Quantum Mechanics in Chemistry: Photoelectric Effect

Introduction

• Quantum mechanics offers fascinating insights into the behavior of metals when exposed to light.
• Key concept: Ejection of electrons from metal surfaces through light exposure.

Photoelectric Effect

• Definition: When light of the right frequency hits a metal, electrons can be ejected from its surface.
• Conditions:
  • Light energy must exceed a certain threshold (work function) specific to the metal.
  • Energy of light > Work function = Electrons ejected.
  • Energy of light < Work function = No electrons ejected.
• Excess Energy: If light energy > work function, excess energy converts into kinetic energy of electrons.

Key Equation of the Photoelectric Effect

• Components:
  • Kinetic Energy (KE): Dependent on the velocity of ejected electrons.
  • Photon Energy: Energy of the incoming light.
  • Work Function: Minimum energy required to free an electron from the metal.
• Equation: KE = Photon Energy - Work Function.

Experiment Scenario

• Light (red) shining on metal surface.
• Given: Light energy < Work function.
  • Result: Light intensity increase only adds more photons, not more energy per photon.
  • Conclusion: No electron ejection regardless of light intensity.

Derivation of Electron Velocity

• Objective: Derive the formula for velocity of an ejected electron.
• Kinetic Energy Formula: KE = 1/2 * mass * velocity^2.
• Steps to Solve for Velocity:
  1. Multiply both sides by 2.
  2. Divide by mass.
  3. Take square root of both sides.
• Formula Derived: Velocity = sqrt((2 * KE) / mass).

Application Example

• Given: Kinetic energy = 7.2 * 10^-20 J.
• Mass of an Electron: 9.11 * 10^-31 kg.
• Calculation: Plug into the velocity formula.
• Result: Speed of the photoelectron ≈ 397,000 m/s.
• Remark: Photoelectron, a quantum particle, moves very fast.

Conclusion

• The photoelectric effect illustrates fundamental principles of quantum mechanics in chemistry.
• Understanding these principles enables the calculation of significant parameters like electron velocity post-ejection.