Wave Properties of Electromagnetic Radiation

Electromagnetic Radiation as "Radiant Energy" (Light)

Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate through space as waves. Light is a form of electromagnetic radiation and can be described by its wave properties.

• Wavelength (λ): The distance between two consecutive peaks (or troughs) of a wave. Measured in meters (m), nanometers (nm), or angstroms (Å).

• Frequency (ν): The number of wave cycles that pass a given point per second. Measured in hertz (Hz), where 1 Hz = 1 s-1.

• Speed (c): The speed of light in a vacuum is a constant, m/s.

Relationship between speed, wavelength, and frequency:

Where is the speed of light, is the wavelength, and is the frequency.

Different wavelengths correspond to different colors of visible light.

• Longer wavelength = lower frequency

• Shorter wavelength = higher frequency

Example: If three waves (A, B, C) are shown, the one with the longest wavelength has the lowest frequency.

Practice: Frequency-Wavelength Calculations

To find the wavelength of red light emitted by a barcode scanner at a frequency s-1:

Substitute values:

Result: m (or 649 nm)

The Photoelectric Effect

What Happens When Light Shines on Metals?

The photoelectric effect describes the emission of electrons from a metal surface when light of sufficient frequency shines on it. This phenomenon provided evidence for the particle nature of light.

• If the frequency of light () is below a threshold value (), no electrons are emitted, regardless of intensity.

• If , electrons are emitted. Increasing intensity increases the number of electrons emitted, but not their energy.

• If , electrons are emitted with kinetic energy ().

Kinetic energy of emitted electrons:

Where is Planck's constant ( J·s), is the frequency of incident light, and is the work function (minimum energy required to remove an electron from the metal).

Energy Quantization and Photons

Energy is absorbed or emitted in discrete packets called quanta. A photon is a quantum of electromagnetic radiation.

Energy of a photon:

Where is Planck's constant and is the frequency.

• Energy is quantized: only certain energy values are allowed.

• Electromagnetic radiation exhibits both wave and particle properties (wave-particle duality).

Practice: Energy-Frequency-Wavelength Calculations

Example: UV radiation can break chemical bonds. To find the longest wavelength of light that can break a C–C bond (energy required: 348 kJ/mol):

1. Convert energy per mole to energy per photon:

2. Use to solve for .

Result: m (or 579 nm)

The Electromagnetic Spectrum

Overview and Classification

The electromagnetic spectrum encompasses all types of electromagnetic radiation, classified by wavelength and frequency.

Visible light is only a small portion of the spectrum, ranging from about 400 nm (violet) to 700 nm (red).

Absorption and Emission Spectra

Discrete Spectral Lines and Element Identification

When a hydrogen lamp emits light, it produces discrete wavelengths (lines), not a continuous spectrum. These lines are unique to each element and are used for identification.

• Balmer and Rydberg developed equations to predict the wavelengths of hydrogen's spectral lines.

• Absorption/emission spectra are unique to each element and are used in flame tests and instrumental analysis.

The Bohr Model of the Atom

Quantized Energy Levels in Hydrogen

The Bohr model proposes that electrons in a hydrogen atom move in certain allowed circular orbits around the nucleus, each with a specific energy. Energy levels are quantized, and electrons can only occupy these discrete levels.

Energy of an electron in the nth energy level:

J

Energy change for a transition between levels:

J

• Ground state: Lowest energy level ()

• Excited state: Any energy level higher than ground state ()

• Energy is absorbed when an electron moves from lower to higher energy level.

• Energy is emitted when an electron moves from higher to lower energy level.

Example: An electron transition from to emits energy as a photon.

Practice: Identifying Energy Level Transitions

Which energy level transitions result in absorption or emission of a photon?

• Absorption: Electron moves to a higher energy level (e.g., to )

• Emission: Electron moves to a lower energy level (e.g., to )

Shortest wavelength (highest energy) photon: Largest energy difference between levels.

Summary Table: Key Equations

Additional info: These notes cover foundational concepts in atomic structure, electromagnetic radiation, and quantum theory, which are essential for understanding chemical bonding and periodic properties in General Chemistry.