Atomic Structure to Organic Chemistry: Key Concepts

Posted on Jan 25, 2026 in Chemistry

Unit I: Atomic Structure

Bohr’s Atomic Theory

Bohr proposed that electrons revolve in specific circular orbits around the nucleus without radiating energy. These orbits are quantized and labeled by the principal quantum number n. The angular momentum of the electron is given by mvr = n(h/2π). The energy of an electron in a hydrogen-like atom is E = −13.6 Z²/n² eV. When an electron jumps between energy levels, radiation is absorbed or emitted: ΔE = hν = hc/λ.

Limitations of Bohr’s Theory

Bohr’s model could not explain the spectra of atoms with more than one electron. It failed to account for the splitting of spectral lines in the presence of magnetic (Zeeman effect) and electric (Stark effect) fields. It did not explain the relative intensities of spectral lines or fine structures. Most importantly, it contradicted Heisenberg’s uncertainty principle and was purely classical in nature, ignoring the wave nature of electrons.

Dual Behaviour of Matter and Radiation

Electromagnetic radiation shows both wave and particle properties (for example, the photoelectric effect shows particle nature, diffraction shows wave nature). Similarly, matter such as electrons also exhibits wave properties, as demonstrated in electron diffraction experiments.

de Broglie’s Relation

Louis de Broglie proposed that all matter has wave-like properties. The wavelength of a particle is given by λ = h/p = h/mv. This was experimentally verified in the Davisson–Germer experiment.

Heisenberg’s Uncertainty Principle

This principle states that it is impossible to simultaneously know the exact position and momentum of a particle. Mathematically, Δx · Δp ≥ h/4π. This sets a fundamental limit on how precisely we can determine the motion of subatomic particles and invalidates Bohr’s fixed-orbit concept.

Hydrogen Atom Spectra

Hydrogen displays a line spectrum with distinct series based on electronic transitions between energy levels:

Lyman (UV region) — transitions ending at n = 1
Balmer (visible) — transitions ending at n = 2
Paschen, Brackett, Pfund (IR region) — transitions ending at n = 3, 4, 5, etc.

Need for a New Approach to Atomic Structure

Bohr’s model was unable to handle the complexities of multi-electron systems. It ignored the wave nature of electrons and the probabilistic interpretation of their position. Therefore, a new approach based on quantum mechanics became necessary to explain atomic behavior accurately.

Time-Independent Schrödinger Equation

This quantum mechanical equation is written as Ĥψ = Eψ, where Ĥ is the Hamiltonian operator (total energy), ψ is the wave function, and E is the energy of the system. The square of the wave function, |ψ|², gives the probability density of finding an electron in a particular region of space.

Quantum Numbers and Their Significance

Four quantum numbers describe the state of an electron:

Principal quantum number (n) — determines the energy level and size of the orbital.
Azimuthal quantum number (l) — determines the shape (s, p, d, f) of the orbital.
Magnetic quantum number (m) — indicates the orientation of the orbital.
Spin quantum number (s) — describes the spin of the electron (+½ or −½).

These quantum numbers are essential in identifying the unique position and energy of an electron in an atom.

Rules for Filling Electrons in Various Orbitals

Aufbau principle: electrons fill orbitals in order of increasing energy.
Pauli exclusion principle: no two electrons in an atom can have the same set of four quantum numbers.
Hund’s rule: electrons occupy degenerate orbitals singly first, with parallel spins, before pairing up.

Electronic Configurations of Atoms

Electronic configuration represents the distribution of electrons in atomic orbitals. Electrons are filled in the order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p, and so on. For example, the configuration of oxygen is 1s² 2s² 2p⁴.

Stability of Half-Filled and Completely Filled Orbitals

Subshells like d⁵ and d¹⁰ have extra stability due to symmetrical arrangement and exchange energy. For instance, chromium has configuration [Ar] 3d⁵ 4s¹ instead of [Ar] 3d⁴ 4s², and copper has [Ar] 3d¹⁰ 4s¹ instead of [Ar] 3d⁹ 4s². This is because such configurations lead to lower energy and higher stability.

Concept of Exchange Energy

Exchange energy arises when electrons with parallel spins in degenerate orbitals can exchange places. This exchange reduces repulsion and contributes to extra stability, especially in half-filled and completely filled subshells.

