3.12 In-Depth Notes on the Photoelectric Effect and Related Calculations

Overview of the Photoelectric Effect

• The photoelectric effect occurs when light interacts with materials, usually metals, causing electrons to jump energy levels.
• When energy from ultraviolet or visible light is absorbed by atoms:
  • Electrons absorb this energy, moving from ground state (normal energy levels) to an excited state (higher energy levels).
  • This excited state is unstable; electrons eventually return to the ground state, emitting energy in the form of visible light.
• Photons are particles of light ejected when electrons fall to ground state.

Characteristics of Electromagnetic Waves

• All waves (including those in the electromagnetic spectrum) share several characteristics:
  • Wavelength (BB): Distance between two peaks or troughs in a wave.
  • Frequency (BD): Number of waves passing a point per second, measured in hertz (Hz or (s^{-1})).
  • Speed of Light (C): All waves travel at the same speed, which is a constant (approximately $3.00 \times 10^8 \text{ m/s}$).

Important Equations

• Wave Equation:
  • $C = \lambda \cdot \nu$
  • Where (C) is the speed of light, (\lambda) is the wavelength (in meters), and (\nu) is the frequency (in Hz).
• Energy Equation:
  • $E = h \cdot \nu$
  • Where (E) is energy (in joules), (h) is Planck's constant (approximately $6.626 \times 10^{-34} \text{ J s}$), and (\nu) is frequency.
• Note: The wavelength must be converted to meters when plugging into these equations.

Sample Problem 1: Photoelectron Spectrum Calculation

• Task: Calculate the wavelengths of electromagnetic radiation needed to remove an electron from the valence shell of an atom.
• Approach:
  1. Identify the valence energy level from the photoelectron spectrum (PES) graph.
  2. Use the energy equation to calculate frequency first, then use the wave equation to find wavelength in meters.

Sample Problem 2: Ozone Molecule Energy Calculation

• Given: Ozone absorbs a photon with a specific frequency.
• Task: Calculate energy absorbed per photon:
  • Use the energy equation: $E = h \cdot \nu$.
  • Typical calculations are per photon.

Understanding Bond Energy and Avogadro's Number

• Given that minimum energy to break an O-O bond in ozone is $387 \text{ kJ/mol}$:
  • Convert kJ to joules (1 kJ = 1000 J) to get the energy for one mole of bonds.
  • To find energy for one bond:
  1. Calculate energy per bond using Avogadro's number (approximately $6.022 \times 10^{23} \text{ molecules/mol}$).
  2. Verify if the energy from the photon calculated previously is sufficient to break one bond.