CHEM 1411 Chapter 6 Notes Quantum Trends

Electromagnetic Spectrum

  • Regions of the Electromagnetic Spectrum

    • Wavelength (λ): distance a wave travels in one cycle (measured in nm, pm, Å)

    • Frequency (ν): cycles per second for a wave (1/sec)

    • Speed of electromagnetic radiation is described by the equation:

      • Speed (c) = ν × λ

      • c = 3.00 × 10^8 m/s (in vacuum)

Energy Quantization

  • Energy is Quantized:

    • Max Planck and Albert Einstein showed that energy is not continuous but comes in discrete packets called photons.

    • Energy can be calculated using the formula:

      • E = hν

      • where, h = Planck's constant = 6.63 × 10^-34 J·s

Atomic Theory: The Bohr Atom

  • Bohr’s Model of the Atom:

    • Electrons exist in specific energy levels around the nucleus, known as quantization of energy.

    • Absorption of energy elevates an electron to a higher energy level (promotion), creating an excited state.

    • When electrons release energy, they fall back to lower energy levels (relaxation).

Energy States

  • Energy Levels:

    • Ground state: lowest possible energy state.

    • Excited state: higher energy level.

    • Change in energy (ΔE) can be calculated as:

      • ΔE = E_C - E_B = E_photon = "quantum" of light.

Bohr Atom Model

  • Key Features:

    • Atoms absorb energy through excitation of electrons to higher levels.

    • Atoms release energy via relaxation, observed as a single wavelength of light (spectral lines).

    • Allowed energy levels are quantized and correspond to orbits; highest-energy levels are farthest from the nucleus.

Quantum Numbers and Energy Levels

  • Quantum Numbers:

    • Identified as n = 1, 2, 3, etc.

    • Relaxation of electrons releases energy observed as spectral lines correlated with wavelength.

Electron Transition and Spectra

  • Hydrogen Emission Spectrum:

    • Light emitted from excited hydrogen gas exhibits distinct wavelengths (e.g., 434.1 nm, 486.1 nm, etc.) corresponding to electron transitions from high to lower energy states.

Modern Atomic Theory

  • Revisions to Bohr’s Model:

    • Electrons do not move in orbits but exist in regions called atomic orbitals.

    • Probability of finding electrons in orbitals increases with electron density.

Heisenberg’s Uncertainty Principle

  • Principle:

    • It is impossible to determine the exact location and momentum of an electron simultaneously.

Schrödinger Equation

  • Developed mathematical representations for the behavior of electrons, defining principal energy levels and proposing sublevels (s, p, d, f).

  • The probability of finding an electron in a specific region in space is determined by these equations.

Energy Levels and Orbitals

  • Energy Levels:

    • Principal quantum number (n) identifies energy levels.

    • Sublevels defined by angular momentum quantum number (l):

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

  • Orbitals: Defined by three quantum numbers (n, l, ml) and can hold a maximum of two electrons with opposite spins according to the Pauli exclusion principle.

Trends in Atomic Properties

  • Atomic Size, Ionization Energy, and Electron Affinity:

    • Atomic size increases down a group and decreases across a period.

    • Ionization energy increases across a period and decreases down a group.

    • Electron affinity shows trends depending on group; halogens exhibit high negative affinities.

Key Comparisons and Comparisons Within Groups

  • Similar Reactivities:

    • Elements in the same group have similar outer electron configurations leading to similar chemical properties.