Photoelectric Effect

Student Expectation

The student is expected to describe the photoelectric effect and the dual nature of light.

Key Concepts

• • Light has both wave and particle characteristics.

  • Light shows behavior characteristic of waves, such as diffraction and interference.

  • Light acts as a quantum particle, or photon, carrying a discrete amount of energy. The amount of energy the photon carries depends upon its wavelength.

  • When the photon has enough energy, its collision with an electron will free the electron from the surface of a material. This is called the photoelectric effect.

  • Increasing the number of photons by increasing the light intensity leads to an increase in the number of ejected electrons, not an increase in their energy. This supports the quantum or particle nature of light.

THE PHOTOELECTRIC EFFECT

THE DUEL NATURE OF LIGHT

The Photoelectric Effect - Evidence for Light as a Particle

Light has a dual nature, and hence it has both the properties of a wave and a particle. In 1887, Heinrich Hertz observed a property of light called the photoelectric effect that wave theory could not explain. The photoelectric effect is the observation that when certain wavelengths of light strike a piece of metal, the electrons in the metal move, creating a current.

In 20th century physics, two ideas stand out as being totally revolutionary: relativity and quantum theory. Although Einstein is best known for his theory of relativity, he also played a major role in developing quantum theory. And it was his contribution to quantum theory - explaining the photoelectric effect - which won Einstein his Nobel Prize in 1921. He realized that the beam of light must be liberating electrons from one metal plate, which are attracted to the other plate by electrostatic forces resulting in a current flow. Using this knowledge Einstein thought light could also be described as discrete photons, not in continuous waves. He showed light acts as a quantum particle carrying a discrete amount of energy (E). The amount of energy the light particle carries depends upon its wavelength.

Formula for the energy of a light particle.

• • Photon Energy Depends on Frequency Not Light Intensity: In the equation, “h” is the Planck constant and “f” is the frequency of incident photon. When the photon has enough energy, its collision with an electron will free it from the surface of a material. If you increase the intensity of the light, more photons are colliding with and ejecting electrons, but the energy being carried and transferred by the photons is the same. This explained why the energy of photoelectrons was dependent only on the frequency of the incident light and not on its intensity: a low-intensity, high-frequency source could supply a few high energy photons. This supports the quantum or particle nature of light. The ejected electrons maximum kinetic energy can be expressed as

Formula for the maximum kinetic energy of an ejected electron.

In which “W” means the work function. It is the minimum energy for an electron to leave a metal surface, expressing as

Formula for the minimum energy for an electron to leave a metal surface.

And this frequency is the metal’s threshold frequency.

Formula for the maximum kinetic energy of an ejected electron.

Light has a dual nature, and hence it has both the properties of a wave and a particle. The photoelectric effect helps to explain the quantum or particle nature of light and thus supports the argument for the dual nature of light.

According to the wave theory, more light shined on a surface would provide more energy to the electrons being ejected from the surface. However, this does not happen in experiments, so the wave theory cannot explain the photoelectric effect. The frequency and wavelength have the relationship:

Formula for the speed of light.

This tells us the product of wavelength and frequency is a constant that is equal to the speed of light. Thus, we have

Formula for the maximum kinetic energy of an ejected electron.

From this equation, we see the kinetic energy of an escaped electron depends upon the photons wavelength “λ” only, not on the number of photons.

Summary of Photoelectric Effect Factors

The two factors affecting maximum kinetic energy of photoelectrons are the frequency of the incident radiation and the material on the surface. The energy-frequency relation is constant for all materials. Below the threshold frequency photoemission does not occur. Each curve has a different intercept on the energy-axis, which shows that threshold frequency is a function of material. Most elements have threshold frequencies in the ultraviolet, but a few dip down low enough to be visible, with potassium’s lying somewhere between yellow and green. The materials with the lowest values are all semiconductors with some even reaching down into the near infrared.

Behavior of Light as a Wave

• • Wave Reflection and Refraction: Light also shows properties characteristic of waves. Reflection is the bouncing of light rays off a surface. Refraction is the change in the direction of light as it moves at an angle from one material into another. Both of these phenomena can be explained if light is composed of waves. However, they can also be explained if light is assumed to be a stream of particles.

  • Wave Diffraction, Interference, and Polarization: Other phenomena can be explained only if light is composed of waves. Diffraction is the spreading of waves that move through a gap or around a boundary and display wave interference. Polarization is the process of restricting light so it vibrates in a chosen direction. As shown in the figures below, if light had only particle-like properties, it would not exhibit diffraction or polarization.