ionization
e → Removed
-------------
| |
| Nucleus |
| (+ Protons) |
-------------
Na
The stronger the attraction between the nucleus and the electron, the higher the ionization
energy.
Variation of Ionization Energy in the Periodic Table
1. Across a Period (Left to Right)
As we move from left to right across a period, the ionization energy generally increases.
Why?
The number of protons increases.
Nuclear charge becomes stronger.
Electrons are pulled closer to the nucleus.
Atomic size decreases.
Therefore, removing an electron becomes more difficult.
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Example
Li → Be → B → C → N → O → F → Ne
Ionization Energy
Low -------------------------> High
Remember: Noble gases like Neon (Ne) have the highest ionization energy because their
outer shell is completely filled and very stable.
2. Down a Group (Top to Bottom)
As we move from top to bottom in a group, the ionization energy generally decreases.
Why?
More electron shells are added.
Atomic size increases.
Outer electrons are farther from the nucleus.
Inner electrons shield the outer electrons from the nucleus.
Therefore, less energy is needed to remove an electron.
Example
Li
↓
Na
↓
K
↓
Rb
↓
Cs
Ionization Energy
High
↓
Medium
↓
Low
Trend Summary
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Direction
Ionization Energy
Left → Right in a Period
Increases
Top → Bottom in a Group
Decreases
Factors Affecting Ionization Energy
Several factors determine whether an atom has high or low ionization energy.
1. Nuclear Charge
Nuclear charge is the positive charge of the nucleus due to protons.
More protons = stronger attraction for electrons.
Strong attraction means more energy is needed to remove an electron.
Example:
Carbon has a higher ionization energy than boron because carbon has more protons
attracting its electrons.
2. Atomic Size
Atomic size is the distance between the nucleus and the outermost electron.
Small atom → electrons are close to the nucleus → difficult to remove → high
ionization energy.
Large atom → electrons are far away → easy to remove → low ionization energy.
Example:
Helium has a much smaller atomic size than sodium, so helium has a much higher ionization
energy.
3. Shielding (Screening) Effect
Inner-shell electrons block or shield the attraction between the nucleus and the outermost
electron.
Nucleus (+)
Inner Electrons
● ●
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Outer Electron
●
Because of shielding:
The outer electron feels less attraction.
It can be removed more easily.
Ionization energy decreases.
The shielding effect increases as we move down a group.
4. Effective Nuclear Charge
The effective nuclear charge is the actual attractive force experienced by the outermost
electron after considering the shielding effect.
High effective nuclear charge → electrons are held tightly → high ionization energy.
Low effective nuclear charge → electrons are held weakly → low ionization energy.
5. Electronic Configuration
Atoms with completely filled or half-filled electron shells are more stable.
Since stable atoms do not easily lose electrons, they have higher ionization energy.
Examples
Noble gases (He, Ne, Ar) have completely filled shells and very high ionization
energies.
Nitrogen has a half-filled p-orbital, making it more stable than oxygen, so nitrogen
has a slightly higher ionization energy.
6. Distance of the Outermost Electron
The farther the outermost electron is from the nucleus:
the weaker the attraction,
the easier it is to remove,
and the lower the ionization energy.
This is another reason why ionization energy decreases down a group.
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Easy Trick to Remember
Across a Period (→): More protons, smaller atom, ionization energy increases.
Down a Group (↓): More shells, larger atom, more shielding, ionization energy
decreases.
Conclusion
Ionization energy is the minimum energy required to remove the outermost electron from
a gaseous atom. It tells us how strongly an atom holds its electrons. In the periodic table,
ionization energy increases from left to right across a period because nuclear charge
increases and atomic size decreases. On the other hand, it decreases from top to bottom in
a group because atomic size and shielding effect increase. The main factors affecting
ionization energy are nuclear charge, atomic size, shielding effect, effective nuclear charge,
electronic configuration, and the distance of the outermost electron from the nucleus.
Understanding these trends helps explain the chemical behavior and reactivity of different
elements.
4. Mention Slater's rule. Calculate the effective nuclear charge for outer electron (4s) of:
(i) Potassium atom (At. No. = 19)
(ii) Copper atom (At. No. = 29)
Ans: What is Slater's Rule?
