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

Introduction to Atomic Models and Periodicity

This chapter explores the development of atomic models, focusing on how electrons are arranged in atoms and how these arrangements explain the chemical properties and periodic trends of elements. The discussion includes the Bohr model, the quantum-mechanical model, and their implications for understanding the periodic table.

Blimps, Balloons, and Models of the Atom

Hydrogen and Helium in Airships

• Hydrogen was used in the Hindenburg airship due to its low density, but its high reactivity and flammability led to disaster.

• Helium is now used in modern blimps because it is inert and non-flammable, providing a safer alternative.

• The difference in reactivity between hydrogen and helium is rooted in their atomic structure and electron configurations.

• Key Question: What makes hydrogen reactive and helium inert?

Models of the Atom

Mendeleev's Periodic Law

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

• Group 1A elements (like hydrogen, lithium, sodium) are highly reactive; noble gases (helium, neon, argon) are inert.

• Models and theories help explain these periodic behaviors.

Bohr Model

• Neils Bohr proposed that electrons travel in circular orbits at specific, fixed distances from the nucleus.

• This model successfully explained the emission spectrum of hydrogen but failed for elements with more than one electron.

• Electrons in the Bohr model occupy quantized energy levels, denoted by the principal quantum number n.

• Limitation: Could not explain spectra of multi-electron atoms.

Quantum-Mechanical Model

• Replaced the Bohr model in the early 20th century.

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

• Unlike Bohr orbits, quantum-mechanical orbitals do not represent exact paths.

• Key contributors: Niels Bohr, Erwin Schrödinger, and Albert Einstein.

Quantum Mechanical Model: Orbitals and Quantum Numbers

Principal Quantum Number (n)

• Principal quantum number (n): Specifies the main energy level (shell) of an electron.

• Lowest energy orbital: 1s (n = 1).

• As n increases, energy and average distance from the nucleus increase.

Subshells and Orbital Shapes

• Each shell contains one or more subshells (s, p, d, f), each with a characteristic shape:

  • s: Spherical

  • p: Dumbbell-shaped

  • d: Cloverleaf-shaped

  • f: Complex shapes

• Number of subshells in a shell equals the value of n.

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

Ground State and Excited State

• Ground state: The lowest energy state of an atom, with electrons in the lowest available orbitals.

• Excited state: When an electron absorbs energy and moves to a higher-energy orbital.

Electron Probability Maps and Orbital Representations

• Orbitals are visualized as regions of space where the probability of finding an electron is high.

• Dot density diagrams: Higher density near the nucleus indicates higher probability.

• Geometric shapes (e.g., spheres for s orbitals) represent the volume where the electron is found 90% of the time.

Electron Configurations and Orbital Diagrams

Electron Configuration

• Shows the distribution of electrons among orbitals for an atom in its ground state.

• Example for hydrogen: 1s1

• Example for helium: 1s2

Orbital Diagrams

• Boxes represent orbitals; arrows represent electrons and their spins.

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

• Hund's rule: Electrons occupy orbitals singly before pairing up in orbitals of equal energy.

Filling Order and Energy of Orbitals

• Orbitals fill in order of increasing energy, not always strictly by principal quantum number.

• For example, the 4s orbital fills before the 3d orbital.

• Order can be summarized as: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p, etc.

Valence and Core Electrons

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

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

• The number of valence electrons determines an element's chemical properties.

Electron Configurations and the Periodic Table

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

• The periodic table is divided into blocks (s, p, d, f) based on the type of orbital being filled.

• Main-group elements: Valence electron count equals the group number (except helium).

• Transition metals: d orbitals are being filled; the principal quantum number for d orbitals is the row number minus one.

• Electron configuration can be abbreviated using the noble gas core notation (e.g., Na: [Ne]3s1).

Periodic Trends

Atomic Size

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

• Increases down a group as additional shells are added, increasing the distance from the nucleus.

Ionization Energy

• Energy required to remove an electron from a gaseous atom.

• Increases across a period (harder to remove electrons as nuclear charge increases).

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

Metallic Character

• Metals tend to lose electrons easily (form cations); nonmetals tend to gain electrons.

• Metallic character decreases across a period and increases down a group.

Summary Table: Periodic Trends

Trend	Across a Period (→)	Down a Group (↓)
Atomic Size	Decreases	Increases
Ionization Energy	Increases	Decreases
Metallic Character	Decreases	Increases

Key Learning Objectives

• Understand the Bohr and quantum-mechanical models of the atom.

• Write electron configurations and orbital diagrams for atoms.

• Identify valence and core electrons.

• Relate electron configurations to the periodic table and periodic trends.

• Explain how valence electrons determine chemical properties and reactivity.