1. Rydberg formula

$\frac{1}{\lambda} = R_H \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$

Where:

$\lambda$ = wavelength
$R_H$ = Rydberg constant = $1.097 \times 10^7 \, \text{m}^{-1}$
$n_1, n_2$ = integers, $n_2 > n_1$

It gives the wavelength of light emitted when an electron jumps between energy levels in a hydrogen atom.

2. de Broglie equation

$\lambda = \frac{h}{mv}$

Where:

$\lambda$ = wavelength
$h$ = Planck’s constant
$m$ = mass
$v$ = velocity

Significance: It shows that matter (like electrons) has wave nature.

3. Spectral series of Hydrogen

Series	Transition	Region
Lyman	$n_2 \to 1$	Ultraviolet
Balmer	$n_2 \to 2$	Visible
Paschen	$n_2 \to 3$	Infrared
Brackett	$n_2 \to 4$	Infrared
Pfund	$n_2 \to 5$	Infrared

Visible region: Balmer series.

4. Limitations of Rutherford’s model

Could not explain the stability of atom.
Could not explain line spectra of elements.
Could not explain chemical behavior of atoms.

5. Postulates of Rutherford’s model

Atom has a small, dense, positively charged nucleus.
Electrons revolve around the nucleus in circular orbits.
Most of the atom is empty space.

6. Black body radiation

It is the radiation emitted by a perfect black body — an object that absorbs and emits all wavelengths of radiation.

7. Planck’s quantum hypothesis

Energy is not continuous but emitted or absorbed in small packets called quanta.

$E = h\nu$

where $E$ = energy, $h$ = Planck’s constant, $ν$ = frequency.

8. Photoelectric effect

When light of certain frequency falls on a metal surface, electrons are ejected from it.

9. Diffraction and Interference

Diffraction: Bending of light waves around obstacles or through small openings.
Interference: Overlapping of two waves to form a pattern of bright and dark bands.

12. Lyman series

It is a series of lines in the hydrogen spectrum when electrons fall to the n = 1 level from higher levels (n₂ = 2, 3, 4...).
Region: Ultraviolet

13. de Broglie hypothesis

All moving particles have wave nature.

$\lambda = \frac{h}{mv}$

Relation:

$\lambda \propto \frac{1}{m}$ (inversely with mass)
$\lambda \propto \frac{1}{v}$ (inversely with velocity)

17. Wave-particle duality

Matter and radiation show both wave-like and particle-like behavior (e.g., electrons behave as waves and particles).

18. Modern periodic law

“The physical and chemical properties of elements are the periodic functions of their atomic numbers.”
Explanation: Elements are arranged by increasing atomic number, showing repeating properties.

19. Inner transition elements

These are lanthanides and actinides.
They are called so because electrons enter the inner f-orbital.

20. Cl vs Cl⁻

Cl⁻ is larger because it gains an electron → more repulsion → larger size.

21. Be electron affinity ≈ 0

Beryllium has a stable filled 2s² configuration, so it does not easily gain an electron.

22. Fluorine has lower electron affinity than chlorine

Due to its small size → strong electron-electron repulsion → less energy released.

23. Modern periodic law

Properties of elements are periodic functions of their atomic numbers.

24. Na vs Na⁺

Na⁺ is smaller because it loses one electron → fewer shells → stronger attraction.

25. Cation smaller than atom

Cation loses electrons → fewer shells → nucleus pulls remaining electrons closer.

26. Anion larger than atom

Anion gains electrons → more repulsion → larger electron cloud.

27. N³⁻, O²⁻, F⁻ size comparison

Size ↓ with ↑ nuclear charge.
So: N³⁻ > O²⁻ > F⁻

29. Ionic radii of Na⁺, Mg²⁺, Al³⁺

All have same electrons (isoelectronic), but charge ↑ → size ↓
So: Na⁺ > Mg²⁺ > Al³⁺

30. Electron gain enthalpy

Energy released when an electron is added to a neutral gaseous atom.

31. Electronegativity

Tendency of an atom to attract shared electrons towards itself in a chemical bond.

32. Ionisation energy

Minimum energy required to remove one electron from an isolated gaseous atom.

33. Ionisation energy trend

Increases across a period (left to right) due to increase in nuclear charge.

34. More energy needed for M⁺ → M²⁺

Because the second electron is removed from a positive ion, which has stronger nuclear attraction.

