3.1

Introduction to Light and Quantum Mechanics

  • Light is defined as electromagnetic radiation, a type of energy.

  • Fundamental entity of light: Photons.

    • Photons are packets of energy that comprise light.

  • Photons exhibit oscillating electric and magnetic fields.

    • Einstein's contribution: introduced the concept of photons as energy packets.

Speed of Light

  • The speed of light, denoted as c.

    • Common value: c=3.00imes108 m/sc = 3.00 imes 10^8 \text{ m/s}.

    • More accurate value: c=2.998imes108 m/sc = 2.998 imes 10^8 \text{ m/s}.

Properties of Photons

Concepts of Wavelength and Frequency

  • Photons are characterized by their wavelength and frequency.

    • Relation: Energy is correlated with both wavelength and frequency.

Wavelength

  • Wavelength (denoted as λ).

    • Defined as the distance between consecutive peaks (crests) of the wave.

    • Measurement unit: meters (m).

Frequency

  • Frequency (denoted as ν).

    • Defined as the number of cycles (waves) passing a stationary point per second.

    • Measurement unit: Hertz (Hz), equivalent to cycles per second.

Amplitude

  • Amplitude is the peak height of the wave.

    • Impacts the intensity of light; the larger the amplitude, the brighter the light.

Electromagnetic Spectrum

  • The electromagnetic spectrum encompasses all types of electromagnetic radiation.

  • Waves are classified based on their wavelength.

Regions of the Electromagnetic Spectrum

  1. Radio Waves

    • Wavelength: Approximately 10−1 m10^{-1} \text{ m}.

    • Applications: Radio transmission.

  2. Microwaves

    • Wavelength: Between 10−1 m10^{-1} \text{ m} and 10−3 m10^{-3} \text{ m}.

    • Applications: Microwave ovens (energizes bonds in water molecules).

  3. Infrared

    • Wavelength: Between 10−3 m10^{-3} \text{ m} and 10−6 m10^{-6} \text{ m}.

    • Applications: Remote controls, thermal imaging.

  4. Visible Light

    • Wavelength: Roughly between 400 nm (10−7 m10^{-7} \text{ m}) and 750 nm (10−6 m10^{-6} \text{ m}).

    • Colors represented: ROYGBIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet).

  5. Ultraviolet

    • Wavelength: Approximately between 10−8 m10^{-8} \text{ m} and 10−9 m10^{-9} \text{ m}.

    • Applications include UV lamps and sterilization.

  6. X-rays

    • Wavelength: Around 10−11 m10^{-11} \text{ m}.

    • Applications: Medical imaging (can penetrate tissues).

  7. Gamma Rays

    • Wavelength: Roughly 10−15 m10^{-15} \text{ m}.

    • Applications: Cancer treatment and radioactive decay.

Energy Relation in Waves

  • The relationship between wavelength, frequency, and energy can be expressed as:

    • ν=cλ\nu = \frac{c}{\lambda}

    • \lambda = \frac{c}{3nu}

  • Energy of a photon can be found using:

    • E=h<br>uE = h <br>u

    • with Planck's constant h=6.626×10−34 Jsh = 6.626 \times 10^{-34} \text{ Js}.

  • Energy per particle is typically expressed in joules (J).

Example Calculation

Light from Sodium Vapor Lamps

  • The orangish glow from sodium vapor lamps occurs at a wavelength of 582 nm.

  • Objective: Calculate frequency and energy per mole of photons.

Step 1: Calculate Frequency

  • Convert 582 nm to meters.

    • 582 nm=582×10−9 m582 \text{ nm} = 582 \times 10^{-9} \text{ m}.

  • Use the frequency equation:

    • ν=cλ=3.00×108 m/s582×10−9 m\nu = \frac{c}{\lambda} = \frac{3.00 \times 10^8 \text{ m/s}}{582 \times 10^{-9} \text{ m}}

    • Result: ν=5.15×1014 Hz\nu = 5.15 \times 10^{14} \text{ Hz}.

Step 2: Calculate Energy Per Mole

  • Energy per photon:

    • E=hν=(6.626×10−34 Js)(5.15×1014 Hz)E = h \nu = (6.626 \times 10^{-34} \text{ Js})(5.15 \times 10^{14} \text{ Hz})

    • Result: E=3.41×10−19 J/photonE = 3.41 \times 10^{-19} \text{ J/photon}.

  • Convert to per mole:

    • Using Avogadro's number, NA=6.022×1023 molecules/molN_A = 6.022 \times 10^{23} \text{ molecules/mol}:

    • Energy per mole=3.41×10−19 J/photon×NA=2.06×105 J/mol\text{Energy per mole} = 3.41 \times 10^{-19} \text{ J/photon} \times N_A = 2.06 \times 10^5 \text{ J/mol}.

Photoelectric Effect

  • Discovered by Robert Millikan.

  • Photoelectric Effect: The emission of electrons from a metal when exposed to light.

  • Each metal has a threshold frequency below which no electrons are emitted.

Threshold Frequency and Binding Energy

  • Threshold frequency is tied to binding energy, denoted as Φ.

  • Relationship: Φ=h⋅νthreshold\Phi = h \cdot \nu_{threshold}.

  • Explains why different metals have different threshold frequencies based on how tightly electrons are held to nuclei.

Diagram of the Photoelectric Effect

  • Experiment setup involves a metal surface between two electrodes.

  • When the appropriate frequency of light is applied, electrons are emitted and current flows.

Kinetic Energy of Ejected Electrons

  • Kinetic energy (KE) of emitted electrons:

    • KE=h⋅ν−ΦKE = h \cdot \nu - \Phi.

Example of Binding Energy Calculation

  • Given: Threshold frequency νthreshold=1.23×1015extHz\nu_{threshold} = 1.23 \times 10^{15} ext{ Hz}.

  • Calculate binding energy per mole.

Step 1: Calculate Binding Energy per Electron

  • Φ=h⋅νthreshold\Phi = h \cdot \nu_{threshold}

  • Calculation results in Φ=8.14×10−19 J/electron\Phi = 8.14 \times 10^{-19} \text{ J/electron}.

Step 2: Convert to Per Mole

  • Φ<em>mole=8.14×10−19 J/electron×N</em>A=4.90×105 J/mol\Phi<em>{mole} = 8.14 \times 10^{-19} \text{ J/electron} \times N</em>A = 4.90 \times 10^5 \text{ J/mol}, or 490 kJ/mol.

Conclusion

  • Understanding light as electromagnetic radiation and its properties is fundamental to quantum mechanics.

  • The relationship between wavelength, frequency, and energy is essential for calculations in quantum chemistry.