Slater's Rule is a simple method used to calculate the Effective Nuclear Charge (Zₑff)
experienced by an electron in an atom.
The formula is:
Where:
Z = Atomic number (number of protons)
S = Shielding (screening) constant
Zₑff = Effective nuclear charge
Think of it like this:
Imagine the nucleus is a teacher, and the outer electron is a student trying to hear the
teacher. Between them are many other students (inner electrons). These students block
part of the teacher's voice.
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Teacher = Nucleus
Voice = Nuclear attraction
Other students = Inner electrons
Outer student = Valence electron
So, the outer electron does not feel the full positive charge of the nucleus.
Simple Diagram
Outermost Electron (4s)
●
↑
Shielding by inner electrons
(They reduce nuclear attraction)
○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○
Inner Electrons
+++++++++
Nucleus
(Protons = Z)
The outer electron feels only the effective nuclear charge, not the total nuclear charge.
Rules for Calculating Shielding (S)
For a 4s electron, Slater's Rule says:
Electrons in the same shell (4s, 4p) contribute 0.35 each.
Electrons in the (n−1) shell (3s,3p,3d) contribute 0.85 each.
Electrons in (n−2) or lower shells contribute 1.00 each.
(i) Potassium (K)
Atomic Number:
Electronic Configuration:
1s²
2s² 2p⁶
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3s² 3p⁶
4s¹
The outer electron is 4s¹.
Step 1: Calculate Shielding (S)
Same shell (4s)
No other electron
Contribution
0 × 0.35 = 0
Third shell (3s²3p⁶)
8 electrons
8 × 0.85 = 6.8
First and Second shells
10 electrons
10 × 1.00 = 10
Total shielding
Step 2: Calculate Effective Nuclear Charge
Answer
(ii) Copper (Cu)
Atomic Number
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Electronic Configuration
1s²
2s²2p⁶
3s²3p⁶3d¹⁰
4s¹
Again, the outer electron is 4s¹.
Step 1: Shielding
Same shell (4s)
No other electron
0 × 0.35 = 0
Third shell
There are
3s²
3p⁶
3d¹⁰
Total = 18 electrons
Contribution
18 × 0.85 = 15.3
First and Second shells
10 electrons
10 × 1.00 = 10
Total shielding
Step 2: Effective Nuclear Charge
Answer
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Final Answers
Atom
Atomic Number (Z)
Shielding (S)
Effective Nuclear Charge (Zₑff)
Potassium (K)
19
16.8
2.2
Copper (Cu)
29
25.3
3.7
Key Points to Remember
Slater's Rule estimates how much inner electrons shield an outer electron from the
nucleus.
Effective Nuclear Charge (Zₑff) is the actual positive charge felt by an electron after
shielding.
Formula: Zₑff = Z − S.
A higher Zₑff means the nucleus attracts the electron more strongly.
Copper has a higher Zₑff (3.7) than Potassium (2.2), so its outer 4s electron is held
more strongly by the nucleus despite the presence of more inner electrons. This
concept helps explain periodic trends such as atomic size, ionization energy, and
electron affinity.
SECTION-C
5. Explain the main features of VSEPR theory. Using VSEPR theory, describe the shapes of
the following:
(i) SF4
(ii) IC/2.
Ans: (i) SF₄ (Sulfur Tetrafluoride)
(ii) ICl₂⁻ (Dichloroiodide Ion)
The VSEPR Theory (Valence Shell Electron Pair Repulsion Theory) is a simple theory used to
predict the shape of molecules. The main idea is very easy to remember:
Electron pairs around the central atom always try to stay as far away from each other as
possible because they repel one another.
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Think of a group of people standing in a small room. If everyone dislikes being too close to
others, they will spread out as much as possible. Electron pairs behave in exactly the same
way. This arrangement gives the molecule its final shape.
Main Features of VSEPR Theory
1. Electron pairs repel each other. They arrange themselves to minimize repulsion.
2. Both bonding pairs and lone pairs are considered.
o Bonding pair (BP): Shared between two atoms.
o Lone pair (LP): Present only on the central atom.
