Chemistry Atomic Structure and Periodicity Notes

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.

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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.

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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.

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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.

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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.

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6. Black body radiation

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

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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.

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8. Photoelectric effect

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

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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.

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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

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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)

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17. Wave-particle duality

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

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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.

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19. Inner transition elements

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

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20. Cl vs Cl⁻

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

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21. Be electron affinity ≈ 0

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

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22. Fluorine has lower electron affinity than chlorine

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

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23. Modern periodic law

Properties of elements are periodic functions of their atomic numbers.

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24. Na vs Na⁺

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

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25. Cation smaller than atom

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

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26. Anion larger than atom

Anion gains electrons → more repulsion → larger electron cloud.

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27. N³⁻, O²⁻, F⁻ size comparison

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

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29. Ionic radii of Na⁺, Mg²⁺, Al³⁺

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

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30. Electron gain enthalpy

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

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31. Electronegativity

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

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32. Ionisation energy

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

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33. Ionisation energy trend

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

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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

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🌍 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

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📘 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.

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⚛️ 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

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⚙️ 4. Modern Concept of Periodicity

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

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📏 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.

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(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.

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(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).

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(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).

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(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.

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(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).

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🔰 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).

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🧭 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.

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⚡ 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

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🧠 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

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⚛️ 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.

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(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.

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(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.

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💎 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.

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🔄 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.

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🧬 Hybridization

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

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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°

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🧪 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

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🔺 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:

1. Electron pairs around the central atom repel each other.

2. They arrange themselves to minimize repulsion.

3. Lone pair–lone pair > lone pair–bond pair > bond pair–bond pair repulsion.

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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°

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⚡ 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.

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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.

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🌫️ 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.

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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.

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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).

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🧠 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)