Chapter 2: Atomic Theory

Chapter 2: Atomic Theory

Quantum Model

A History of the Atom: Theories and Models

  • Exploration of how ideas about atoms have evolved through history.

  • The development of various atomic models:

    • Solid Sphere Model (1803) by John Dalton

    • Plum Pudding Model (1897) by J.J. Thomson

    • Nuclear Model (1911) by Ernest Rutherford

    • Planetary Model (1913) by Niels Bohr

    • Quantum Mechanical Model (1926) by Erwin Schrödinger

Major Atomic Models

  • Solid Sphere Model (John Dalton):

    • Atoms are indivisible.

    • Atoms of a particular element are identical.

    • Compounds are combinations of different types of atoms.

    • Recognition that atoms of different elements are distinct.

  • Plum Pudding Model (J.J. Thomson):

    • Discovery of electrons (initially called 'corpuscles') in 1897.

    • Model depicts atoms as electrons scattered within a positive charge cloud.

    • Identified electrons as components of atoms but did not account for the nucleus nor later experimental observations.

  • Nuclear Model (Ernest Rutherford):

    • Based on the gold foil experiment where positively charged alpha particles were directed at gold foil.

    • Most alpha particles passed through with slight deflection; significant deflection indicated a small, dense nucleus.

    • Positively charged particles concentrated in the nucleus and most of the atom consists of empty space.

    • Failed to explain how electrons could remain in orbit around the nucleus.

  • Planetary Model (Niels Bohr):

    • Modified Rutherford's model by suggesting electrons orbit the nucleus at fixed distances.

    • Introduced quantization of electron energy levels; electrons could only occupy certain energy levels.

    • Explained some elements' emission spectra but struggled with heavier atoms due to energy emissions suggesting electron should spiral into the nucleus.

  • Quantum Mechanical Model (Erwin Schrödinger):

    • Electrons are not confined to orbits; instead, they exist in ‘clouds of probability’ (orbitals).

    • Probability distribution of finding an electron at any point around the nucleus.

    • Widely regarded as the most accurate atomic model throughout current scientific understanding.

Electromagnetic Waves

  • Wavelength ($ ext{λ}$), frequency ($ ext{ν}$), and speed of light ($c$) are interrelated:

    • A: Longer wavelength corresponds to lower frequency.

    • B: Shorter wavelength corresponds to higher frequency.

    • C: Wave amplitude may vary.

  • Light exhibits dual characteristics: behaves as both wave and particle.

    • Photon: Basic unit of light energy.

    • Planck’s constant (h): $h = 6.626 imes 10^{-34} ext{ J s}$.

Electromagnetic Spectrum

  • Complete spectrum includes various radiation types characterized by varying wavelength and frequency.

    • Gamma rays, X-rays, Ultraviolet, Visible (400-750 nm), Infrared, Microwave, Radio.

  • Interaction between matter and light results in absorption or emission of photons, with energy determined by photon frequency or wavelength:

    • $E = h
      u$ (energy of a photon).

Hydrogen Spectra

  • Absorption Spectrum shows wavelengths absorbed by hydrogen; Emission Spectrum demonstrates wavelengths emitted.

  • The Balmer series specifies electron transitions within hydrogen, correlating with discrete wavelengths emitted upon electron excitation.

Bohr Model Development

  • Johann Balmer, Theodore Lyman, Friedrich Paschen, Johannes Rydberg:

    • Identified spectral lines related to electron transitions in hydrogen.

    • Rydberg formula: Relates energy level transitions to emitted wavelength.

    • Basic transitions provided defined energies corresponding to light.

Team Modules

Example Problem 2.1.2: Interpreting Balmer Series

  • Find principal quantum numbers $(n, m)$ for the red line in the Balmer series using the Rydberg formula and wavelengths.

Understanding Electron Behavior

  • Experimental evidence substantiates wave-particle duality of electrons:

    • The double-slit experiment confirms interference patterns demonstrating wave-like behavior.

    • De Broglie’s hypothesis about electron wave properties expanded understanding of quantum mechanics:

    • $ ext{λ} = rac{h}{mv}$ where $h$ is Planck's constant, $m$ is mass, and $v$ is velocity.

    • Electrons behave as standing waves confined in atomic orbitals, quantifying energy levels at which they oscillate.

Quantum Mechanical Model Parameters

  • Four quantum numbers specify each electron:

    1. Principal quantum number (n): Determines energy and size (positive integer).

    2. Azimuthal quantum number (l): Determines shape of orbital (s, p, d, f).

    3. Magnetic quantum number (mᵡ): Orientation in space.

    4. Spin quantum number (mₛ): Describes electron spin direction (+1/2 or -1/2).

  • Pauli Exclusion Principle dictates that no two electrons in an atom can have identical quantum numbers.

Shapes of Atomic Orbitals

  • n=1: Only one orbital type indicated as $ ext{Ψ}_{1s} $.

    • Wavefunctions shape probability density.

  • n=2: Includes s (spherical) and p (dumbbell) orbitals with distinct orientations.

  • n=3: Provides additional orbitals with higher complexity.

Electron Configuration Overview

  • Arrangement of electrons crucial for understanding chemistry and predicting bonding reactions.

  • Arranged by filling orbitals based on increasing energy levels according to the Aufbau principle.

  • Cations & Anions defined by electron gain/loss corresponding to charge changes in atoms.

Summary of Periodic Trends

  • Effective Nuclear Charge (Z*): Represents net positive charge experienced by electrons in an atom, affecting atomic and ionic sizes, ionization energies, and electron affinities.

  • Ionization Energy (IE): Energy necessary to remove an electron; higher for noble gases due to their full valence shells.

  • Electron Affinity (EA): Measures how likely an atom is to gain an electron.

  • Electronegativity (EN): Ability to attract electrons in a bond; varies across the periodic table.

Types of Bonds

  • Ionic Bonds: Formed by complete transfer of electrons due to large electronegativity difference (>1.9).

  • Covalent Bonds: Characterized by sharing electrons with smaller electronegativity differences.

  • Polar vs Nonpolar Bonds: Based on the unequal or equal sharing of electron density, respectively.

Examples of Chemical Reactions & Structures

  • Lewis Structures guide electron distribution in molecules but do not indicate 3D shape.

  • Formal Charges calculate electron ownership in bonds based on the defined rules for electron sharing.

  • Examine reactions and propose structures considering octets or expanded octets for appropriate examples in bonding scenarios.