3. Lone pairs repel more strongly than bonding pairs.
4. The order of repulsion is:
LPLP > LPBP > BPBP
This means lone pairs occupy more space and push bonding pairs closer together.
5. The molecular shape depends mainly on the total number of electron pairs around the
central atom.
(i) Shape of SF₄
In SF₄, sulfur (S) is the central atom.
Sulfur has 6 valence electrons.
It forms 4 bonds with four fluorine atoms.
1 lone pair remains on sulfur.
Therefore,
Bonding pairs = 4
Lone pairs = 1
Total electron pairs = 5
Five electron pairs first arrange themselves in a trigonal bipyramidal arrangement.
The lone pair prefers an equatorial position because this position has less repulsion than
the axial position.
As a result, the molecule takes a see-saw shape.
Simple Diagram
F (axial)
|
S
/ | \
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F LP F
|
F (axial)
(Actual molecular shape: See-Saw)
Explanation:
The lone pair pushes the bonded fluorine atoms slightly away. Because of this extra
repulsion, the molecule is no longer symmetrical and becomes see-saw shaped.
(ii) Shape of ICl₂⁻
In ICl₂⁻, iodine (I) is the central atom.
Iodine has 7 valence electrons.
One extra electron comes from the negative charge.
It forms 2 bonds with chlorine atoms.
3 lone pairs remain on iodine.
Therefore,
Bonding pairs = 2
Lone pairs = 3
Total electron pairs = 5
Again, the electron-pair arrangement is trigonal bipyramidal.
The three lone pairs occupy the three equatorial positions because this minimizes
repulsion.
The two chlorine atoms remain opposite each other in the axial positions, giving a linear
shape.
Simple Diagram
Cl
|
I
|
Cl
Linear Molecule (180°)
Three lone pairs are present around iodine
(in the equatorial positions).
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Summary Table
Molecule
Bond Pairs
Lone Pairs
Electron Pair Geometry
Molecular Shape
SF₄
4
1
Trigonal Bipyramidal
See-Saw
ICl₂⁻
2
3
Trigonal Bipyramidal
Linear
Conclusion
VSEPR theory helps us predict molecular shapes by considering the repulsion between
electron pairs around the central atom. Electron pairs always arrange themselves to remain
as far apart as possible. In SF₄, one lone pair distorts the structure, producing a see-saw
shape. In ICl₂⁻, three lone pairs occupy the equatorial positions, leaving the two chlorine
atoms opposite each other, resulting in a linear shape. Thus, by counting bonding pairs and
lone pairs, we can easily determine the shape of any molecule using VSEPR theory.
6. (a) Calculate the percentage ionic character in HBr molecule. Given electronegativity
values of H and Br are 2.1 and 2.8, respectively.
(b) Discuss the limitations of Valence Bond Theory.
(c) Draw MO diagrams of nitrogen molecule. Also calculate its bond order.
Ans: 6. (a) Calculate the Percentage Ionic Character in HBr Molecule
When two atoms join together, they form a chemical bond. This bond can be either
covalent (sharing of electrons) or ionic (transfer of electrons). In reality, most bonds are a
mixture of both. The percentage ionic character tells us how much ionic nature is present in
a covalent bond.
The ionic character depends on the difference in electronegativity between the two atoms.
Electronegativity of Hydrogen (H) = 2.1
Electronegativity of Bromine (Br) = 2.8
Step 1: Calculate Electronegativity Difference
Step 2: Use the Formula
Ionic Character
Substitute the value:
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Answer:
Percentage Ionic Character of HBr = 11.5% (approximately).
Simple Explanation
Think of Hydrogen and Bromine as two friends sharing a ball (electron). Bromine is stronger
and pulls the ball slightly more towards itself because it has higher electronegativity. Since
the electron is not completely transferred, the bond remains mainly covalent, but it has
about 11.5% ionic character.
6. (b) Limitations of Valence Bond Theory (VBT)
Valence Bond Theory explains that chemical bonds are formed when two atomic orbitals
overlap and electrons are shared. Although this theory successfully explains many simple
molecules, it has several limitations.
1. Cannot Explain Magnetic Properties
According to VBT, oxygen (O₂) should have all paired electrons, so it should be non-
magnetic.
But experiments show that oxygen is paramagnetic, meaning it has two unpaired electrons.
