Chapter 6: Electronic Structure of Atoms

6.1 The Wave Nature of Light

Electromagnetic radiation, also known as radiant energy, exhibits wave-like behavior. This property is fundamental to understanding the behavior of light and other forms of electromagnetic radiation, such as radio waves and infrared waves.

• Wavelength (λ): The distance between two consecutive peaks (crests) of a wave.

• Frequency (ν): The number of complete wavelengths that pass a given point per second. Frequency is measured in hertz (Hz), which is equivalent to s-1.

• Speed of Light (c): All electromagnetic radiation travels through a vacuum at the speed of light, which is m/s.

• Relationship between Frequency and Wavelength: Frequency and wavelength are inversely related, as described by the equation .

• A wave with a high frequency has a short wavelength, and vice versa.

• Electromagnetic Spectrum: The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by wavelength and frequency. The visible region is only a small part of the spectrum.

Key Equations:

• Speed of light:

• Wavelength and frequency are inversely proportional: as one increases, the other decreases.

6.2 Quantized Energy and Photons

The wave model of light explains many phenomena, but certain observations require the concept of quantized energy.

• Quantization of Energy (Planck): Electromagnetic energy can be absorbed or emitted only in discrete amounts called quanta. The energy of a quantum is given by , where J·s (Planck's constant).

• The Photoelectric Effect (Einstein): When light of sufficient energy strikes a metal surface, electrons are emitted. This demonstrates that light energy is quantized in particles called photons.

• Energy of a Photon:

6.3 Line Spectra and the Bohr Model

When radiation is separated into its component wavelengths, a spectrum is produced. There are two main types:

• Continuous Spectrum: Contains all wavelengths of light (e.g., white light from a bulb).

• Line Spectrum: Contains only specific wavelengths, characteristic of the element emitting the light.

The Bohr model explains the line spectra of hydrogen by proposing that electrons occupy only certain allowed orbits with specific energies. Transitions between these orbits result in the emission or absorption of photons with energy .

Bohr's Equation for Energy Levels:

• Energy of an allowed orbit: , where J

• Change in energy for a transition:

Absorption and Emission:

• Absorption: Electron moves to a higher energy level ()

• Emission: Electron moves to a lower energy level ()

The Rydberg Equation:

• Used to calculate the wavelength of spectral lines in hydrogen: , where

6.4 The Wave Behavior of Matter

Louis de Broglie proposed that particles such as electrons have wave-like properties. The wavelength of a particle is given by:

• de Broglie Wavelength: , where is mass and is velocity.

6.5 Quantum Mechanics and Atomic Orbitals

Quantum mechanics, developed by Schrödinger, describes electrons in terms of wave functions (). The square of the wave function () gives the probability density of finding an electron in a particular region.

Orbitals are described by three quantum numbers:

• Principal quantum number (n): Indicates the size and energy of the orbital (n = 1, 2, 3, ...).

• Angular momentum quantum number (l): Defines the shape of the orbital (l = 0 to n-1). l = 0 (s), l = 1 (p), l = 2 (d), l = 3 (f)

• Magnetic quantum number (ml): Specifies the orientation of the orbital (ml = -l to +l).

• Spin quantum number (ms): Describes the spin of the electron (ms = +1/2 or -1/2).

6.6 Representations of Orbitals

The probability of finding an electron at a certain distance from the nucleus is described by the radial probability function. The shapes of s, p, and d orbitals are characteristic and can be visualized as regions of high probability density.

6.7 Many-Electron Atoms and the Pauli Exclusion Principle

The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers. Each orbital can hold a maximum of two electrons with opposite spins.

6.8 Electron Configurations

Electron configuration describes the arrangement of electrons in an atom's orbitals. The Aufbau principle states that electrons fill orbitals in order of increasing energy. Hund's rule states that electrons occupy degenerate orbitals singly before pairing up.

• Condensed Electron Configurations: Use the noble-gas core to simplify notation (e.g., Al: [Ne] 3s2 3p1).

• Core vs. Valence Electrons: Valence electrons are in the outermost shell and participate in bonding; core electrons are in inner shells.

• Electron Configurations of Ions: Electrons are removed from the highest energy level (largest n) when forming cations and added to the lowest available orbital when forming anions.

• Isoelectronic Series: A group of atoms and ions with the same electron configuration.

Example Table: Relationship among Quantum Numbers (n, l, ml)

Additional info: These notes cover the foundational quantum mechanical concepts necessary for understanding atomic structure, electron configurations, and the periodic properties of elements. Mastery of these topics is essential for further study in general chemistry.