Electrons in Atoms and the Periodic Table: Models, Configurations, and Periodic Trends

Electrons in Atoms and the Periodic Table

Introduction

This chapter explores the structure of atoms, focusing on how electrons are arranged and how these arrangements explain the chemical properties and periodic trends of elements. Key models such as the Bohr model and the quantum-mechanical model are discussed, along with their implications for electron configurations and the organization of the periodic table.

Models of the Atom

Bohr Model

The Bohr model was developed to explain the emission spectra of elements, particularly hydrogen. In this model, electrons travel in circular orbits around the nucleus at specific, fixed distances, each associated with a quantized energy level.

• Quantized Energy Levels: Electrons can only occupy certain orbits, each with a specific energy, denoted by the principal quantum number $n$ (where $n = 1, 2, 3, ...$).

• Transitions: Electrons can move between orbits by absorbing or emitting energy, resulting in spectral lines.

• Limitations: The Bohr model accurately predicts hydrogen's spectrum but fails for multi-electron atoms.

Example: The hydrogen atom's electron transitions between $n=2$ and $n=1$ produce visible spectral lines.

Quantum-Mechanical Model

The quantum-mechanical model replaced the Bohr model, providing a more accurate description of electron behavior in atoms.

• Orbitals: Electrons occupy orbitals, which are probability maps indicating where an electron is likely to be found, rather than fixed paths.

• Principal Quantum Number ($n$): Specifies the principal shell and energy level of an orbital.

• Subshells: Indicated by letters (s, p, d, f), each with a distinct shape and energy.

• Ground State and Excited State: The lowest energy configuration is the ground state; absorption of energy can promote electrons to higher-energy (excited) states.

Example: The 1s orbital is spherical and represents the region where the hydrogen atom's electron is most likely to be found.

Quantum Numbers and Atomic Orbitals

Principal Quantum Number ($n$)

• Defines the main energy level (shell) of an electron.

• Possible values: $n = 1, 2, 3, ...$

• Energy increases as $n$ increases.

Subshells and Orbital Shapes

• s orbital: Spherical shape.

• p orbital: Dumbbell shape.

• d orbital: More complex, cloverleaf shapes.

• f orbital: Even more complex shapes.

Example: The 2p orbitals have a dumbbell shape and are higher in energy than 2s.

Electron Configurations

Writing Electron Configurations

Electron configurations show how electrons occupy orbitals in an atom.

• Notation: Indicates the number of electrons in each orbital (e.g., H: 1s1).

• Orbital Diagrams: Use boxes and arrows to represent orbitals and electron spins.

• Electron Spin: Each orbital can hold up to two electrons with opposite spins (Pauli exclusion principle).

• Hund's Rule: Electrons fill orbitals of equal energy singly before pairing.

Example: Carbon (6 electrons): 1s2 2s2 2p2; the two 2p electrons occupy separate p orbitals with parallel spins.

Energy Ordering of Orbitals

• In multi-electron atoms, subshells within a shell have different energies due to electron-electron interactions.

• General order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s

Noble Gas Core Notation

• Electron configurations for elements beyond a noble gas can be abbreviated using the noble gas symbol in brackets.

• Example: Sodium (Na, atomic number 11): [Ne] 3s1

Valence and Core Electrons

Definitions

• Valence electrons: Electrons in the outermost principal shell (highest $n$); involved in chemical bonding.

• Core electrons: Electrons in inner shells; not involved in bonding.

Example: Silicon (Si): 1s2 2s2 2p6 3s2 3p2; 4 valence electrons (3s and 3p), 10 core electrons.

Periodic Table and Electron Configurations

Blocks of the Periodic Table

• s block: Groups 1A and 2A (left side).

• p block: Groups 3A to 8A (right side).

• d block: Transition metals (center).

• f block: Lanthanides and actinides (bottom).

Patterns in Electron Configurations

• Elements in the same group have the same number of valence electrons and similar outer electron configurations.

• The group number for main-group elements equals the number of valence electrons (except helium).

• The row number equals the highest principal quantum number ($n$) for main-group elements.

Example: Chlorine (Cl, group 7A, row 3): 7 valence electrons, highest $n = 3$.

Transition Elements

• Transition metals have electron configurations with trends that differ from main-group elements.

• The principal quantum number of the d orbital is the row number minus one.

• Exceptions: Chromium (Cr) is 4s13d5; Copper (Cu) is 4s13d10.

Explanatory Power of the Quantum-Mechanical Model

Chemical Properties and Valence Electrons

• Chemical properties are largely determined by the number of valence electrons.

• Elements with the same number of valence electrons have similar properties.

• Noble gases (8 valence electrons) are very stable and inert.

• Elements near noble gases are most reactive, as they can easily gain or lose electrons to achieve noble gas configurations.

Example: Alkali metals (group 1A) form +1 cations; halogens (group 7A) form -1 anions, both achieving noble gas configurations.

Periodic Trends

Trends Across Periods and Down Groups

• Across a period (left to right): Atomic size decreases, ionization energy increases, metallic character decreases.

• Down a group: Atomic size increases, ionization energy decreases, metallic character increases.

Summary Table: Electron Configuration Blocks

Block	Groups	Type of Orbitals Filled
s block	1A, 2A	s orbitals
p block	3A–8A	p orbitals
d block	Transition metals	d orbitals
f block	Lanthanides, Actinides	f orbitals

Key Equations

• Energy of a photon: $E = h \nu$

• Relationship between wavelength and frequency: $c = \lambda \nu$

Learning Objectives

• Understand and explain the nature of electromagnetic radiation.

• Predict relative wavelength, energy, and frequency of different types of light.

• Explain the key characteristics of the Bohr and quantum-mechanical models of the atom.

• Write electron configurations and orbital diagrams for atoms.

• Identify valence and core electrons.

• Explain periodic trends in atomic size, ionization energy, and metallic character.