Therefore, VBT fails to explain the magnetic behavior of oxygen.
2. Cannot Explain Molecular Shapes Completely
VBT gives only a basic idea of bonding.
It cannot accurately explain why some molecules have different shapes without using
additional theories like hybridization.
3. Cannot Explain Bond Energies Correctly
Different molecules have different bond strengths.
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VBT cannot accurately predict or compare these bond energies.
4. Cannot Explain Colour of Molecules
Many compounds, especially transition metal compounds, are coloured.
VBT cannot explain why these colours are produced.
5. Cannot Explain Electron Delocalization
In molecules like benzene, electrons are spread over the entire ring.
VBT assumes electrons remain localized between two atoms only.
Hence it cannot explain resonance properly.
6. Cannot Explain Molecular Orbital Formation
Electrons in a molecule often belong to the whole molecule instead of individual bonds.
VBT cannot explain this concept.
This is why Molecular Orbital Theory (MOT) was developed.
Easy Way to Remember
Imagine VBT as an old map.
It can help you reach nearby places, but it cannot show highways, traffic, or satellite view.
Similarly, VBT explains simple bonds but fails to explain many advanced properties of
molecules.
6. (c) Molecular Orbital (MO) Diagram of Nitrogen (N₂) and Bond Order
Molecular Orbital Theory states that when two atoms come together, their atomic orbitals
combine to form molecular orbitals.
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There are two types:
Bonding Molecular Orbitals (Lower Energy) Increase stability.
Antibonding Molecular Orbitals (Higher Energy) Decrease stability.
Each nitrogen atom has 7 electrons.
Therefore,
electrons
Out of these,
10 are valence electrons
4 are core electrons
MO Energy Order for Nitrogen
For molecules up to nitrogen (B₂, C₂, N₂), the order is:
Higher Energy
σ*2p
π*2p π*2p
σ2p
π2p π2p
σ2s
σ*2s
σ1s
σ*1s
Lower Energy
Electronic Configuration of N₂
Bond Order Formula
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Where:
= Number of electrons in bonding orbitals
= Number of electrons in antibonding orbitals
For Nitrogen:
Bonding electrons = 10
Antibonding electrons = 4
Therefore,
Bond Order
Final Answer
Bond Order of N₂ = 3
This means nitrogen atoms are connected by a triple bond (N≡N).
MO Diagram (Simplified)
Energy ↑
σ*2p ( )
π*2p π*2p ( ) ( )
σ2p (↑↓)
π2p π2p
(↑↓) (↑↓)
σ2s (↑↓)
σ*2s (↑↓)
σ1s (↑↓)
σ*1s (↑↓)
Why is N₂ So Stable?
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Nitrogen has a bond order of 3, meaning the two nitrogen atoms share three pairs of
electrons. A triple bond is very strong and difficult to break. That is why nitrogen gas is
chemically less reactive and makes up about 78% of Earth's atmosphere.
Quick Revision
Percentage ionic character of HBr ≈ 11.5%, because bromine attracts shared
electrons more strongly than hydrogen.
Valence Bond Theory explains bonding by overlap of atomic orbitals but cannot
explain magnetic properties, molecular orbital formation, resonance, colours, and
several other advanced properties.
Molecular Orbital Theory explains electron distribution across the whole molecule.
In N₂, there are 10 bonding electrons and 4 antibonding electrons, giving a bond
order of 3, which represents a strong triple bond (N≡N) and explains the exceptional
stability of the nitrogen molecule.
SECTION-D
7. (a) Write a brief note on radius ratio rules.
(b) Sketch and explain Born-Haber cycle for NaCl(s).
Ans: 7. (a) Radius Ratio Rule
The Radius Ratio Rule is a simple method used to predict how positive ions (cations) and
negative ions (anions) arrange themselves in an ionic crystal. It tells us how many anions
can surround one cation and helps us understand the shape (geometry) and stability of
ionic compounds.
What is Radius Ratio?
The radius ratio is the ratio of the radius of the cation to the radius of the anion.
Radius Ratio
Radius of Cation (
)
Radius of Anion (
)
Cation (r⁺): Positively charged ion (smaller in size).
