Chapter 8 Lecture Notes - CHEM 1113 Broering

Chapter 8: Quantum Theory

Wave Nature of Light

• Electromagnetic Radiation:

  • Description: Any form of radiant energy embodied in oscillating electric and magnetic fields.

  • Components:

    • Magnetic Field: Region where magnetic particles experience a force.

    • Electric Field: Region where electrically charged particles experience a force.

Electromagnetic Spectrum

• Visible Light: A small component of the broader spectrum of radiant energy.

Frequency and Wavelength

• Wavelength (λ):

  • Definition: Distance between successive wave crests, typically measured in meters (m) or nanometers (nm).

  • Inverse relationship with frequency.

• Frequency (ν):

  • Definition: Number of wave crests that pass a fixed point per second, measured in Hertz (Hz).

  • Relationship: Longer wavelengths correlate with lower frequencies and shorter wavelengths with higher frequencies.

• Amplitude:

  • Definition: Vertical distance from the midline of the wave to its peak or trough.

Speed of Light

• Speed of Light (c):c = 2.998 × 10⁸ m/s

• Relationship: Wavelength × Frequency = Speed of Light.

  • Rearrangement: Frequency = Speed of Light / Wavelength.

Example Problem (Emission Calculation)

• Given frequency of light (7.30 × 10¹⁴ s⁻¹):

  • Formula: λ = c / ν = 2.998 × 10⁸ m/s / 7.30 × 10¹⁴ s⁻¹

  • Result: λ = 4.11 × 10⁻⁷ m or 411 nm

Practice Problem (Frequency Calculation)

• Given wavelength (511 nm):

  • Rearranging ν = c / λ:

  • ν = 2.998 × 10⁸ m/s / 5.11 × 10⁻⁹ m = 5.87 × 10¹⁴ s⁻¹

The Electromagnetic Spectrum

• The electromagnetic spectrum includes various forms of light differing in their wavelengths and frequencies:

  • From longer wavelengths to shorter: Radio Waves, Microwaves, Infrared, Visible Light, Ultraviolet, X-rays, Gamma Rays.

Max Planck and the Quantum Theory

• Classical physics posited radiant energy as continuous.

• Max Planck: Proposed that radiant energy is emitted or absorbed in discrete quantities (quanta).

  • Quantum: Smallest quantity of energy that can be emitted or absorbed.

The Particle Nature of Light

• Energy of a Quantum: E = hν (where h is Planck's constant).

• Planck's Constant: h = 6.626 × 10⁻³⁴ J•s

• Energy Quantization: Like steps in a staircase, energy is emitted in whole-number multiples of specific values.

Photons of Energy

• Definition: Photons represent the smallest units of electromagnetic radiation, bearing quantum energy.

Practice Problem: Photon Energy Calculation

• Given wavelength (3.00 × 10⁻⁷ m):

  • Energy (E) can be calculated using E = hν.

  • Result: Energy of one UV photon is 6.62 × 10⁻¹⁹ J.

  • Energy per mole of photons: 3.98 × 10² J/mol.

The Photoelectric Effect

• Einstein's Contribution: Proposed the particle theory showcasing light as a stream of photons.

• Photoelectric Effect: The release of electrons from a material when exposed to light of certain frequencies.

  • Threshold Frequency (ν₀): Minimum frequency required to release electrons from a material.

Threshold Experiment of the Photoelectric Effect

• If light frequency is greater than ν₀, electrons will be ejected, with excess energy converting to kinetic energy (KE).

Work Function (Φ)

• Definition: Minimum energy needed to eject photoelectrons from a surface.

  • Relationship: KE = hν - Φ

Electron Energy Calculations (Example Problem)

• Given work function (3.78 × 10⁻¹⁹ J):

  • Step to find threshold frequency from work function using ν = Φ/h.

  • Calculating wavelength corresponding to threshold frequency.

Atomic Spectra: Absorption and Emission

• Emission Spectra: Observable bright lines at specific wavelengths when an atom emits energy.

• Absorption Spectra: Dark lines present in the spectrum when an atom absorbs light.

• Relationship: Dark lines in absorption correspond to the bright lines in emission spectra of the same element.

Bohr Model of the Atom

• Describes electrons as revolving around the nucleus in definite orbits/energy levels.

• Ground State: Minimum energy state, and excited states are any states above this.

• Electron Transitions: Movement between energy states can emit or absorb radiation.

Chapter 8: Quantum Theory

Wave Nature of Light

• Electromagnetic Radiation: Radiant energy in oscillating electric/magnetic fields.

  • Magnetic Field: Region affecting magnetic particles.

  • Electric Field: Region affecting charged particles.

• Electromagnetic Spectrum: Visible light is a small part.

Frequency and Wavelength

• Wavelength (λ): Distance between wave crests (m or nm). Inversely related to frequency.

• Frequency (ν): Number of crests per second (Hz). Long wavelengths = low frequency, short wavelengths = high frequency.

• Amplitude: Distance from wave midline to peak.

Speed of Light

• c = 2.998 × 10⁸ m/s. Relationship: Wavelength × Frequency = Speed of Light.

Example Problem

• Frequency (7.30 × 10¹⁴ s⁻¹) → λ = 4.11 × 10⁻⁷ m (411 nm).

• Practice Problem: Given wavelength (511 nm) → ν = 5.87 × 10¹⁴ s⁻¹.

The Electromagnetic Spectrum

• Ranges from Radio Waves to Gamma Rays.

Max Planck and Quantum Theory

• Challenged classical physics; proposed energy emitted in discrete quantities (quanta).

• Quantum: Smallest energy unit, E = hν (h = Planck's constant, 6.626 × 10⁻³⁴ J•s).

Photons of Energy

• Photons: Smallest units of electromagnetic radiation.

• Energy of a UV photon for λ = 3.00 × 10⁻⁷ m is 6.62 × 10⁻¹⁹ J.

The Photoelectric Effect

• Light as photons; electrons released from materials at specific frequencies.

• Threshold Frequency (ν₀): Minimum frequency for electron release.

• Work Function (Φ): Minimum energy to eject electrons, KE = hν - Φ.

Atomic Spectra

• Emission Spectra: Bright lines from energy emission.

• Absorption Spectra: Dark lines from energy absorption.

Bohr Model of the Atom

• Electrons exist in defined orbits. Ground state: lowest energy; excited states: higher energy. Transitions emit/absorb radiation