97 The Photoelectric Effect

The Photoelectric Effect

One of the experiments that fundamentally changed our understanding of light is the photoelectric effect. When light shines on certain materials, it can eject electrons from their surface. This phenomenon demonstrated that light behaves not only as a wave but also as a collection of discrete packets of energy called photons, providing some of the strongest early evidence for quantum mechanics. The photoelectric effect is widely used in modern technology. Light sensors in cameras, automatic doors, smoke detectors, and photovoltaic (solar) cells all rely on the ability of light to release or move electrons within a material. Similar principles are also used in scientific instruments and medical imaging equipment.

The experiment shown in Figure 97.1 has been used for more than a century to investigate the interaction between light and matter. The apparatus consists of an evacuated tube containing a metal plate and a collector electrode connected to a variable voltage source. When electromagnetic radiation strikes the metal plate, electrons may be emitted from its surface. These emitted electrons, called photoelectrons, travel toward the collector, producing an electric current that can be measured. The voltage between the plate and the collector can be adjusted to oppose the motion of the emitted electrons. As the retarding voltage becomes more negative, fewer electrons have enough kinetic energy to reach the collector. The voltage required to stop even the fastest electrons provides a direct measurement of their maximum kinetic energy. For example, if a retarding potential of −3.00 V is just sufficient to stop the electrons, their maximum kinetic energy is 3.00 eV. The number of emitted electrons can also be measured by recording the current flowing through the circuit. Increasing the brightness (intensity) of the light generally increases the number of emitted electrons, making this type of device useful as a light detector or light meter.

The true importance of the photoelectric effect lies not in the experiment itself, but in the conclusions that Albert Einstein drew from it in 1905. Classical wave theory predicted that increasing the intensity of light should eventually provide enough energy to eject electrons from any material. Experimental observations, however, contradicted this prediction. Einstein proposed that electromagnetic radiation is itself quantized. Instead of being a continuous flow of energy, light consists of individual particles, or photons, each carrying a specific amount of energy that depends only on the light's frequency.

where E is the energy of a photon, f is its frequency, and h is Planck's constant. This idea resembles Planck's explanation of blackbody radiation, but it goes one step further. Planck proposed that matter exchanges energy in discrete amounts. Einstein proposed that the electromagnetic radiation itself is quantized. In other words, light is composed of individual photons rather than being an entirely continuous wave. Each photon carries an energy equal to hf. When a photon interacts with an electron, the electron absorbs the photon's entire energy in a single event. Because ordinary light sources emit enormous numbers of photons every second, we normally perceive light as a continuous beam rather than as individual particles. In the next section, we will examine photons in greater detail and explore how their energies vary across the electromagnetic spectrum. First, however, we will use Einstein's photon model to explain the remarkable observations of the photoelectric effect.

The photoelectric effect exhibits several remarkable properties that cannot be explained by treating light as a purely classical electromagnetic wave. Instead, they are naturally explained if light consists of individual photons that interact one at a time with individual electrons. For simplicity, we will consider monochromatic light, in which every photon has the same energy, [latex]E=hf[/latex].

1. There is a threshold frequency. Every material has a minimum frequency, called the threshold frequency ([latex]f_0[/latex]), below which no electrons are emitted, regardless of how intense the light is. If the energy of an individual photon is too small to overcome the attraction holding an electron within the material, the electron cannot escape. Classical wave theory predicts that increasing the light intensity should eventually provide enough energy, but experiments show that this never happens.
2. Electrons are emitted without delay. As soon as a photon with sufficient energy strikes the material, an electron is ejected almost instantaneously. There is no measurable waiting time while energy accumulates. This immediate response is exactly what we expect if a single photon transfers all of its energy directly to a single electron.
3. The number of emitted electrons depends on light intensity. Increasing the intensity of monochromatic light increases the number of photons striking the surface each second. Consequently, more electrons are emitted per unit time. However, the energy of each emitted electron remains unchanged because each electron still absorbs only one photon.
4. The maximum kinetic energy depends only on the photon energy. Increasing the light intensity does not increase the maximum kinetic energy of the emitted electrons. Instead, it simply increases the number of emitted electrons. The kinetic energy depends only on the energy of the individual photons, which is determined by the light's frequency.
5. Einstein's photoelectric equation. When a photon is absorbed by an electron, part of the photon's energy is required to free the electron from the material. The remaining energy becomes the electron's kinetic energy.
   [latex]K_{\mathrm{max}}=hf-\mathrm{BE},[/latex]

   where [latex]K_{\mathrm{max}}[/latex] is the maximum kinetic energy of the emitted electron, [latex]hf[/latex] is the energy of the incident photon, and [latex]\mathrm{BE}[/latex] is the binding energy, also known as the work function, of the material. The binding energy is related to the threshold frequency by

   [latex]\mathrm{BE}=hf_0.[/latex]

   If the photon energy is less than the binding energy, no electrons are emitted. If the photon energy exceeds the binding energy, the excess energy appears as kinetic energy of the emitted photoelectron. Figure 97.3 illustrates this relationship graphically.

Einstein's explanation of the photoelectric effect marked one of the major turning points in modern physics. By proposing that electromagnetic radiation is composed of discrete particles called photons, he successfully explained experimental observations that classical wave theory could not. His model showed that each photon interacts with a single electron, transferring all of its energy in one event. Although Einstein introduced the photon concept to explain the photoelectric effect, the idea applies to all electromagnetic radiation. Radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays can all be described as streams of photons. The energy of each photon depends only on its frequency, while the intensity of the radiation depends on the number of photons arriving each second. In the next section, we will see that many properties of electromagnetic radiation can only be understood from the photon perspective. For example, the biological effects of ultraviolet radiation and the penetrating power of X-rays depend on the energy carried by individual photons rather than simply on the total intensity of the radiation.

Einstein proposed the photon model in 1905, the same year he published his groundbreaking work on special relativity. Although he is most widely recognized for relativity, it was his explanation of the photoelectric effect that earned him the 1921 Nobel Prize in Physics. His work laid one of the foundations of quantum mechanics and transformed our understanding of the interaction between light and matter.