Anion (r⁻): Negatively charged ion (larger in size).
The value of this ratio determines how many anions can fit around one cation without
making the crystal unstable.
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Why is the Radius Ratio Important?
Imagine trying to place a small ball in the middle of several large balls.
If the small ball is too tiny, it cannot touch all the surrounding balls and the
arrangement becomes unstable.
If the small ball is large enough, it touches all surrounding balls and forms a stable
crystal.
This is exactly how ions behave in ionic solids.
Radius Ratio and Coordination Number
Radius Ratio (r⁺/r⁻)
Coordination Number
Shape
0.155 0.225
3
Triangular
0.225 0.414
4
Tetrahedral
0.414 0.732
6
Octahedral
0.732 1.00
8
Cubic
Easy Example
In NaCl (Sodium Chloride):
Sodium ion (Na⁺) is smaller.
Chloride ion (Cl⁻) is larger.
Their radius ratio falls in the 0.4140.732 range.
Therefore:
Coordination Number = 6
Each Na⁺ is surrounded by 6 Cl⁻ ions.
Each Cl⁻ is surrounded by 6 Na⁺ ions.
This forms an octahedral arrangement, making NaCl highly stable.
Simple Diagram
Cl
|
ClNaCl
|
Cl
(Two more Cl⁻ are above
and below the plane)
Coordination Number = 6
Key Points
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Radius ratio predicts crystal structure.
It decides the coordination number.
Larger radius ratio → more neighbouring ions.
Smaller radius ratio → fewer neighbouring ions.
It is mainly applicable to ionic compounds.
7. (b) BornHaber Cycle for NaCl(s)
The BornHaber Cycle is a thermochemical cycle used to calculate the lattice energy of an
ionic compound such as NaCl. Since lattice energy cannot be measured directly, we
calculate it indirectly using Hess's Law, which states that the total energy change is the
same regardless of the path taken.
Think of building a house. Instead of building it in one step, you first collect bricks, then
cement, then labour, and finally assemble everything. The total cost is the sum of all these
individual costs. Similarly, the formation of NaCl occurs through several energy changes.
Step-by-Step BornHaber Cycle
Step 1: Sublimation of Sodium
Solid sodium changes into gaseous sodium atoms.
Energy absorbed = Sublimation Energy (ΔHₛᵤᵦ)
Step 2: Ionization of Sodium
A gaseous sodium atom loses one electron.
Energy absorbed = Ionization Energy (IE)
Step 3: Dissociation of Chlorine
Chlorine molecules break into chlorine atoms.
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Energy absorbed = Bond Dissociation Energy
Step 4: Electron Affinity
A chlorine atom gains an electron.
Energy is released because chlorine likes to gain an electron.
This is called Electron Affinity (EA).
Step 5: Formation of NaCl Crystal
Now the gaseous ions come together.
A large amount of energy is released.
This released energy is called Lattice Energy.
Simple BornHaber Cycle Diagram
Na(s) + ½Cl(g)
│
│ ΔHf (Formation of NaCl)
▼
NaCl(s)
▲
│ Lattice Energy
Na(g) + Cl(g)
▲ ▲
│IE │EA
Na(g) Cl(g)
▲ ▲
│ │
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Sublimation ½ Bond Dissociation
│ │
Na(s) ½Cl(g)
BornHaber Equation
According to Hess's Law,
where:
ΔHf = Enthalpy of formation
ΔHsub = Sublimation energy
IE = Ionization energy
D = Bond dissociation energy of Cl₂
EA = Electron affinity
U = Lattice energy
Importance of the BornHaber Cycle
It helps calculate lattice energy, which cannot be measured directly.
It explains why ionic compounds such as NaCl are very stable.
It shows how energy is absorbed and released during ionic bond formation.
It confirms Hess's Law by showing that total energy change remains the same
regardless of the pathway.
Conclusion
The Radius Ratio Rule explains how ions are arranged in an ionic crystal by comparing the
sizes of cations and anions. It helps determine the coordination number and crystal
geometry. The BornHaber Cycle explains how NaCl is formed through a series of energy
changes and allows us to calculate lattice energy using Hess's Law. Together, these concepts
help us understand the structure, stability, and formation of ionic compounds, making
them fundamental topics in solid-state and inorganic chemistry.
