Quantum-Mechanical Model of the Atom: Electromagnetic Radiation and Wave Properties

Unit 1: Chapter 2 – The Quantum-Mechanical Model of the Atom

Topics Overview

• Electromagnetic Spectrum

• Wavelength & Frequency

• Atomic Line Spectra

• The Balmer-Rydberg Equation

• Particle-like Properties of Electromagnetic Energy

• Wavelike Properties of Matter

• Bohr’s Model of the Atom

• Quantum Mechanics and the Heisenberg Uncertainty Principle

• Wave Functions and Quantum Numbers

• The Shapes of Atomic Orbitals

Electromagnetic Radiation

Student Learning Objectives

• Define and understand electromagnetic radiation.

• Define and understand amplitude, wavelength, and frequency.

• Use the speed of light to convert between wavelength and frequency.

• Identify the electromagnetic spectrum and its different forms of radiation.

• Explain interference and diffraction and how they demonstrate the wave nature of light.

• Use equations to interconvert energy, wavelength, and frequency of electromagnetic radiation.

Introduction to Electromagnetic Radiation

Electromagnetic radiation is a form of energy that exhibits both wave-like and particle-like properties. It consists of oscillating electric and magnetic fields that propagate through space perpendicular to each other and to the direction of travel.

• Electric field component: Oscillates in one plane.

• Magnetic field component: Oscillates in a plane perpendicular to the electric field.

These oscillating fields together form electromagnetic waves, which include visible light, radio waves, X-rays, and more.

Wave Properties of Light

Key Wave Characteristics

• Wavelength (λ): The distance between two consecutive crests or troughs of a wave. It is typically measured in meters (m), nanometers (nm), or other units of length.

• Frequency (ν): The number of wave cycles that pass a given point per unit time, measured in hertz (Hz), where 1 Hz = 1 cycle/second.

• Amplitude (A): The height of the wave crest or the depth of the trough. Amplitude is related to the intensity or brightness of the wave.

Relationship Between Wavelength and Frequency

Wavelength and frequency are inversely related through the speed of light:

• Speed of light (c): $c = 2.998 \times 10^8$ m/s (in vacuum)

The fundamental equation relating these quantities is:

$c = \lambda \nu$

• $\lambda$ = wavelength (m)

• $\nu$ = frequency (Hz)

• $c$ = speed of light (m/s)

As wavelength increases, frequency decreases, and vice versa.

Visual Representation of Wave Properties

• Different wavelengths correspond to different colors in the visible spectrum.

• Higher amplitude waves are brighter or more intense.

• Frequency determines the type of electromagnetic radiation (e.g., radio, microwave, visible, ultraviolet).

Examples and Applications

• Visible light: Has wavelengths between approximately 400 nm (violet) and 700 nm (red).

• Radio waves: Have much longer wavelengths and lower frequencies than visible light.

• X-rays: Have very short wavelengths and high frequencies.

Summary Table: Wave Properties of Light

Property	Symbol	Definition	Unit
Wavelength	λ	Distance between crests/troughs	m, nm
Frequency	ν	Number of cycles per second	Hz (s-1)
Amplitude	A	Height of crest/depth of trough	varies

Additional info:

• Electromagnetic radiation encompasses a wide range of wavelengths and frequencies, forming the electromagnetic spectrum.

• Wave properties are fundamental to understanding phenomena such as interference, diffraction, and the behavior of light in various media.