Physics Chapter on Light and Electromagnetic Waves

Light

• Light, in the 19th century, was shown to exhibit wave-like behavior. Thomas Young's experiments demonstrated interference patterns.
• Newtonian particle models couldn't explain this, but wave models could.
• James Clerk Maxwell further demonstrated light as part of a spectrum of electromagnetic waves.
• Particles and waves are connected on a fundamental duality level.
• A wave is an oscillation or periodic movement, transporting energy through space (example: a rope or pebble in a pond).

Properties of Light

• Electromagnetic radiation is a form of energy exhibiting wave-like behavior. Examples include X-rays, UV, infrared, microwaves, and radio waves. These together form the electromagnetic spectrum.
• Light moves at a constant speed (c), 3.0 x 10⁸ m/s.

Properties of Light (Continued)

• Wavelength (λ): Distance between corresponding points on adjacent waves. Measured in meters.
• Frequency (ν): Number of waves passing a given point per second, measured in Hertz (Hz).
• Speed, Frequency & Wavelength are related: c = λν

Properties of Waves

• Wavelength (λ): Distance from crest to crest.
• Speed of light (c): 300,000 km/sec (rate of motion of crests or troughs).
• Period (T): Time between passage of successive crests.
• Frequency (ν): Number of crest passages per unit time.
• Amplitude (A): Distance from level of crest to level of trough.

Relationship between wavelength, frequency and speed

• One dimensional sinusoidal waves showing the relationship among wavelength, frequency, and speed.
• The wave with the shortest wavelength has the highest frequency.
• Amplitude is half the height of the wave from peak to trough.

Electromagnetic Spectrum

• The electromagnetic spectrum is the range of all types of electromagnetic radiation.
• Visible light is a small portion.
• Visible light colors have specific frequencies and wavelengths.

Wave Mechanics

• Wavelength: Distance between peaks, measured in nanometers (nm).

• Frequency: Number of peaks passing a point per second, measured in Hertz (Hz).

• The speed of radiation (c) is determined by: c = λν (speed = wavelength x frequency).

Problems using the Speed Equation

• Example: Calculate the frequency of light with a wavelength of 4.257 x 10⁻⁹ cm, given the speed of light is 3.0 x 10⁸ m/s.
• To solve, convert cm to m, substitute values for speed (c) and wavelength ( λ), and then solve for frequency (ν): V = c/λ
• Result: Frequency ≅ 7.0 x 10¹⁶ Hz

Relationship of Energy and Frequency

• The relationship between energy (E) and frequency (ν) of a photon is: E = hν, where h is Planck's constant (6.626 x 10⁻³⁴ J•s).
• Example: Calculate the energy of a photon with a frequency of 4.50 x 10¹⁴ Hz. Energy (E)=hν= 2.98 x 10⁻¹⁹ J

Planck and Einstein

• Planck developed a theoretical expression for blackbody radiation, an ideal emitter.
• Planck's Constant: h = 6.626 x 10⁻³⁴ J•s.
• Einstein's equation: E = mc²

More Contributors and Concepts

• Balmer (Balmer Series): Empirical equation for hydrogen line spectrum.
• Rydberg: Empirical formula predicting hydrogen emission lines.
• Rydberg Constant: 1.097 x 10⁷ m⁻¹.
• De Broglie: Wavelength associated with particles, not just waves.
• Heisenberg Uncertainty Principle and Schrödinger's Equation: Birth of quantum mechanics.

Electron Configuration (Ground State vs. Excited State)

• Ground state: All electrons in lowest available orbitals.
• Excited state: Electrons absorb energy and jump to higher energy levels. (Absorption)
• Electrons fall back to the ground state, releasing energy as visible light. (Emission)

Absorption

• When an electron "jumps" to a higher energy level, it absorbs energy.
• The excited state is a temporary state.

Emission

• The electron falls back to the ground state, emitting energy in the form of light.
• Each element has a unique spectrum (think about a prism).

Light and Atomic Spectra (bright line spectra)

• Atomic emission spectra produce narrow lines of color called bright line spectra.
• Each line corresponds to an exact wavelength.
• The electromagnetic spectrum shows wavelength in meters, frequencies in Hz, and a portion of the spectrum showing wavelengths in nanometers, and colors.

Experiments (Flame Tests)

• Demonstrates the emission spectrum of a substance.
• Elements heated to high temperatures enter the excited state.
• Characteristic emitted color occurs when electrons return to the ground state. This is used to determine metal ion presence in a substance.

Experiments (Spectroscopy)

• Spectroscopy is used for viewing bright line spectra of gases.
• Performed by viewing a gas tube through which an electric current passes.
• A spectroscope (using a prism) separates emitted light into line spectra.

Quantum Theory

• Developed to explain atomic chemical behavior.
• Quantum numbers describe electron location in an atom.
• Quantum: Minimum quantity of energy lost or gained by an atom.

Electrons

• Found in orbitals, three-dimensional regions around the nucleus.
• Orbitals indicate probable electron location.
• Chemical properties are based on the number of outer energy levels.

Electrons (Continued)

• Electrons occupy the lowest sublevel possible.
• Sublevels are orbitals with different shapes (s, p, d, f).

The Quantum Model of the Atom

• The study of emission spectra of elements leads to the development of principal quantum level and the model of electron arrangement.
• Three levels are: 1. principal quantum level (n), 2. sublevel (s, p, d, f), 3. orbital (s=1, p=3, d=5, f=7).

Rules of Occupancy

• Seven main energy levels.
• Number of sublevels = the principle quantum number (e.g., n=3 has 3 sublevels).
• Number of orbitals per sublevel: s=1, p=3, d=5, f=7.
• Two electrons per orbital.
• Maximum electrons per main energy level = 2n².

Putting it Together

• "n" describes the orbital size and principle energy level of the shell..
• There are n² orbitals per shell.
• Size of the orbital increases as n increases, and electrons are further away from the nucleus.

Electron Configurations and Periodic Table

• The table orders elements by similar physical and chemical properties.

• Groups have similar valence electron configurations.

• Valence electrons are those of the highest principle energy level (highest n value).

• These are important for chemical reactions.

• Example: Gallium (Ga) [Ar]4s²3d¹⁰4p¹

• The completely filled 3d orbitals count as core, not valence electrons.

Transition Elements

• Metals in which the last electron added is in a d orbital.
• Valence electrons : ns and (n-1)d electrons.
• Example: Vanadium (V) [Ar] 4s²3d³

Inner Transition Elements

• Metals in which the last electron added is in an f orbital.
• Valence electrons: ns,(n-2)f , and if present (n-1) d electrons.
• Example: Promethium (Pm) [Ar] 6s²4f⁵

Electron Configurations of Ions

• Ions are formed when atoms gain or lose electrons.
• Cations (positive ions) have electrons removed. Main group elements lose the externally added electrons first, transition metals lose ns electrons first then (n-1) d.
• Anions (negative ions) have electrons added. Added according to the Aufbau principle.

Predicting Electron Configurations of Ions

• Example calculation to determine electronic configurations of ions.

Summary

• The above study notes explain the periodicity observed in the periodic table, which is due to patterns in electron configurations.

This quiz covers the fundamental properties and behaviors of light as explored in the 19th century. It includes topics such as wave-particle duality, the electromagnetic spectrum, and the measurements of wavelength and frequency. Test your understanding of these concepts related to light and electromagnetic radiation.