Atomic Structure & Atomic Properties of Elements

Introduction

The atomic structure of elements is fundamental to understanding their chemical and physical properties. This topic explores the interactions of electromagnetic radiation with matter, the quantum mechanical model of the atom, and the arrangement of electrons as described by quantum numbers and electron configurations.

Electromagnetic Radiation

Nature of Electromagnetic Radiation

Electromagnetic (EM) radiation encompasses a broad range of phenomena, including microwaves, infrared, visible light, X-rays, and gamma rays. EM waves consist of energy propagated by oscillating electric and magnetic fields that are perpendicular to each other and vary in intensity as they move through space.

• Key Point 1: EM radiation can be described as waves with oscillating electric and magnetic fields.

• Key Point 2: The electromagnetic spectrum includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

• Example: Visible light is a small portion of the EM spectrum, ranging from approximately 400 nm (violet) to 750 nm (red).

Electromagnetic Spectrum

The electromagnetic spectrum is a continuous range of wavelengths and frequencies of EM radiation.

Wave Properties: Wavelength, Frequency, and Amplitude

Three variables describe the wave nature of EM radiation:

• Wavelength (λ): The distance from one wave peak to the next (units: meters).

• Frequency (ν): The number of wave peaks passing a given point per unit time (units: s-1, Hz).

• Amplitude: The height of the wave; brightness of light is proportional to amplitude.

The relationship between wavelength and frequency is given by:

where is the speed of light ( m/s).

Wave-Particle Duality and Quantum Theory

Key Discoveries Leading to Quantum Theory

Classical physics could not explain certain phenomena, such as blackbody radiation and the photoelectric effect. Quantum theory introduced the concept that energy is quantized and can be absorbed or emitted only in discrete packets called quanta or photons.

• Blackbody Radiation: Max Planck proposed that energy is emitted in discrete amounts (), where is Planck's constant ( J·s).

• Photoelectric Effect: Albert Einstein explained that light behaves as a stream of photons, each with energy .

Photoelectric Effect

When light of sufficient frequency shines on a metal surface, electrons are emitted. The energy of the emitted electrons depends on the frequency of the incident light, not its intensity.

• Threshold Frequency: Electrons are emitted only if the light's frequency exceeds a certain threshold.

• Equation:

• Example: If the frequency is below the threshold, no electrons are emitted regardless of intensity.

Atomic Spectra and Energy Levels

Atomic Emission and Absorption Spectra

Atoms emit or absorb light at specific wavelengths, producing line spectra. These spectra provide clues to the arrangement of electrons inside atoms.

• Continuous Spectrum: Produced by white light (e.g., sunlight).

• Line Spectrum: Produced by excited atoms emitting light at discrete wavelengths.

• Example: The Balmer series in hydrogen's emission spectrum corresponds to electron transitions to the energy level.

Bohr Model of the Atom

Niels Bohr proposed that electrons occupy fixed orbits with quantized energies. Energy is absorbed or emitted only when an electron transitions between these orbits.

• Energy Levels: Only certain allowed energy levels exist.

• Equation for Energy Change:

• Rydberg Equation: , where m-1

Quantum Mechanical Model of the Atom

Schrödinger Equation and Atomic Orbitals

The quantum mechanical model treats electrons as wavefunctions described by the Schrödinger equation. Solutions to this equation yield atomic orbitals, which are regions of space with high probability of finding an electron.

• Wavefunction (ψ): Mathematical function describing the electron's behavior.

• Probability Density: gives the probability of finding an electron at a given location.

• Quantum Numbers: Each orbital is defined by a set of quantum numbers: , , , .

Quantum Numbers

• Principal Quantum Number (): Indicates energy level and size of orbital ().

• Azimuthal Quantum Number (): Indicates shape of orbital ( for s, $1 for d, $3$ for f).

• Magnetic Quantum Number (): Indicates orientation in space ( to ).

• Spin Quantum Number (): Indicates electron spin ( or ).

Pauli Exclusion Principle

No two electrons in an atom can have the same set of four quantum numbers. Each orbital can hold a maximum of two electrons with opposite spins.

Hund's Rule

When electrons occupy degenerate orbitals (orbitals of the same energy), they fill them singly with parallel spins before pairing up.

Electron Configurations and the Periodic Table

Aufbau Principle

Electrons fill orbitals in order of increasing energy, starting with the lowest energy orbital available.

• Order of Filling:

• Example: Carbon ():

Periodic Table Blocks

The periodic table is divided into blocks based on the subshell being filled:

Valence Electrons and Chemical Properties

Valence electrons are those in the outermost shell and determine the chemical properties of elements. Elements in the same group have similar valence electron configurations and thus similar chemical behavior.

Examples of Electron Configurations

• Phosphorus (Z=15): [Ne]

• Tin (Z=50): [Kr]

• Sn2+ ion: [Kr]

Summary Table: Quantum Numbers and Orbital Designations

Conclusion

The quantum mechanical model provides a comprehensive framework for understanding atomic structure, electron configurations, and the periodic properties of elements. Mastery of these concepts is essential for further study in physics and chemistry.

Additional info: Some explanations and tables have been expanded for clarity and completeness based on standard academic sources.