Relative Energies of Atomic Orbitals

The relative energy of orbitals depends on the (n + l) rule. Orbitals with lower (n + l) values have lower energy. If (n + l) is the same, the orbital with lower n has lower energy. Thus, 4s is filled before 3d even though 3d belongs to a lower principal energy level.

Anomalous Electronic Configurations

Some elements do not follow the expected order of orbital filling due to the stability associated with half-filled and fully-filled d orbitals. Chromium (Z = 24) has configuration [Ar] 3d⁵ 4s¹, and copper (Z = 29) has [Ar] 3d¹⁰ 4s¹, instead of what is predicted by the Aufbau principle.

Unit II: Chemical Bonding and Molecular Structure

Covalent Bonding

Covalent bonding is the mutual sharing of electrons between atoms (usually nonmetals) to achieve stable configurations. Each shared pair equals one covalent bond. These bonds are directional and have specific shapes. Bond strength and length depend on shared pairs and orbital overlap.

Valence Bond Approach

Bonds form by overlap of half-filled atomic orbitals. Two types: σ (head-on) and π (sideways). Greater overlap results in stronger bonds. This approach explains bond formation but not magnetic or spectral behavior in all cases.

VSEPR Theory and Molecular Shapes

VSEPR predicts shape based on repulsion between bonding and lone pairs. Examples:

Linear (sp): BeCl₂, CO₂ — 180°
Trigonal planar (sp²): BF₃ — 120°
Tetrahedral (sp³): CH₄ — 109.5°
Trigonal bipyramidal (sp³d): PCl₅ — 90°, 120°
Octahedral (sp³d²): SF₆ — 90°
Square planar (dsp²): XeF₄ — 90°

Hybridization

Mixing of atomic orbitals forms new hybrid orbitals:

sp: linear
sp²: trigonal planar
sp³: tetrahedral
sp³d: trigonal bipyramidal
sp³d²: octahedral
dsp²: square planar

Hybrid orbitals form σ-bonds; unhybridized orbitals form π-bonds.

Resonance and Resonating Structures

Resonance occurs when more than one valid Lewis structure exists. The real structure is a hybrid of resonance forms. Examples include:

Benzene — alternating double bonds (delocalized π electrons)
Carbonate ion — delocalized π electrons
Ozone — two resonance forms

Resonance increases stability via delocalization.

Molecular Orbital Theory (MO)

Atomic orbitals (AOs) combine to form bonding, antibonding, and nonbonding molecular orbitals (MOs) that extend over the molecule. Electrons fill MOs following the Aufbau, Pauli, and Hund’s rules.

LCAO Method

The linear combination of atomic orbitals (LCAO) combines AOs mathematically. Constructive overlap yields bonding MOs; destructive overlap yields antibonding MOs. Effective combination requires similar energy and symmetry of AOs.

Bonding and Antibonding Orbitals

Bonding (σ, π) orbitals are lower in energy and have high electron density between nuclei. Antibonding (σ*, π*) orbitals are higher in energy and have nodal regions between nuclei. Bonding orbitals stabilize a molecule, while occupation of antibonding orbitals destabilizes it.

s-s, s-p, p-p Combinations

Typical combinations:

s-s: σ and σ*
s-p: σ and σ*
p-p: σ (head-on) and π (side-on), each with antibonding counterparts

Nonbonding Orbitals

Nonbonding orbitals form when AOs do not combine properly. They do not form bonds but affect dipole moments and electronic transitions.

MO of Homonuclear Diatomic Molecules

For homonuclear diatomics:

For Z ≤ 7 (B₂, C₂, N₂): π2p < σ2p
For Z ≥ 8 (O₂, F₂): σ2p < π2p

Bond order = ½(bonding e⁻ − antibonding e⁻). Examples: O₂ bond order = 2 (paramagnetic), N₂ bond order = 3 (very stable), He₂ bond order = 0 (unstable).

s-p Mixing

s-p mixing (or s-p interaction) occurs in lighter elements (Z ≤ 7) due to the close energy of 2s and 2p orbitals. It alters MO energy ordering and affects bond order and magnetism.

Heteronuclear Diatomic Molecules (CO, NO, NO⁺)

Different elements have different AO energies, producing asymmetric MOs. Examples:

CO: bond order 3, diamagnetic
NO: bond order 2.5, paramagnetic
NO⁺: bond order 3, more stable

Electronegativity differences affect MO energy levels.