🧪 Chapter: The Periodic Table and Periodic Trends

🌍 1. The Periodic Table

The modern periodic table is based on Modern Periodic Law:

“The physical and chemical properties of elements are the periodic functions of their atomic numbers.”

Structure of the Periodic Table

Horizontal rows → Periods
Vertical columns → Groups

📘 2. Periods and Groups

Periods

There are 7 periods in the modern periodic table.
1st period → 2 elements (H, He)
2nd & 3rd periods → 8 elements each
4th & 5th periods → 18 elements each
6th period → 32 elements (includes lanthanides)
7th period → incomplete (includes actinides)

Groups

There are 18 groups.
Elements in the same group have similar chemical properties due to same number of valence electrons.

⚛️ 3. Classification of Elements (Blocks)

Based on the type of orbital that receives the last electron:

Block	Last electron enters	Examples	Position
s-block	s-orbital	H, Li, Na, K	Groups 1 & 2
p-block	p-orbital	B, C, N, O, F, Ne	Groups 13–18
d-block	d-orbital	Fe, Cu, Zn	Groups 3–12
f-block	f-orbital	Lanthanides & Actinides	Separate at bottom

⚙️ 4. Modern Concept of Periodicity

Periodicity in properties is due to the repetition of similar electronic configurations at regular intervals.

📏 5. Periodic Trends

(a) Atomic Radius

Definition: Distance from the nucleus to the outermost electron.

Trends:

Across a period: ↓ Decreases
→ due to increase in nuclear charge pulling electrons closer.
Down a group: ↑ Increases
→ due to addition of new shells.

(b) Ionic Radius

Definition: Radius of an ion.

Trends:

Cations → smaller than parent atoms (loss of electron).
Anions → larger than parent atoms (gain of electron).
Across a period: decreases for cations and anions separately.
Down a group: increases.

(c) Covalent Radius

Definition: Half the distance between two atoms joined by a covalent bond.

Trends:

Across a period: decreases (↑ nuclear charge).
Down a group: increases (more shells).

(d) Ionization Energy / Ionization Potential

Definition: Minimum energy required to remove one electron from a gaseous atom.

Trends:

Across a period: increases (↑ nuclear charge, ↓ atomic size).
Down a group: decreases (↑ distance from nucleus, ↑ shielding).

(e) Electron Gain Enthalpy

Definition: Energy change when an electron is added to a gaseous atom.

Trends:

Across a period: becomes more negative (↑ attraction for electron).
Down a group: becomes less negative (↓ attraction due to large size).

Note: Fluorine has lower value than chlorine due to high electron repulsion in small size.

(f) Electronegativity

Definition: Tendency of an atom to attract shared electrons in a chemical bond.

Trends:

Across a period: increases (↑ nuclear charge).
Down a group: decreases (↑ atomic size).

🔰 6. Effective Nuclear Charge (Zeff)

Definition: The net positive charge experienced by valence electrons after screening by inner electrons.

$Z_{\text{eff}} = Z - S$

where
$Z$ = atomic number (nuclear charge),
$S$ = screening constant.

Trend:

Across a period: increases (electrons added to same shell, poor shielding).
Down a group: decreases (more inner shells → more shielding).

🧭 7. Screening Effect (Shielding Effect)

Definition: Reduction in the nuclear attraction on outer electrons due to the presence of inner shell electrons.

Trend:

Increases down a group (more inner shells).
Remains almost constant across a period.

⚡ 8. Summary of Periodic Trends

Property	Across a Period	Down a Group
Atomic Radius	↓ Decreases	↑ Increases
Ionic Radius	↓ Decreases	↑ Increases
Covalent Radius	↓ Decreases	↑ Increases
Ionization Energy	↑ Increases	↓ Decreases
Electron Gain Enthalpy	More Negative	Less Negative
Electronegativity	↑ Increases	↓ Decreases
Effective Nuclear Charge	↑ Increases	↓ Decreases
Screening Effect	≈ Constant	↑ Increases

🧠 Key Points to Remember

Periodic properties repeat due to similar outer electronic configuration.
s, p, d, and f-block classification is based on the orbital being filled.
Atomic size and metallic nature increase down a group, non-metallic nature increases across a period.
Ionization energy, electron affinity, and electronegativity are closely related.

