Atomic Structure and Periodic Trends

Electron Configuration and Quantum Numbers

Understanding the arrangement of electrons in atoms is fundamental to predicting chemical behavior. Electrons occupy orbitals defined by quantum numbers, and their configuration determines atomic properties.

• Quantum Numbers: Four quantum numbers describe the state of an electron in an atom:

  • Principal quantum number (n): Indicates the energy level (shell).

  • Angular momentum quantum number (l): Defines the subshell (s, p, d, f).

  • Magnetic quantum number (ml): Specifies the orbital within a subshell.

  • Spin quantum number (ms): Indicates the electron's spin (+1/2 or -1/2).

• Allowed Sets: Not all combinations of quantum numbers are allowed. For example, for n = 2, l can be 0 or 1, but not 2.

• Example: The set (4, 2, -2, +1/2) is allowed, but (4, 4, 1, -1/2) is not, since l cannot equal n.

Periodic Trends

Elements show periodic variation in properties such as atomic radius, ionization energy, and electron affinity.

• Atomic Radius: Increases down a group and decreases across a period.

• Ionization Energy: The energy required to remove an electron from a gaseous atom. Increases across a period and decreases down a group.

• Electron Affinity: The energy change when an electron is added to a neutral atom. Generally becomes more negative across a period.

• Example: Cl has a smaller atomic radius and higher ionization energy than S.

Atomic and Molecular Orbitals

Atomic Orbitals and Electron Density

Atomic orbitals describe regions in space where electrons are likely to be found. The radial distribution function shows the probability of finding an electron at a certain distance from the nucleus.

• Types of Orbitals: s, p, d, f, each with characteristic shapes and energies.

• Radial Distribution: The 5s orbital has a greater radial extension than 4d or 4p orbitals.

Molecular Orbitals and Bond Order

Molecular orbital theory explains bonding by combining atomic orbitals to form molecular orbitals, which can be bonding or antibonding.

• Bond Order: Calculated as .

• Example: The bond order in B2 is 1.

Electromagnetic Radiation and Photons

Energy, Wavelength, and Frequency

Light exhibits both wave and particle properties. The energy of a photon is related to its frequency and wavelength.

• Energy of a Photon:

• Wavelength-Frequency Relationship:

• Example: A photon with frequency Hz has a wavelength of 127 nm.

Chemical Bonding and Molecular Geometry

Lewis Structures and Formal Charge

Lewis structures represent the arrangement of electrons in molecules. Formal charge helps identify the most stable resonance structure.

• Formal Charge:

• Example: In OCN-, the most stable resonance structure has -1 on O and 0 on N.

VSEPR Theory and Molecular Shape

The Valence Shell Electron Pair Repulsion (VSEPR) theory predicts molecular geometry based on electron pair repulsions.

• Linear: 2 electron groups, 180° bond angle (e.g., XeF2).

• Tetrahedral: 4 electron groups, 109.5° bond angle.

• Trigonal Planar: 3 electron groups, 120° bond angle.

• Example: The electron geometry around O in the given molecule is tetrahedral, with a bond angle of 110°.

Hybridization

Atomic orbitals mix to form hybrid orbitals, which explain molecular shapes and bond angles.

• sp: Linear geometry, 180° bond angle.

• sp2: Trigonal planar geometry, 120° bond angle.

• sp3: Tetrahedral geometry, 109.5° bond angle.

• Example: The carbon labeled x is sp2 hybridized, with a bond angle of 120°.

Sigma and Pi Bonds

Sigma (σ) and pi (π) bonds are types of covalent bonds formed by the overlap of atomic orbitals.

• Sigma Bond (σ): Formed by head-on overlap; all single bonds are sigma bonds.

• Pi Bond (π): Formed by side-on overlap; present in double and triple bonds.

• Example: The molecule shown has 18 sigma and 5 pi bonds.

Polarity and Dipole Moments

Molecular polarity depends on the shape and the difference in electronegativity between atoms.

• Permanent Dipole: Occurs when there is an uneven distribution of electron density.

• Example: Molecules I and III (from the given set) have permanent dipole moments.

Ionic Compounds and Lattice Energy

Ionic Radii and Lattice Energy

Ionic compounds are held together by electrostatic forces. The size of ions and their arrangement affect lattice energy and ionic distance.

• Ionic Radius: Cations are smaller, anions are larger than their parent atoms.

• Lattice Energy: Increases with higher charge and smaller ionic radius.

• Example: The order of ionic distance for K+, Rb+, F-, and Cl- is: RbF > KF > RbCl > KCl.

Ionization Energy and Electron Affinity

Successive Ionization Energies

Successive ionization energies increase as more electrons are removed, with a large jump when removing a core electron.

• Example: An atom with ionization energies 7.9, 16, 32, 44 MJ/mol is likely Mg.

Wave-Particle Duality and Mass of Photons

De Broglie Wavelength and Particle Velocity

Particles such as electrons and neutrons exhibit wave-like properties, described by the de Broglie equation.

• de Broglie Equation:

• Photon Mass: , where

• Example: The mass of a photon with frequency Hz is kg.

• Velocity Comparison: A neutron moves with a much lower velocity than an electron if they have the same wavelength.

Practice Table: Quantum Numbers

The following table summarizes allowed and disallowed sets of quantum numbers:

Additional info:

• Some context and explanations have been expanded for clarity and completeness.

• Examples and formulas have been added to reinforce key concepts.