Atomic Structure & Periodic Properties of Elements – Study Notes

Atomic Structure & Periodic Properties of Elements

Introduction

This chapter explores the fundamental principles of atomic structure and how these principles relate to the periodic properties of elements. Understanding the behavior of electrons and their arrangement in atoms is essential for explaining chemical properties and trends in the periodic table.

Electromagnetic Radiation and Atomic Structure

Electromagnetic Spectrum

The electromagnetic spectrum is a continuous range of radiant energy that includes gamma rays, X-rays, ultraviolet (UV) radiation, visible light, infrared (IR) radiation, microwaves, and radio waves. All forms of electromagnetic radiation are types of radiant energy and play a crucial role in chemistry, especially in determining the energies of electrons within atoms.

• Electromagnetic radiation: Any form of radiant energy within the electromagnetic spectrum.

• Visible light: The portion of the spectrum detectable by the human eye, ranging from approximately 400 nm (violet) to 700 nm (red).

• Different elements emit different colors of light due to their unique electronic structures.

Electromagnetic Spectrum Table

Type	Wavelength (m)	Frequency (Hz)
Gamma rays	< 10-12	> 1020
X-rays	10-12 – 10-10	1018 – 1020
Ultraviolet	10-10 – 4x10-7	1016 – 1018
Visible	4x10-7 – 7x10-7	4x1014 – 7.5x1014
Infrared	7x10-7 – 10-3	1012 – 4x1014
Microwave	10-3 – 10-1	109 – 1012
Radio	> 10-1	< 109

Waves and Their Properties

A wave is an oscillation that can transport energy from one place to another. Electromagnetic waves travel at the same constant speed in a vacuum, known as the speed of light ($c = 2.998 \times 10^8$ m/s).

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

• Frequency (ν): The number of wave cycles that pass a given point per second.

• Wavelength and frequency are inversely related.

The relationship between wavelength, frequency, and the speed of light is given by:

$\lambda \nu = c$ or $\nu = \frac{c}{\lambda}$

Where $\lambda$ is wavelength, $\nu$ is frequency, and $c$ is the speed of light.

Spectrum of Sunlight

The spectrum of sunlight is not continuous; it contains a series of very narrow dark lines called Fraunhofer lines. These lines are due to the absorption of specific wavelengths by elements in the sun's atmosphere.

• William Wollaston and Joseph Fraunhofer mapped the wavelengths of these lines.

• Fraunhofer lines are important for identifying elements present in stars.

Atomic Spectra and Quantum Theory

Emission and Absorption Spectra

When elements are excited, they emit light at specific wavelengths, producing an emission spectrum. Conversely, when elements absorb energy, they produce an absorption spectrum with dark lines at the same wavelengths as the bright lines in the emission spectrum.

• Emission spectrum: Bright lines on a dark background, characteristic of each element.

• Absorption spectrum: Dark lines on a bright background, corresponding to wavelengths absorbed by the element.

• These spectra provide evidence for quantized energy levels in atoms.

Quantization of Energy

Max Planck proposed that energy is quantized and can only be emitted or absorbed in discrete amounts called quanta. The energy ($E$) of a single quantum is given by:

$E = h \nu$

• $h$ is Planck's constant ($6.626 \times 10^{-34}$ J·s).

• $\nu$ is the frequency of radiation.

Photoelectric Effect

Albert Einstein explained the photoelectric effect by proposing that light consists of particles called photons. When light of sufficient frequency strikes a metal surface, electrons are ejected. The kinetic energy of the ejected electrons depends on the frequency of the light, not its intensity.

• Supports the particle nature of light.

• Demonstrates quantization of energy.

Atomic Models and Electron Configuration

Hydrogen Spectrum and the Balmer/Rydberg Equations

The emission spectrum of hydrogen can be described by the Balmer equation and the more general Rydberg equation:

$\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$

• $R$ is the Rydberg constant ($1.097 \times 10^7$ m-1).

• $n_1$ and $n_2$ are positive integers, $n_2 > n_1$.

• Different series (Lyman, Balmer, Paschen, etc.) correspond to different values of $n_1$.

Bohr Model of the Atom

Niels Bohr proposed a model in which electrons revolve around the nucleus in quantized orbits, each corresponding to a specific energy level. The energy of an electron in orbit $n$ is:

$E_n = -2.178 \times 10^{-18} \left( \frac{Z^2}{n^2} \right)$

• Transitions between energy levels result in absorption or emission of photons.

