3.12+The+Photoelectric+Effect

3.12 The Photoelectric Effect

Enduring Understanding

  • SAP-8: Spectroscopy can determine the structure and concentration in a mixture of a chemical species.

Learning Objective

  • SAP-8B: Explain the properties of an absorbed or emitted photon in relationship to an electronic transition in an atom or molecule.

Overview of the Photoelectric Effect

  • Definition: When light shines on the surface of metal, electrons can be ejected from the surface (photoelectric effect).

  • Nature of Light: Light exhibits both wave-like and particle-like properties, as described by Einstein.

  • Photons: Light is composed of photons which are defined by energy measurement using the formula:

    • E = energy

    • h = Planck's constant

    • v = frequency

Energy and Electron Ejection

  • Energy Input and Electron Output: Energy (from light) is required to remove electrons, indicating how tightly they are held within the atom (binding energy).

  • Greater Energy Implications: Higher energy values indicate:

    • Electrons are closer to the nucleus, or

    • The nucleus has a higher charge.

Threshold Frequency and Wavelength

  • Threshold Frequency (vo): The minimum frequency of light required to eject an electron.

    • Red light does not provide enough energy; frequencies above this threshold will eject electrons with increased kinetic energy.

  • Threshold Wavelength (λmax): The longest wavelength that can still eject electrons, with shorter wavelengths providing sufficient energy.

Energy, Frequency, and Wavelength

  • Energy-Frequency Relationship: Energy is directly proportional to frequency and inversely proportional to wavelength.

  • Wavelength Measurement: Wavelength is commonly measured in nanometers (1 x 10^-9 meters).

Summary of the Photoelectric Effect

  • Minimum Energy Requirement: The photon energy must meet or exceed the threshold frequency (vo) or must have a shorter wavelength than λmax for electron ejection.

  • Kinetic Energy Dependency: If the minimum energy requirements are met, the kinetic energy of emitted photoelectrons is determined by the energy of the incident light.

Calculations Involving the Photoelectric Effect

  • When a metal surface is exposed to light with increasing frequency and energy, electrons begin to ejected when photon energy reaches 3.3 x 10^-19 J.

    • Calculate:

      • Frequency corresponding to 3.3 x 10^-19 J.

      • Wavelength for light with 3.3 x 10^-19 J, and

      • Identify the color of this light.

Example Calculation

  • CuSO4 Solutions: Absorb light at a wavelength of 635 nm.

    • Task: Calculate the approximate energy of one photon of this light.