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

Models of the Atom

Blimps, Balloons, and Atomic Reactivity

Understanding the reactivity and inertness of gases such as hydrogen and helium provides insight into atomic structure and chemical properties.

• Hydrogen is highly reactive and flammable, as seen in the Hindenburg disaster. Its atoms readily combine to form diatomic hydrogen molecules.

• Helium is inert and used in modern blimps due to its stable electron configuration.

• The difference in reactivity between hydrogen and helium is explained by atomic models and electron configurations.

• Mendeleev's periodic law: When elements are arranged by increasing atomic number, sets of properties recur periodically.

Bohr Model of the Atom

The Bohr model was developed to explain the emission spectra of elements, particularly hydrogen.

• Electrons travel in circular orbits around the nucleus at specific, fixed distances.

• Each orbit is associated with a quantum number (n), which determines its energy.

• The Bohr model successfully predicted the hydrogen emission spectrum but failed for multi-electron atoms.

• It was replaced by the more advanced quantum-mechanical model.

• Equation: $E_n = - rac{R_H}{n^2}$ (energy of an electron in the nth orbit, where $R_H$ is the Rydberg constant)

Quantum-Mechanical Model of the Atom

This model provides a more accurate description of electron behavior in atoms.

• Electrons are described by orbitals, which are probability maps indicating where an electron is likely to be found.

• Unlike Bohr orbits, orbitals do not represent exact paths but statistical distributions.

• Electron behavior is fundamentally different from classical particles (e.g., a baseball's path is predictable, but an electron's position is probabilistic).

Quantum Mechanical Orbitals

Principal Quantum Numbers and Subshells

Orbitals are specified by a principal quantum number (n) and a subshell letter (s, p, d, f).

• Principal quantum number (n): Indicates the principal shell and energy level.

• Subshell letter: Specifies the shape of the orbital (s = spherical, p = dumbbell, d = cloverleaf, f = complex).

• 1s orbital: Lowest energy, spherical shape.

• Ground state: Electron occupies the lowest energy orbital.

• Excited state: Electron occupies a higher energy orbital after absorbing energy.

Energy and Orbital Shapes

Energy increases with the principal quantum number, and orbital shapes vary by subshell.

• Energy ordering: $n = 1, 2, 3, ...$ with energy increasing as n increases.

• Orbital shapes:

  • s: Spherical

  • p: Two lobes (dumbbell)

  • d: Four-lobed (cloverleaf)

  • f: Complex shapes

• Dot density diagrams show the probability of finding an electron; highest near the nucleus for s orbitals.

Table: Number of Subshells per Principal Shell

Shell (n)	Number of Subshells	Letters Specifying Subshells
n = 1	1	s
n = 2	2	s, p
n = 3	3	s, p, d
n = 4	4	s, p, d, f

Electron Configurations

Writing Electron Configurations

Electron configurations describe the arrangement of electrons in orbitals for an atom.

• Electrons fill lower-energy orbitals first (Aufbau principle).

• Each orbital holds a maximum of two electrons with opposite spins (Pauli exclusion principle).

• Orbitals of equal energy are filled singly before pairing (Hund's rule).

• Example: Hydrogen: $1s^1$; Helium: $1s^2$; Lithium: $1s^2 2s^1$

• Orbital diagrams: Boxes represent orbitals, arrows represent electrons and their spins.

Noble Gas Core Notation

Electron configurations for elements beyond neon can be abbreviated using the previous noble gas in brackets.

• Example: Sodium: [Ne] $3s^1$

Valence and Core Electrons

Valence electrons are in the outermost principal shell and are crucial for chemical bonding.

• Core electrons: All other electrons not in the outermost shell.

• Example: Silicon: 4 valence electrons (n = 3 shell), 10 core electrons.

Periodic Table and Electron Configuration Patterns

Blocks and Groups

The periodic table is organized into blocks based on electron configurations.

• s block: Groups 1A and 2A

• p block: Groups 3A to 8A

• d block: Transition metals

• f block: Lanthanides and actinides

Main-Group and Transition Elements

• Main-group elements: Number of valence electrons equals the group number.

• Transition elements: d orbital filling; principal quantum number for d orbitals is row number minus one.

• Exceptions: Chromium ($4s^1 3d^5$) and Copper ($4s^1 3d^{10}$) due to stability of half-filled and fully-filled d subshells.

Periodic Trends

Atomic Size

Atomic size is determined by the distance between the outermost electrons and the nucleus.

• Decreases across a period (left to right) due to increased nuclear charge pulling electrons closer.

• Increases down a group due to higher principal quantum number (electrons farther from nucleus).

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in the gaseous state.

• Increases across a period (harder to remove electrons as atoms approach noble gas configuration).

• Decreases down a group (electrons are farther from nucleus, easier to remove).

Metallic Character

Metallic character refers to the tendency of an element to lose electrons and form cations.

• Decreases across a period (left to right).

• Increases down a group.

Review and Learning Objectives

Key Concepts

• Bohr and quantum-mechanical models explain atomic structure and periodic trends.

• Electron configurations and orbital diagrams are essential for understanding chemical properties.

• Periodic table organization reflects electron configurations and recurring chemical properties.

• Periodic trends in atomic size, ionization energy, and metallic character are explained by electron arrangements.

Learning Objectives

1. Understand and explain the Bohr and quantum-mechanical models of the atom.

2. Write electron configurations and orbital diagrams for atoms.

3. Identify valence and core electrons.

4. Write electron configurations based on periodic table position.

5. Explain how valence electrons determine chemical properties.

6. Identify and understand periodic trends in atomic size, ionization energy, and metallic character.

Additional info: These notes are based on textbook slides for Chapter 9, "Electrons in Atoms and the Periodic Table," and are suitable for introductory college chemistry students.