• Works well for hydrogen but not for multi-electron atoms.

de Broglie Hypothesis

Louis de Broglie suggested that electrons exhibit both wave and particle properties. The wavelength ($\lambda$) of a particle is given by:

$\lambda = \frac{h}{mv}$

• $m$ is mass, $v$ is velocity.

• Demonstrates the dual nature of matter.

Heisenberg Uncertainty Principle

Werner Heisenberg stated that it is impossible to simultaneously know the exact position ($x$) and momentum ($p$) of a particle:

$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$

• Limits the precision of measurements for microscopic particles.

Quantum Mechanical Model

Erwin Schrödinger developed a mathematical model describing the wavelike behavior of electrons. Solutions to the Schrödinger equation are called wave functions ($\psi$), which describe the probability of finding an electron in a particular region of space, known as an orbital.

• The square of the wave function ($|\psi|^2$) gives the probability density.

• Orbitals differ from Bohr orbits; they are regions of space, not fixed paths.

Quantum Numbers and Atomic Orbitals

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them:

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

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

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

• Spin quantum number ($m_s$): Indicates the spin of the electron ($m_s = +\frac{1}{2}$ or $-\frac{1}{2}$).

Quantum Numbers Table

Quantum Number	Symbol	Allowed Values	Orbital Type
Principal	n	1, 2, 3, ...	Shell
Angular Momentum	l	0 to n-1	s, p, d, f
Magnetic	m_l	-l to +l	Orbital orientation
Spin	m_s	+1/2, -1/2	Electron spin

Shapes of Atomic Orbitals

• s orbitals: Spherical shape.

• p orbitals: Dumbbell shape; three orientations (px, py, pz).

• d orbitals: Cloverleaf shape; five orientations.

Electron Configuration and the Periodic Table

Electron Configuration Principles

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

• Pauli exclusion principle: No two electrons in the same atom can have the same set of four quantum numbers.

• Hund's rule: Electrons occupy degenerate orbitals singly before pairing.

Writing Electron Configurations

• Use the previous noble gas to abbreviate core electrons.

• Example for lithium: 1s22s1 or [He]2s1

• Valence electrons are those in the outermost shell and are involved in bonding.

Electron Configuration of Alkali Metals

Element	Electron Configuration
Lithium	[He]2s1
Sodium	[Ne]3s1
Potassium	[Ar]4s1

Alkali metals have similar valence electron configurations, leading to similar chemical properties.

Exceptions to Expected Filling Patterns

• Some transition metals (e.g., Cr, Cu) have electron configurations that differ from the expected pattern due to increased stability of half-filled or fully filled d subshells.

Electron Configuration of Ions

• Main group elements form cations (metals) or anions (nonmetals) to achieve noble gas configurations.

• Transition metals lose ns electrons before (n-1)d electrons when forming cations.

• Isoelectronic species have identical electron configurations but different nuclear charges.

Periodic Properties of Elements

Effective Nuclear Charge ($Z_{eff}$)

The effective nuclear charge is the net positive charge experienced by valence electrons, accounting for shielding by inner electrons.

• $Z_{eff} = Z - S$ (where $Z$ is the atomic number, $S$ is the shielding constant)

• $Z_{eff}$ increases across a period and slightly decreases down a group.

Atomic and Ionic Radii

• Atomic radius increases down a group and decreases across a period.

• Cations are smaller than their parent atoms; anions are larger.

• Isoelectronic series: For species with the same electron configuration, the one with the highest nuclear charge is smallest.

Ionization Energy (IE)

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

• IE increases across a period and decreases down a group.

• Successive ionization energies increase for the same atom.

Electron Affinity (EA)

Electron affinity is the energy change when an electron is added to a gaseous atom.

• EA generally increases across a period.

• EA trends down a group are less predictable.

• Metals have low EA; nonmetals have high EA.

Summary Table: Periodic Trends

Property	Trend Across Period	Trend Down Group
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Increases	Variable
$Z_{eff}$	Increases	Slightly decreases

Example: Sodium (Na) has a lower ionization energy and larger atomic radius than chlorine (Cl), reflecting their positions in the periodic table.

Additional info: These notes expand on the provided slides and text, filling in missing context and definitions for clarity and completeness.