General Chemistry: Atomic Structure, Bonding, and Periodic Trends Study Guide

Models of the Atom

Historical Development of Atomic Models

The understanding of atomic structure has evolved through a series of experiments and theoretical models. Key discoveries include the identification of subatomic particles and the arrangement of electrons within atoms.

• Cathode Ray Experiments: Demonstrated the existence of electrons as negatively charged particles within atoms.

• Plum Pudding Model (J.J. Thomson): Proposed that electrons were embedded in a positively charged 'pudding.'

• Rutherford Gold Foil Experiment: Showed that atoms have a small, dense, positively charged nucleus, with electrons occupying the surrounding space.

• Bohr Model: Electrons travel in quantized orbits around the nucleus, with discrete energy levels.

Example: The Rutherford experiment overturned the plum pudding model by demonstrating that most of the atom is empty space and that the positive charge is concentrated in the nucleus.

Electromagnetic Radiation

Properties and Energy of Electromagnetic Waves

Electromagnetic radiation consists of waves characterized by their wavelength (λ), frequency (ν), and energy (E). The energy of a photon is related to its frequency by Planck's equation:

• Wavelength (λ): The distance between successive peaks of a wave.

• Frequency (ν): The number of wave cycles per second (Hz).

• Energy (E): The energy of a photon is given by:

$E = h\nu$

where $h$ is Planck's constant.

• Relationship between wavelength and frequency:

$c = \lambda \nu$

where $c$ is the speed of light.

Photoelectric Effect: Demonstrates that light can behave as particles (photons) and that energy is quantized.

Bohr Atom

Quantized Energy Levels and Spectra

The Bohr model explains the discrete emission and absorption spectra of hydrogen-like atoms by proposing that electrons occupy specific energy levels.

• Ground State: The lowest energy level of an atom.

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

• Energy Transitions: Electrons absorb or emit energy when moving between levels:

$\Delta E = E_{final} - E_{initial} = h\nu$

Example: When an electron in hydrogen drops from a higher to a lower energy level, it emits a photon with energy equal to the difference between the two levels.

Modern Atomic Theory (Wave Mechanics)

Wave-Particle Duality and Quantum Mechanics

Modern atomic theory incorporates the wave nature of electrons, described by the de Broglie equation and the Schrödinger equation.

• de Broglie Equation: Relates the wavelength of a particle to its momentum:

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

• Heisenberg Uncertainty Principle: It is impossible to simultaneously know the exact position and momentum of an electron.

• Quantum Numbers: Describe the properties of atomic orbitals and the electrons in them.

Example: The velocity of a baseball with a given mass and de Broglie wavelength can be calculated using the de Broglie equation.

Solutions of the Schrödinger Equation

Quantum Numbers and Atomic Orbitals

The Schrödinger equation provides solutions that describe the allowed energy states of electrons in atoms, characterized by quantum numbers:

• Principal Quantum Number (n): Indicates the energy level and size of the orbital.

• Angular Momentum Quantum Number (l): Defines the shape of the orbital (s, p, d, f).

• Magnetic Quantum Number (ml): Specifies the orientation of the orbital.

• Spin Quantum Number (ms): Indicates the spin direction of the electron (+1/2 or -1/2).

Atomic Orbitals: Regions in space where the probability of finding an electron is high. Each type of orbital (s, p, d, f) has a characteristic shape and number of orientations.

• Node: A region where the probability of finding an electron is zero.

Example: The dxy orbital has two nodal planes and a characteristic cloverleaf shape.

Electron Configurations

Rules and Principles

Electron configurations describe the arrangement of electrons in an atom's orbitals, following specific rules:

• Aufbau Principle: Electrons fill orbitals starting with the lowest energy first.

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers; each orbital can hold a maximum of two electrons with opposite spins.

• Hund's Rule: Electrons occupy degenerate orbitals singly before pairing up.

Example: The electron configuration of Zn (Zinc) is $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10}$.

Lewis Dot Structure and Chemical Bonding

Valence Electrons and Bonding

Lewis dot structures represent the valence electrons of atoms and are used to predict bonding in molecules.

• Valence Electrons: Electrons in the outermost shell, involved in chemical bonding.

• Bonding Pairs: Shared pairs of electrons between atoms.

• Lone Pairs: Non-bonding pairs of electrons on an atom.

• Resonance Structures: Multiple valid Lewis structures for a molecule, differing only in the placement of electrons.

Example: The Lewis structure for $SF_6$ shows six bonding pairs and no lone pairs on the central sulfur atom.

Molecular Orbital Theory and Chemical Bonding

Bonding and Antibonding Orbitals

Molecular orbital (MO) theory describes the combination of atomic orbitals to form molecular orbitals, which can be bonding or antibonding.

• Bond Order: Indicates the strength and stability of a bond:

$\text{Bond Order} = \frac{1}{2} (\text{number of bonding electrons} - \text{number of antibonding electrons})$

• Paramagnetic: Molecules with unpaired electrons, attracted to magnetic fields.

• Diamagnetic: Molecules with all electrons paired, weakly repelled by magnetic fields.

Example: $O_2$ is paramagnetic due to two unpaired electrons in its molecular orbital configuration.

Periodic Trends

Trends in the Periodic Table

Elements in the periodic table exhibit predictable trends in their physical and chemical properties:

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

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

• Electron Affinity: Generally becomes more negative across a period.

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

Example: Fluorine has the highest electronegativity and electron affinity in the periodic table.

Dipole Moment and Polar Bonds

Bond Polarity and Molecular Polarity

The polarity of a bond depends on the difference in electronegativity between the two atoms involved. A molecule's dipole moment is a measure of its overall polarity.

• Polar Covalent Bond: Electrons are shared unequally between atoms with different electronegativities.

• Nonpolar Covalent Bond: Electrons are shared equally between atoms with similar electronegativities.

Example: The H–F bond is highly polar due to the large difference in electronegativity between hydrogen and fluorine.

Sigma (σ) and Pi (π) Bonding in Lewis Structures

Types of Covalent Bonds

Covalent bonds can be classified as sigma (σ) or pi (π) bonds based on the type of orbital overlap:

• Sigma (σ) Bond: Formed by head-on overlap of orbitals; present in all single bonds.

• Pi (π) Bond: Formed by side-on overlap of p orbitals; present in double and triple bonds in addition to a sigma bond.

Example: In ethylene (C2H4), the double bond consists of one sigma and one pi bond.

Table: Comparison of Atomic Models

Model	Main Features	Key Experiment
Plum Pudding Model	Electrons embedded in a positively charged sphere	Cathode Ray Tube
Rutherford Model	Dense nucleus, electrons orbiting nucleus, mostly empty space	Gold Foil Experiment
Bohr Model	Electrons in quantized orbits, discrete energy levels	Hydrogen Emission Spectrum
Quantum Mechanical Model	Electrons as waves, probability distributions (orbitals)	Schrödinger Equation

Table: Quantum Numbers and Their Significance

Quantum Number	Symbol	Possible Values	Significance
Principal	n	1, 2, 3, ...	Energy level, size of orbital
Angular Momentum	l	0 to n-1	Shape of orbital (s, p, d, f)
Magnetic	ml	-l to +l	Orientation of orbital
Spin	ms	+1/2, -1/2	Spin direction of electron

Additional info: Some explanations and examples have been expanded for clarity and completeness, following standard general chemistry curriculum.