🧪 Chapter: Chemical Bonding

⚛️ 1. Types of Chemical Bonds

Atoms combine to achieve a stable electronic configuration (like noble gases).
There are three main types of chemical bonds:

(a) Ionic Bond (Electrovalent bond)

Formed by complete transfer of electrons from one atom to another.
Between metal and non-metal.
One atom loses electrons → cation, another gains → anion.
Strong electrostatic attraction between ions.

Example:
NaCl → Na⁺ + Cl⁻

Properties:

High melting and boiling points.
Soluble in water.
Conduct electricity in molten or aqueous state.

(b) Covalent Bond

Formed by sharing of electrons between atoms.
Between non-metals.
Each shared pair = one covalent bond.

Example:
H₂ (H–H), O₂ (O=O), Cl₂ (Cl–Cl)

Properties:

Low melting and boiling points.
Poor conductors of electricity.
Exist as gases or liquids mostly.

(c) Coordinate (Dative) Bond

Formed when both shared electrons come from one atom.
Represented by an arrow (→).

Example:
NH₃ + H⁺ → NH₄⁺ (N donates a lone pair to H⁺)
→ is the coordinate bond.

💎 Lattice Energy

Definition: Energy released when 1 mole of an ionic solid is formed from its gaseous ions.

\text{Na}^+ (g) + \text{Cl}^- (g) \rightarrow \text{NaCl (s)} + \text{Lattice energy}

Importance:

Higher lattice energy → stronger ionic bond → higher melting point.

🔄 2. Orbital Overlapping & Hybridization

Orbital Overlap Concept

A covalent bond is formed by the overlapping of half-filled atomic orbitals, resulting in the pairing of electrons with opposite spins.

σ (sigma) bond: Formed by head-on overlap.
π (pi) bond: Formed by sidewise overlap.

🧬 Hybridization

Definition: Mixing of atomic orbitals of similar energy to form new equivalent orbitals called hybrid orbitals.

Types of Hybridization

Type	Orbitals mixed	Example	Shape	Bond Angle
sp	1 s + 1 p	BeCl₂	Linear	180°
sp²	1 s + 2 p	BF₃	Trigonal planar	120°
sp³	1 s + 3 p	CH₄	Tetrahedral	109.5°
sp³d	1 s + 3 p + 1 d	PCl₅	Trigonal bipyramidal	120°, 90°
sp³d²	1 s + 3 p + 2 d	SF₆	Octahedral	90°
d²sp³	2 d + 1 s + 3 p	[Co(NH₃)₆]³⁺	Octahedral	90°
dsp²	1 d + 1 s + 2 p	[Ni(CN)₄]²⁻	Square planar	90°

🧪 Shapes of Some Organic Molecules

Molecule	Hybridization	Shape
Methane (CH₄)	sp³	Tetrahedral
Ethane (C₂H₆)	sp³	Tetrahedral around each C
Ethylene (C₂H₄)	sp²	Trigonal planar around each C
Acetylene (C₂H₂)	sp	Linear

🔺 VSEPR Theory (Valence Shell Electron Pair Repulsion Theory)

Main Idea:
The shape of a molecule depends on repulsion between electron pairs (bonding and lone pairs) in the valence shell.

Rules:

Electron pairs around the central atom repel each other.
They arrange themselves to minimize repulsion.
Lone pair–lone pair > lone pair–bond pair > bond pair–bond pair repulsion.

Shapes of Molecules (According to VSEPR Theory)

Molecule	Central Atom	Type	Shape	Bond Angle
BeF₂	Be	sp	Linear	180°
BF₃	B	sp²	Trigonal planar	120°
NH₃	N	sp³ (1 lone pair)	Pyramidal	107°
H₂O	O	sp³ (2 lone pairs)	Bent / Angular	104.5°
NH₄⁺	N	sp³	Tetrahedral	109.5°
PCl₅	P	sp³d	Trigonal bipyramidal	90°, 120°
SF₆	S	sp³d²	Octahedral	90°
ClF₃	Cl	sp³d	T-shaped	<90°

⚡ 3. Valence Bond Theory (VBT)

Main idea:
A covalent bond is formed when two half-filled atomic orbitals overlap to form a shared electron pair.

Examples:

(a) Formation of H₂ molecule:

Each H atom has 1s¹.
Overlap of two 1s orbitals → σ bond → H–H.

(b) Formation of N₂ molecule:

N (1s² 2s² 2p³) → each N forms 3 bonds.
One σ bond (head-on) and two π bonds (sideways).
→ Total one σ + two π bonds.

