Chapter 9: Electrons in Atoms and the Periodic Table

Maximum Number of Electrons in Energy Levels

The arrangement of electrons in atoms is governed by quantum mechanics. Each principal energy level (n) can hold a maximum number of electrons, determined by the formula:

• Formula:

• Example: For n = 2, maximum electrons =

Wavelength and Frequency Calculations

Light behaves as both a wave and a particle. The relationship between the speed of light (c), wavelength (\(\lambda\)), and frequency (\(\nu\)) is given by:

• Key Equation:

• Where: c = speed of light (3.00 × 108 m/s), \(\lambda\) = wavelength (m), \(\nu\) = frequency (Hz)

• Example: If \(\lambda = 500 \text{ nm}\), then

Key Vocabulary

• Electron configuration: The arrangement of electrons in an atom's orbitals.

• Pauli exclusion principle: No two electrons in an atom can have the same set of four quantum numbers.

• Aufbau principle: Electrons fill the lowest energy orbitals first.

• Hund’s rule: Every orbital in a subshell is singly occupied before any orbital is doubly occupied.

• Photons: Particles of light, each carrying a quantum of energy.

• Electromagnetic spectrum: The range of all types of electromagnetic radiation.

• Atomic emission spectrum: The set of frequencies of light emitted by atoms of an element.

• Ground state: The lowest energy state of an atom.

• Excited state: Any energy state higher than the ground state.

• Quantum mechanical model: The modern description of electrons in atoms, using probabilities.

• Bohr model: Early model with electrons in fixed orbits around the nucleus.

• Wavelength (\(\lambda\)): Distance between two consecutive peaks of a wave.

• Frequency (\(\nu\)): Number of wave cycles per second.

• Orbitals: Regions in an atom where there is a high probability of finding electrons.

Relative Wavelength, Energy, and Frequency of Light

Different types of electromagnetic radiation have different wavelengths, frequencies, and energies:

• Shorter wavelength → higher frequency → higher energy

• Order (increasing energy): Radio < Ionizing (UV, X-ray, Gamma)

• Example: Gamma rays have shorter wavelengths and higher energy than visible light.

Electron Configurations and Orbital Diagrams

Electron configurations show the distribution of electrons among orbitals. Orbital diagrams use arrows to represent electron spins in each orbital.

• Example: Oxygen: 1s2 2s2 2p4

Valence Electrons

Valence electrons are the outermost electrons involved in chemical bonding.

• Definition: Electrons in the highest principal energy level of an atom.

• Example: Carbon has 4 valence electrons (2s22p2).

Calculating Change in Energy

The energy change associated with electron transitions can be calculated using:

• Equation:

• Where: h = Planck’s constant (6.626 × 10-34 J·s), c = speed of light, \(\lambda\) = wavelength

• Example: If \(\lambda = 400 \text{ nm}\),

Periodic Trends: Ionization Energy, Atomic Size, Electronegativity

Elements show predictable trends in properties across periods and groups:

• Ionization energy: Increases across a period, decreases down a group.

• Atomic size: Decreases across a period, increases down a group.

• Electronegativity: Increases across a period, decreases down a group.

• Explanation: These trends are due to changes in nuclear charge and electron shielding.

Chapter 10: Chemical Bonding

Lewis Dot Structures for Covalent Compounds

Lewis dot structures represent valence electrons as dots around chemical symbols, showing bonding and lone pairs.

• Steps: Count valence electrons, arrange atoms, distribute electrons to satisfy the octet rule.

• Example: H2O: O in center, two H atoms bonded, two lone pairs on O.

Exceptions to Lewis Dot Structures

Some molecules do not follow the octet rule:

• Incomplete octet: e.g., BeCl2, BF3

• Expanded octet: e.g., SF6, PCl5

• Odd-electron species: e.g., NO

The Octet Rule

Atoms tend to gain, lose, or share electrons to achieve eight electrons in their valence shell (octet), similar to noble gases.

• Exceptions: Hydrogen (2 electrons), Helium (2 electrons), elements in period 3 and beyond can have more than 8.

Resonance Structures

Some molecules cannot be represented by a single Lewis structure. Resonance structures are multiple valid Lewis structures for the same molecule, differing only in the placement of electrons.

• Example: Ozone (O3) has two resonance structures with different double bond locations.

VSEPR Theory: Molecular Shape and Bond Angles

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts the 3D shape of molecules based on repulsion between electron pairs.

• SN # (Steric Number): Number of atoms bonded to central atom + number of lone pairs on central atom.

• Common shapes: Linear (180°), Trigonal planar (120°), Tetrahedral (109.5°), Trigonal bipyramidal, Octahedral.

• Example: CH4 is tetrahedral, H2O is bent.

Electronegativity and Bond Classification

Electronegativity is the ability of an atom to attract electrons in a bond. Bonds are classified based on the difference in electronegativity:

• Example: H–Cl is polar covalent; NaCl is ionic.

Polarity of Molecules

Molecules are polar if they have polar bonds arranged asymmetrically, resulting in a net dipole moment. Vectors can be drawn to show the direction of bond polarity (toward the more electronegative atom).

• Example: CO2 has polar bonds but is nonpolar overall due to linear symmetry; H2O is polar.

For more on molecular polarity, see: Supplemental notes on polar vs nonpolar molecules