Electrons in Atoms and the Periodic Table

Wave Properties of Light

Light exhibits both wave-like and particle-like properties, which are fundamental to understanding atomic structure and electron behavior.

• Wavelength (λ): The distance between two consecutive peaks of a wave, typically measured in meters (m) or nanometers (nm).

• Frequency (ν): The number of wave cycles that pass a given point per second, measured in hertz (Hz).

• Speed of Light (c): The constant speed at which light travels in a vacuum, m/s.

• Energy of a Photon (E): The energy carried by a single photon of light, related to its frequency and wavelength.

Key Equations:

• Relationship between speed, wavelength, and frequency:

• Energy of a photon: where is Planck's constant ( J·s).

Example: If a photon has a wavelength of 500 nm, its frequency and energy can be calculated using the above equations.

Light and the Bohr Model of the Atom

The Bohr model explains how electrons occupy specific energy levels in an atom and how light is emitted or absorbed when electrons transition between these levels.

• Electrons move in quantized orbits around the nucleus.

• When an electron jumps from a higher to a lower energy level, it emits a photon of light with energy equal to the difference between the two levels.

• This explains the line spectra observed for elements.

Example: The hydrogen atom emits light at specific wavelengths, corresponding to electron transitions between energy levels.

Quantum Numbers and Atomic Orbitals

Quantum numbers describe the properties and locations of electrons in atoms.

• Principal quantum number (n): Indicates the main energy level or shell.

• Angular momentum quantum number (l): Indicates the shape of the orbital (s, p, d, f).

• Magnetic quantum number (ml): Specifies the orientation of the orbital in space.

• Spin quantum number (ms): Specifies the direction of the electron's spin (+1/2 or -1/2).

Example: For a 2p electron, n = 2, l = 1, ml = -1, 0, or +1, ms = +1/2 or -1/2.

Shapes of Atomic Orbitals

Atomic orbitals have characteristic shapes that influence chemical bonding and molecular structure.

• s orbitals: Spherical in shape.

• p orbitals: Dumbbell-shaped, oriented along x, y, or z axes.

• d orbitals: More complex, often cloverleaf-shaped.

Example: The 1s orbital is a sphere centered on the nucleus; the 2p orbitals are dumbbell-shaped and oriented at right angles to each other.

Electron Configurations and the Periodic Table

Electron configurations describe the arrangement of electrons in an atom or ion, often using the noble gas core abbreviation for simplicity.

• Electrons fill orbitals in order of increasing energy (Aufbau principle).

• Use the format: [Noble gas] + remaining configuration (e.g., [Ne] 3s2 3p4).

• For ions, add or remove electrons according to the charge.

Example: The electron configuration of Cl- is [Ne] 3s2 3p6.

Periodic Trends

Several properties of elements change predictably across the periodic table.

• Atomic size: Increases down a group, decreases across a period.

• Ionization energy: Energy required to remove an electron; increases across a period, decreases down a group.

• Metallic character: Increases down a group, decreases across a period.

• Electron affinity: Tendency to gain electrons; generally becomes more negative across a period.

• Electronegativity: Ability to attract electrons in a bond; increases across a period, decreases down a group.

Example: Fluorine has the highest electronegativity of all elements.

Chemical Bonding

Lewis Structures

Lewis structures represent the arrangement of valence electrons in atoms, ions, and molecules.

• Dots represent valence electrons around element symbols.

• Pairs of dots or lines represent shared electron pairs (bonds).

• Used for elements, ionic compounds, ions, and molecular compounds.

Example: The Lewis structure for water (H2O) shows two single bonds and two lone pairs on oxygen.

Resonance Structures

Some molecules cannot be represented by a single Lewis structure; instead, multiple resonance structures are drawn to show delocalized electrons.

• Resonance structures differ only in the placement of electrons, not atoms.

• The actual structure is a hybrid of all resonance forms.

Example: The carbonate ion (CO32-) has three resonance structures with double bonds in different positions.

Molecular Shapes and Polarity

The shape of a molecule is determined by the arrangement of atoms and electron pairs around the central atom (VSEPR theory). Molecular polarity depends on both bond polarity and molecular shape.

• VSEPR theory: Electron pairs repel each other, arranging themselves as far apart as possible.

• Common shapes: Linear, bent, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral.

• Polarity: A molecule is polar if it has polar bonds arranged asymmetrically, resulting in a net dipole moment.

Example: Water (H2O) is a bent, polar molecule; carbon dioxide (CO2) is linear and nonpolar.