8. (a) What are Fajan's rules? How do they help in deciding the covalent character in a
bond?
(b) Write a brief note on Van der Waals forces.
Ans: 8. (a) What are Fajan's Rules? How do they help in deciding the covalent character in
a bond?
When atoms combine, they usually form either ionic bonds or covalent bonds.
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Ionic bond: One atom gives electrons to another atom.
Covalent bond: Two atoms share electrons.
However, in reality, many compounds are not 100% ionic or 100% covalent. They have a
mixture of both. To predict how much covalent character an ionic compound has, scientists
use Fajan's Rules.
What are Fajan's Rules?
Fajan's Rules were given by the scientist Kazimierz Fajans. These rules explain when an
ionic bond starts behaving like a covalent bond.
The idea is based on polarization.
A positive ion (cation) attracts the electron cloud of the negative ion (anion).
If the electron cloud of the anion is pulled strongly, it becomes distorted. This
distortion is called polarization.
Greater polarization means greater covalent character.
Fajan's Rules
1. Smaller Cation → More Covalent Character
A small positive ion has a strong pulling power because its charge is concentrated in a small
area.
Example:
Li⁺ is smaller than Na⁺.
Therefore, LiCl is more covalent than NaCl.
2. Larger Anion → More Covalent Character
A large negative ion has a loose electron cloud, which can be easily distorted.
Example:
I⁻ is larger than Cl⁻.
Therefore, LiI is more covalent than LiCl.
3. Higher Charge on Cation → More Covalent Character
A cation with a higher positive charge attracts electrons more strongly.
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Example:
Al³⁺ has a higher charge than Na⁺.
Therefore, AlCl₃ is more covalent than NaCl.
Simple Diagram
Positive Ion (+) Negative Ion (-)
(+) -------> ( Electron Cloud )
The positive ion pulls the electron cloud.
More Pull
↓
More Polarization
↓
More Covalent Character
Importance of Fajan's Rules
These rules help us to:
Predict whether a compound is more ionic or more covalent.
Explain properties like melting point, boiling point, and solubility.
Understand the nature of chemical bonding.
(b) Write a Brief Note on Van der Waals Forces
Imagine two people standing close together without holding hands. Even though they are
not directly connected, they still feel a slight attraction because they are near each other.
Similarly, molecules also attract each other through very weak forces called Van der Waals
forces.
These are weak intermolecular forces, meaning they act between molecules, not inside a
molecule.
They are much weaker than ionic or covalent bonds but are very important because they
help hold molecules together.
Types of Van der Waals Forces
1. DipoleDipole Forces
These occur between polar molecules.
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One molecule has a slightly positive end (δ⁺), and another has a slightly negative end (δ⁻).
The opposite charges attract each other.
Example: HCl molecules.
2. London Dispersion Forces
These are present in all molecules, especially non-polar molecules.
Electrons keep moving continuously, creating temporary positive and negative regions.
These temporary charges attract neighboring molecules.
Example: Oxygen (O₂), Nitrogen (N₂), and noble gases.
3. Dipole-Induced Dipole Forces
A polar molecule can temporarily induce a dipole in a nearby non-polar molecule, causing a
weak attraction.
Simple Diagram
Molecule A Molecule B
δ+ -------- δ− δ+ -------- δ−
↑
Weak attraction
(Van der Waals Force)
Importance of Van der Waals Forces
Although these forces are weak, they play an important role in nature.
They help liquids remain in the liquid state.
They affect the melting and boiling points of substances.
They allow gases to condense into liquids.
They help in the folding of proteins and the structure of DNA.
They contribute to the adhesion of substances and many biological processes.
Conclusion
Fajan's Rules help us understand why some ionic compounds show covalent character by
considering the size and charge of ions and the effect of polarization. On the other hand,
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Van der Waals forces are weak attractions between molecules that play a vital role in
determining the physical properties of substances, even though they are much weaker than
chemical bonds. Together, these concepts help explain how atoms and molecules interact
and why different compounds behave differently.
This paper has been carefully prepared for educational purposes. If you notice any mistakes or
have suggestions, feel free to share your feedback.
