Chapter 8: Electromagnetic Waves and Quantum Numbers

Electromagnetic (EM) Waves

Electromagnetic waves are oscillating electric and magnetic fields that travel through space at the speed of light. They are characterized by their wavelength, frequency, and energy, and are organized in the electromagnetic spectrum.

• Speed of Light (c): m/s

• Wavelength (\(\lambda\)): The distance between two consecutive peaks of a wave, measured in meters (m).

• Frequency (\(\nu\)): The number of wave cycles per second, measured in hertz (Hz or s-1).

• Relationship:

• Energy of a Photon: or , where J·s (Planck's constant).

• Visible Light: Wavelength range is approximately 400 nm (violet, highest energy) to 700 nm (red, lowest energy).

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons within them. There are four quantum numbers:

• Principal Quantum Number (n): Indicates the size and energy level of the orbital. Possible values: 1, 2, 3, ...

• Azimuthal Quantum Number (l): Indicates the shape of the orbital. Possible values: 0 to n-1. (l = 0: s, l = 1: p, l = 2: d, l = 3: f)

• Magnetic Quantum Number (ml): Indicates the orientation of the orbital. Possible values: -l to +l.

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

Selection Rules:

• n: 1, 2, 3, ...

• l: 0, 1, 2, ..., n-1

• ml: -l, ..., 0, ..., +l

• ms: ±1/2

Example Problems

• Red light (676 nm): Find frequency and energy.

  • Frequency:

  • Energy:

• Microwave (2.45 GHz): Find energy of a single photon.

• Light wave (2 pm): Find energy of the photon.

• Electron in n=2: Possible l values: 0, 1. For p orbital (l=1), ml = -1, 0, 1.

• Minimum n for f orbital: n = 4 (since l = 3 for f, and l < n).

Chapter 9: Electron Configurations and Periodic Trends

Electron Configurations

Electron configuration describes the arrangement of electrons in an atom's orbitals. The Aufbau principle, Pauli exclusion principle, and Hund's rule guide the filling order.

• Noble Gas Configuration: Use the previous noble gas in brackets to simplify notation (e.g., [Ne] 3s23p4 for sulfur).

• Example: Copper: [Ar] 4s13d10

Periodic Trends

Periodic trends describe how certain properties of elements change across periods and groups in the periodic table.

• Electronegativity: Tendency of an atom to attract electrons. Increases across a period, decreases down a group. Fluorine is the most electronegative element.

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

• Ionization Energy: Energy required to remove an electron. Increases across a period, decreases down a group.

Example Problems

• Electron configuration for Copper: [Ar] 4s13d10

• Noble gas configuration for Sulfur: [Ne] 3s23p4

• Most electronegative element: Fluorine (F)

• Which is larger: Na+ or F-? Answer: F-

Chapter 10: Chemical Bonding and Molecular Geometry

Types of Bonds

Chemical bonds are the forces holding atoms together in compounds. The main types are covalent, ionic, and metallic bonds.

• Covalent Bonds: Sharing of electrons between two nonmetals.

• Ionic Bonds: Transfer of electrons from a metal to a nonmetal.

• Metallic Bonds: Delocalized 'sea' of electrons among metal atoms.

Covalent Bond Polarity:

• Nonpolar: Electronegativity difference 0.0–0.4

• Polar: Electronegativity difference 0.4–1.9

• Ionic: Electronegativity difference 2.0+

Bond Strength and Order:

• Single bond: weakest, longest (1 sigma bond)

• Double bond: intermediate (1 sigma, 1 pi bond)

• Triple bond: strongest, shortest (1 sigma, 2 pi bonds)

• Sigma (σ) bonds are stronger than pi (π) bonds.

Hybridization

Hybridization describes the mixing of atomic orbitals to form new hybrid orbitals for bonding. The number of hybrid orbitals equals the number of sigma bonds plus lone pairs on the central atom.

• sp: 2 hybrid orbitals

• sp2: 3 hybrid orbitals

• sp3: 4 hybrid orbitals

VSEPR Theory and Molecular Geometry

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts the shapes of molecules based on electron pair repulsion around the central atom.

• Electron geometry considers all electron pairs (bonding and lone pairs).

• Molecular geometry considers only the arrangement of atoms.

Lewis Structures and Formal Charge

Lewis structures represent the arrangement of valence electrons in molecules. The octet rule states that atoms tend to have eight electrons in their valence shell. Expanded octets are possible for elements in period 3 or higher.

• Formal Charge: Calculated as: Formal charge = (Valence electrons) - (Nonbonding electrons) - (Bonding electrons/2)

• Negative formal charge indicates extra electrons; positive indicates fewer electrons than the neutral atom.

Example Problems

• Molecular geometry of CH2Cl2: Tetrahedral

• Molecular geometry of NH3: Trigonal pyramidal

• Formal charge of N in NH4+: +1; Hybridization: sp3; Geometry: Tetrahedral

• Formal charge of C in CHOO-: 0; Negative O is sp2 and trigonal planar, neutral O is sp3 and tetrahedral

• Hybridization of C in CH4: sp3

• Electron geometry of H2O: Tetrahedral; Molecular geometry: Bent