VB vs MO Theory

Valence Bond (VB) Theory: localized bonds, uses hybridization, but cannot explain O₂ magnetism.

Molecular Orbital (MO) Theory: delocalized bonding, explains bond order and magnetism; O₂‘s paramagnetism is explained by MO theory.

Unit III: Gases

Kinetic Theory of Gases

The kinetic theory explains gas behavior based on molecular motion.

Postulates:

Gas consists of a large number of small particles (molecules) in constant, random motion.
Particle volume is negligible compared to container volume.
No intermolecular forces except during collisions.
Collisions are perfectly elastic (no loss of kinetic energy).
Average kinetic energy is proportional to temperature (in kelvin).

Kinetic Gas Equation

Derived from kinetic theory, the pressure can be related to molecular motion by:
P = (1/3)(N/V) m <v²>, where P = pressure, V = volume, N = number of molecules, m = mass of a molecule, and <v²> = mean square velocity. This equation relates macroscopic properties to microscopic molecular motion.

Deviation from Ideal Gas Behavior

Real gases deviate from ideal gas laws due to:

Intermolecular attractions reducing pressure
Finite volume of gas molecules

Deviation is quantified by the compressibility factor Z = PV/RT. For ideal gases Z = 1; deviations occur at high pressure and low temperature.

Van der Waals Equation

This equation accounts for real gas behavior by correcting pressure and volume terms:
(P + a/V_m²)(V_m − b) = RT, where V_m = molar volume, a = measure of intermolecular attraction, and b = volume occupied by molecules. This equation explains liquefaction and deviation from ideality.

Velocities in Gases

Characteristic velocities:

Most probable velocity (v_mp): velocity at which the maximum number of molecules is found.
Average velocity (v_avg): mean velocity of all molecules.
Root mean square velocity (v_rms): square root of the average of squared velocities.

Collision Number

The average number of collisions per second per unit volume in a gas is related to molecular speed, cross section, and density.

Mean Free Path

Mean free path is the average distance traveled by a molecule between successive collisions. It decreases with pressure and increases with temperature.

Unit IV: Liquids and Solids

Liquids

Liquids have fixed volume but no fixed shape. The particles are closely packed but can flow past one another. Intermolecular forces are stronger than in gases but weaker than in solids.

Surface Tension

Surface tension is the force acting along the surface of a liquid, causing it to behave like a stretched elastic sheet. It arises due to unbalanced cohesive forces at the surface. It is measured as force per unit length (N/m) and denoted by γ. Liquids tend to minimize surface area due to surface tension.

Phenomena such as capillary rise, droplet formation, and the spherical shape of bubbles are effects of surface tension.

Determination of Surface Tension using Stalagmometer

A stalagmometer is used to compare surface tensions of liquids based on the drop-count method.

Principle: surface tension is proportional to the weight of each drop.

Formula:

(γ₁ / γ₂) = (n₂ ρ₁) / (n₁ ρ₂)

where γ is surface tension, n is number of drops, and ρ is density. This method gives relative surface tension values by comparing with water or another known liquid.

Viscosity of a Liquid

Viscosity is the resistance to flow. It arises from intermolecular forces and is defined as the force per unit area required to maintain a unit velocity gradient between two layers. Unit: poise or Ns/m².

Greater viscosity means slower flow. Water has low viscosity; glycerol has high viscosity.

Determination of Viscosity using Ostwald Viscometer

An Ostwald viscometer compares the flow time of liquids through a capillary tube.

Principle: flow time is proportional to viscosity.

Formula:

η₁ / η₂ = (t₁ ρ₁) / (t₂ ρ₂)

where η is viscosity, t is time, and ρ is density. This allows comparison with a reference liquid like water.

Effect of Temperature on Surface Tension and Viscosity

Surface tension decreases with increasing temperature due to weakening of cohesive forces.
Viscosity also decreases with temperature as increased molecular motion reduces resistance to flow.

Solids

Solids have fixed shape and volume. Particles are closely packed in regular patterns. They are incompressible and show rigidity. Solids are classified into crystalline and amorphous solids.

