BackExam 4 Review: Quantum Mechanics, Electron Configuration, and Chemical Bonding
Study Guide - Smart Notes
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Chapter 8: Electromagnetic Waves and Quantum Numbers
Electromagnetic (EM) Waves
The electromagnetic spectrum encompasses all types of electromagnetic radiation, which differ in wavelength and frequency. Understanding the spectrum is essential for interpreting the energy and behavior of light and other EM waves.
EM Spectrum Diagram: The spectrum ranges from low-energy radio waves to high-energy gamma rays. Visible light occupies a small portion, with wavelengths from approximately 400 nm (violet, highest energy) to 700 nm (red, lowest energy).
Speed of Light: All EM waves travel at the speed of light in a vacuum, given by m/s.
Key Equations:
Relationship between wavelength () and frequency ():
Energy of a photon:
Energy in terms of wavelength:
Planck's constant: Js
Units: Wavelength in meters (m), frequency in hertz (Hz or s-1), energy in joules (J).
Quantum Numbers and Atomic Orbitals
Quantum numbers describe the properties of atomic orbitals and the electrons within them. Each electron in an atom is uniquely identified by a set of 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): Describes the shape of the orbital. Values range from 0 to (n-1): - l = 0: s orbital - l = 1: p orbital - l = 2: d orbital - l = 3: f orbital
Magnetic Quantum Number (ml): Specifies the orientation of the orbital in space. Values: -l to +l.
Spin Quantum Number (ms): Indicates the spin of the electron. Values: +1/2 or -1/2.
Selection Rules:
n: 1, 2, 3, ...
l: 0, 1, ..., 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 = 3.
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 (Group 18) in brackets to simplify notation, e.g., [Ne] 3s23p4 for sulfur.
Example: Copper: [Ar] 4s13d10
Periodic Trends
Periodic trends describe how properties of elements change across periods and groups in the periodic table.
Electronegativity: Tendency of an atom to attract electrons in a bond. Increases across a period (left to right), decreases down a group. Fluorine is the most electronegative element.
Atomic Size (Radius): Increases down a group, decreases across a period.
Ionization Energy: Energy required to remove an electron from an atom. 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-? F- is larger due to greater electron-electron repulsion.
Chapter 10: Chemical Bonding and Molecular Geometry
Types of Bonds
Chemical bonds form between atoms to achieve stability. 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: Even or nearly even sharing (electronegativity difference 0.0–0.4)
Polar: Unequal sharing (difference 0.4–1.9)
Ionic: Difference ≥ 2.0
Radical: A molecule with an odd number of electrons.
Bond Strength and Order
Single Bond: One sigma (σ) bond; weakest and longest.
Double Bond: One sigma and one pi (π) bond.
Triple Bond: One sigma and two pi bonds; strongest and shortest.
Sigma bonds are stronger than pi bonds.
Hybridization
Hybridization explains the mixing of atomic orbitals to form new, equivalent hybrid orbitals for bonding.
Number of Hybrid Orbitals: Equals the number of sigma bonds plus lone pairs on the central atom.
Examples: sp2 hybridization yields 3 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-Pair Geometry: Determined by the number of electron dense areas (bonds and lone pairs).
Molecular Geometry: Determined by the arrangement of atoms (ignoring lone pairs).
Electron Dense Areas | Electron-Pair Geometry | Molecular Geometry (No Lone Pairs) |
|---|---|---|
2 | Linear | Linear |
3 | Trigonal Planar | Trigonal Planar |
4 | Tetrahedral | Tetrahedral |
5 | Trigonal Bipyramidal | Trigonal Bipyramidal |
6 | Octahedral | Octahedral |
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. Formal charge helps identify the most stable Lewis structure.
Octet Rule: Atoms (except H, He, B, etc.) prefer 8 valence electrons.
Expanded Octet: Elements in period 3 or higher can have more than 8 electrons.
Formal Charge: Calculated as:
Negative formal charge is often placed on the most electronegative 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 and molecular geometry of H2O: Electron: tetrahedral; Molecular: bent
