Atomic Structure and Quantum Mechanics

CHEMISTRY: An Atoms-Focused Approach

Chapter 3: Atomic Structure

The Electromagnetic Spectrum

  • Visible Light: Part of the electromagnetic spectrum that human eyes can detect.

  • Electromagnetic Radiation: Any form of radiant energy present in the electromagnetic spectrum.

  • Frequency and Wavelength:

    • Wavelength (λ): Distance between successive peaks, measured in meters (m).

    • Frequency (ν): Number of cycles per unit time, measured in s⁻¹ or Hz.

  • Approximate Frequencies and Wavelengths:

    • Highest energy (shortest wavelength) on the left, gradually decreasing to the longest wavelength (lowest energy), notably including:

    • Gamma rays (highest energy)

    • X-rays

    • Ultraviolet

    • Visible light (400-700 nm)

    • Infrared

    • Microwaves

    • Radio waves (lowest energy)

Observation of Spectrum of Sunlight

  • Fraunhofer Lines: A spectrum of sunlight showing narrow dark lines indicating absorption at specific wavelengths.

  • Discovery: These lines correspond to atomic emission spectra of various elements, establishing a connection between light and atomic structure.

Blackbody Radiation and the Wave Nature of Light

  • Blackbody Radiators: Perfect absorbers of light when cold and perfect emitters when hot, whose spectra depend on the temperature.

  • Challenge to Wave Nature: Indicated the need for a new model to understand energy and matter interaction.

Particle Nature of Light: Photons

  • Max Planck's Quantum Theory: Proposed that electromagnetic energy is emitted in integral multiples of a fundamental unit called a quantum.

    • Radiant Energy: Cannot be truly continuous, quantified as:

    • ν = \frac{E}{h} (where $E$ is energy and $h$ is Planck's constant, $6.626 × 10^{-34} J \, s$).

The Photoelectric Effect

  • Definition: Electrons are emitted from metal surfaces when illuminated with light above a threshold frequency ($ν_0$).

  • Observations:

    • Red light has low frequency and insufficient energy to eject electrons.

    • Green light provides higher energy capable of ejecting electrons.

    • Blue light provides even higher energy, allowing for the ejection of electrons with excess energy.

Electrons as Waves

  • De Broglie's Hypothesis: Electrons exhibit both particle and wave behaviors, with their wavelength defined by:

    • λ = \frac{h}{mv} (where $m$ is mass and $v$ is speed).

  • Bohr Model Stability: The quantization of orbits leads to stability in energy levels for electrons surrounding the nucleus.

Heisenberg Uncertainty Principle

  • Statement: It's impossible to simultaneously know both the exact position and momentum of an electron.

  • Mathematical Formulation:

    • ∆x ∙ ∆p ≥ \frac{h}{4}

    • where $∆x$ is uncertainty in position and $∆p$ is uncertainty in momentum.

Quantum Mechanics

  • Erwin Schrödinger's Contribution: Developed a mathematical framework (quantum mechanics) for the wavelike behavior of electrons.

  • Wave Functions (ψ): Solutions to the Schrödinger wave equation that describe the probability distributions of electrons within the atom.

Orbitals

  • Max Born's Contribution: Proposed that the square of the wave function (ψ²) defines an orbital as a three-dimensional region where the probability of finding an electron is high.

Quantum Numbers

  • Description of Orbitals: Unique combinations of three whole numbers called quantum numbers, designating angular momentum and orbital characteristics.

    • Principal Quantum Number (n): Describes size and energy; positive integers.

    • Angular Momentum Quantum Number (l): Ranges from 0 to (n-1), determines the orbital shape:

    • s (l=0), p (l=1), d (l=2), f (l=3).

    • Magnetic Quantum Number (m_l): Orientation of the orbital, with permissible values ranging from -l to +l.

    • Spin Quantum Number (m_s): Indicates the electron's spin orientation, values of +½ or -½.

Filling of Orbitals

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

    • Electron Configuration Examples:

    • For Nitrogen: 1s² 2s² 2p³ or [He] 2s² 2p³

  • Hund’s Rule: For degenerate orbitals, the lowest-energy configuration has the maximum number of unpaired electrons.

Condensed Electron Configurations

  • Lithium Example: 1s² 2s¹ with core electrons as 1s² and valence electrons as 2s¹, abbreviated as [He] 2s¹.

Deviations from Expected Filling Patterns

  • Chromium (Cr): Expected: [Ar] 3d⁴ 4s²; Observed: [Ar] 3d⁵ 4s¹.

  • Copper (Cu): Expected: [Ar] 3d⁹ 4s²; Observed: [Ar] 3d¹⁰ 4s¹.

Electron Configuration of Ion Examples

  • Main Group Elements:

    • Sodium (Na) loses an electron: Na → Na⁺ + e⁻ gives [Ne].

    • Fluorine gains an electron: F + e⁻ → F⁻ gives [Ne].

  • Isoelectronic Elements: Na⁺ and F⁻ are isoelectronic (same electron configuration).

Effective Nuclear Charge (Z_eff)

  • Example with Lithium:

    • Configuration 1s² 2s¹.

    • Outer electron shielded from nucleus by inner electrons, thus $Z_eff < Z$.

Trends in Atomic and Ionic Radius

  • Atomic Radius: Increases down a group due to higher principal quantum number (n) and decreases across a period due to increased effective nuclear charge.

  • Ionic Size:

    • Cations are smaller than parent atoms.

    • Anions are larger than parent atoms.

Ionization Energies

  • First Ionization Energy (IE₁): Energy required to remove one mole of electrons from one mole of gas-phase atoms.

  • Trends: Generally increases across a period due to increased nuclear charge.

Electron Affinity (EA)

  • Definition: Energy change when one mole of electrons combines with atoms or ions in gas phase, generally becomes less negative with increasing atomic number in selected groups.

Summary of Ionization Energies

  • Table of Successive Ionization Energies:

    • Elements show quantifiable trends in energy levels across successive removals of electrons, with notable energies listed.