Forms of Solids

Covalent solids: atoms bonded by covalent bonds in a 3D network (e.g., diamond, SiO₂) — hard, high melting point, poor conductors.
Molecular solids: molecules held by van der Waals or hydrogen bonds (e.g., ice, dry ice) — soft, volatile.
Ionic solids: cations and anions held by electrostatic forces (e.g., NaCl, KBr) — hard, brittle, high melting, conduct in molten state.
Metallic solids: metal cations in an electron sea (e.g., Cu, Fe) — ductile, good conductors.
Amorphous solids: no definite arrangement (e.g., glass) — isotropic, melt over a range.

Types of Cubic Unit Cells

Crystalline solids have a definite pattern that repeats in space called a unit cell.

Cubic Unit Cells:

Simple cubic (SC): particles at corners only — 1 atom per unit cell.
Body-centered cubic (BCC): corners + 1 in center — 2 atoms per unit cell.
Face-centered cubic (FCC): corners + 6 faces — 4 atoms per unit cell.

Crystal Systems

Seven types of crystal systems exist based on edge lengths and angles:

Cubic
Tetragonal
Orthorhombic
Monoclinic
Triclinic
Rhombohedral
Hexagonal

Each system has characteristic relationships among the cell edges (a, b, c) and angles (α, β, γ).

Bravais Lattices

These are the 14 distinct three-dimensional lattice types formed by arranging unit cells. They represent all possible arrangements of points in 3D space. Each crystal system has a specific number of Bravais lattices.

Defects in Crystals

Crystalline solids may show imperfections in their lattice arrangement.

1. Point Defects: localized irregularities involving one or few atoms:

Vacancy defect: missing atom at a lattice point.
Interstitial defect: extra atom in interstitial space.
Substitutional defect: foreign atom replaces host atom.

2. Line Defects: also called dislocations, occur along a line in the crystal (edge dislocation, screw dislocation) — affect mechanical strength.

Schottky and Frenkel Defects

Schottky defect: equal number of cations and anions missing — common in ionic solids of high coordination number like NaCl — decreases density.

Frenkel defect: ion displaced to an interstitial site — common in small-sized cation systems like AgCl — density unchanged.

Both are types of stoichiometric defects and affect electrical conductivity and properties of solids.

Unit V: Fundamentals of Organic Chemistry

Electronic Displacements

Electronic effects influence reactivity and stability of organic molecules:

Inductive effect: transmission of charge through sigma bonds due to electronegativity differences; electron withdrawing (−I) or donating (+I).
Electromeric effect: temporary shift of π-electrons to one atom in the presence of an attacking reagent; reversible and only during reaction.
Resonance: delocalization of π-electrons over adjacent atoms to stabilize molecules; contributes to resonance hybrid structures.
Hyperconjugation: delocalization of electrons from sigma (C–H or C–C) bonds to adjacent empty or partially filled p-orbitals or π systems, stabilizing carbocations or radicals.

Cleavage of Bonds

Breaking of bonds occurs in two ways:

Homolysis: equal splitting of bond electrons producing radicals (species with unpaired electrons).
Heterolysis: unequal splitting forming ions; one atom gets both electrons (carbocation and carbanion formation).

Structure, Shape and Reactivity of Organic Molecules

Nucleophiles: electron-rich species donating a pair of electrons to electrophiles. Examples: OH⁻, NH₃, Cl⁻.

Electrophiles: electron-deficient species accepting electron pairs. Examples: H⁺, NO₂⁺, carbocations.

Reactive Intermediates

Short-lived species formed during reactions:

Carbocations: positively charged, electron-deficient, planar, sp² hybridized, highly reactive.
Carbanions: negatively charged, electron-rich, often pyramidal, sp³ hybridized.
Free radicals: neutral species with an unpaired electron, highly reactive.

Strength of Organic Acids and Bases

Acid-base strength is measured by pK values and influenced by:

Electronegativity: a more electronegative atom stabilizes the conjugate base → stronger acid.
Resonance: delocalization stabilizes the conjugate base → stronger acid.
Inductive effect: electron-withdrawing groups increase acidity.
Hybridization: higher s-character in the orbital holding negative charge increases acidity (sp > sp² > sp³).
Solvent effects: stabilization/destabilization by solvents.

Aromaticity

Benzenoids: compounds like benzene with conjugated π systems forming planar rings.

Hückel’s rule: a planar, cyclic, conjugated molecule with (4n + 2) π electrons (where n = 0, 1, 2, …) is aromatic and exceptionally stable.

Examples: benzene (6 π electrons), naphthalene, anthracene.