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.

Definition of the Photoelectric Effect

  • The photoelectric effect occurs when light shines on a metal surface, causing electrons to be ejected from the surface.

  • This phenomenon is based on light possessing both wave-like and particle-like properties, as proposed by Albert Einstein.

  • Photons are packets of light energy.

Photon Energy Equation

  • The energy (E) of a photon is calculated using the formula:

    • E = h * v

      • E = energy of the photon

      • h = Planck's constant (6.626 × 10⁻³⁴ Js)

      • v = frequency of the light

Binding Energy

  • When measuring the energy required to eject an electron, one can deduce the binding energy, which indicates how tightly an electron is held in an atom.

  • Higher energy values suggest that electrons are closer to the nucleus or indicate a higher nuclear charge.

Threshold Frequency (vo)

  • Threshold frequency (vo): The minimum frequency required to eject electrons from the metal surface.

  • Lower energy frequencies, such as red light, do not have enough energy to remove electrons.

  • If light frequency exceeds the threshold, electrons will be emitted with increased kinetic energy.

Threshold Wavelength (λmax)

  • The threshold wavelength (λmax) represents the longest wavelength that can still eject an electron.

  • Any wavelength shorter than λmax will have sufficient energy for electron ejection.

Energy and Wavelength Relationship

  • The energy is proportional to frequency but inversely proportional to wavelength:

    • Energy ∝ Frequency

    • Energy ∝ 1/Wavelength

  • Wavelength is measured in nanometers (1 nm = 1 x 10⁻⁹ meters).

Summary of the Photoelectric Effect

  • The energy of the incident photons must exceed a certain threshold for electrons to be emitted.

  • This condition can be satisfied by having a frequency higher than the threshold frequency or a shorter wavelength than the threshold wavelength.

  • If the minimum energy condition is met, the kinetic energy of the emitted photoelectrons depends on the excess energy of the incident light.

Threshold Energy Example

  • For a metal surface, electrons are first ejected when the photon energy is 3.3 x 10⁻¹⁹ J.

  • Questions to consider:

    • What is the frequency of light that corresponds to this energy?

    • Calculate the wavelength for light with energy of 3.3 x 10⁻¹⁹ J.

    • Identify the color of this light.

Practice Problem

  • Given that CuSO4 solutions absorb light at 635 nm, calculate the approximate energy of one photon of this light.