(c) Formation of CH₄ (Methane):

C (2s² 2p²) → undergoes sp³ hybridization → 4 equivalent orbitals.
Each overlaps with 1s of H → 4 σ bonds (C–H).

(d) Formation of CH₂=CH₂ (Ethylene):

Each C → sp² hybridized.
3 σ bonds per C (2 C–H + 1 C–C).
Unhybridized p orbitals form 1 π bond.
→ 1 σ + 1 π bond between C atoms.

🌫️ 4. Molecular Orbital Theory (MOT)

Main idea:
Atomic orbitals combine to form molecular orbitals that are spread over the whole molecule.

Bonding orbital → lower energy
Antibonding orbital → higher energy

Bond order = ½ (Nb – Na)
where Nb = no. of electrons in bonding MOs
Na = no. of electrons in antibonding MOs.

Formation of N₂

Configuration: (σ1s)² (σ1s)² (σ2s)² (σ2s)² (π2pₓ)² (π2p_y)² (σ2p_z)²
Bond order = 3 → Triple bond
→ N₂ is very stable.

Formation of O₂

Configuration: (σ1s)² (σ1s)² (σ2s)² (σ2s)² (σ2p_z)² (π2pₓ)² (π2p_y)² (π2pₓ)¹ (π2p_y)¹
Bond order = 2 → Double bond
→ O₂ is paramagnetic (due to 2 unpaired electrons).

🧠 Summary Table

Concept	Key Idea	Example / Shape
Ionic bond	Transfer of electrons	NaCl
Covalent bond	Sharing of electrons	H₂, Cl₂
Coordinate bond	Shared pair from one atom	NH₄⁺
Hybridization	Mixing of orbitals	sp³ in CH₄
VSEPR	Shape based on repulsion	NH₃ (pyramidal)
VBT	Overlapping orbitals	H₂, N₂, CH₄
MOT	Combination of atomic orbitals	N₂ (bond order 3), O₂ (bond order 2)

Chemistry Atomic Structure and Periodicity Notes

1. Rydberg formula

2. de Broglie equation

3. Spectral series of Hydrogen

4. Limitations of Rutherford’s model

5. Postulates of Rutherford’s model

6. Black body radiation

7. Planck’s quantum hypothesis

8. Photoelectric effect

9. Diffraction and Interference

12. Lyman series

13. de Broglie hypothesis

17. Wave-particle duality

18. Modern periodic law

19. Inner transition elements

20. Cl vs Cl⁻

21. Be electron affinity ≈ 0

22. Fluorine has lower electron affinity than chlorine

23. Modern periodic law

24. Na vs Na⁺

25. Cation smaller than atom

26. Anion larger than atom

27. N³⁻, O²⁻, F⁻ size comparison

29. Ionic radii of Na⁺, Mg²⁺, Al³⁺

30. Electron gain enthalpy

31. Electronegativity

32. Ionisation energy

33. Ionisation energy trend

34. More energy needed for M⁺ → M²⁺

🧪 Chapter: The Periodic Table and Periodic Trends

🌍 1. The Periodic Table

Structure of the Periodic Table

📘 2. Periods and Groups

Periods

Groups

⚛️ 3. Classification of Elements (Blocks)

⚙️ 4. Modern Concept of Periodicity

📏 5. Periodic Trends

(a) Atomic Radius

(b) Ionic Radius

(c) Covalent Radius

(d) Ionization Energy / Ionization Potential

(e) Electron Gain Enthalpy

(f) Electronegativity

🔰 6. Effective Nuclear Charge (Zeff)

🧭 7. Screening Effect (Shielding Effect)

⚡ 8. Summary of Periodic Trends

🧠 Key Points to Remember

🧪 Chapter: Chemical Bonding

⚛️ 1. Types of Chemical Bonds

(a) Ionic Bond (Electrovalent bond)

(b) Covalent Bond

(c) Coordinate (Dative) Bond

💎 Lattice Energy

🔄 2. Orbital Overlapping & Hybridization

Orbital Overlap Concept

🧬 Hybridization

Types of Hybridization

🧪 Shapes of Some Organic Molecules

🔺 VSEPR Theory (Valence Shell Electron Pair Repulsion Theory)

Shapes of Molecules (According to VSEPR Theory)

⚡ 3. Valence Bond Theory (VBT)

Examples:

🌫️ 4. Molecular Orbital Theory (MOT)

Formation of N₂

Formation of O₂

🧠 Summary Table

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