Modern Physics

# Photoelectric effect

Photoelectric effect is a quantum phenomenon in which light behaves like particles, known as photons. The photoelectric effect consists of the ejection of electrons from the surface of some illuminated material that is exposed to a light source of a certain frequency. The photoelectric effect was explained by Albert Einstein and is used worldwide for the production of electrical energy through solar energy .

## Who discovered the photoelectric effect?

The photoelectric effect was discovered by Heinrich Hertz , during his experiments related to the production and capture of electromagnetic waves . In 1886, Hertz was conducting his experiments with metal sheets when he realized that the incidence of ultraviolet light resulted in greater production of sparks. The theoretical explanation for the phenomenon, however, was only made in 1905, by the German physicist Albert Einstein .

The mechanism of the photoelectric effect was controversial , since, according to the knowledge of classical electromagnetism , a body illuminated by a source of light should absorb all light energy radiated on it, however, the photoelectric effect only happened after a certain time. frequency , which varied according to each material.

Albert Einstein was able to interpret the photoelectric effect using Max Planck ‘s mathematical arguments , generalizing them. According to Planck’s theory, thermal radiation is quantized, that is, it has discrete energy values. In this view, light is made up of small packets of energy , which were later named photons.

Einstein assumed that Planck’s hypothesis was valid for all types of electromagnetic radiation, thus showing everyone that light could behave as a wave and as a particle.

## How does the photoelectric effect work?

The photoelectric effect happens when the photons that fall on a material have a certain energy capable of ripping the electrons from that material . Each material needs a specific amount of energy to have its electrons ejected, this amount of energy is called the work function .

The energy contained in a photon is directly proportional to its frequency, as shown in the following formula:

E – energy stored in the photon (eV)

h – Planck’s constant (4.0.10 -15 eV.s)

f – photon frequency (Hz)

This energy is transferred to the electrons of the material in the form of kinetic energy . Thus, if the photon energy is greater than the energy that keeps the electron trapped in the material, the electron will be ejected, and its kinetic energy will be numerically equal to the difference between the energy contained in the photon and the work function.

E – kinetic energy of the ejected electron

Φ – energy that keeps the electron inside the material

## Experiment on the photoelectric effect

The experiment that highlighted the quantum character of the photoelectric effect is known as the experiment of Philipp Lenard , one of Heinrich Hertz’s assistants. Lenard performed a series of experiments and found that the intensity of light did not affect the energy with which electrons were torn from metal plates, contradicting the prevailing theory of electromagnetism in 1903.

Shortly thereafter, Egon Schweidler was able to experimentally prove that the kinetic energy of the ejected electrons was directly proportional to the frequency of the light that illuminated the plates.

Lenard’s experiments were done using two metal plates—an emitting plate, illuminated by a monochromatic light source, and a collecting plate, which served to absorb electrons. In order to detect the absorption of electrons by the collector plate, an ammeter was connected in series with the two plates, in addition, there was a variation of the experiment in which a battery was connected to the plates.

The battery’s function was to create an electric field between the plates that could brake the electrons; by adjusting the electrical voltage, it was possible to discover the value of the kinetic energy of each ejected electron.

## Examples of the photoelectric effect

The photoelectric effect is used in several technologies present in everyday life, let’s check some examples:

• Light detectors: Relays are devices that capture light. The light promotes the ejection of electrons from a photoelectric material, so a circuit is activated so that the external lighting turns on.
• Photovoltaic cells: are the electrical current generating units in solar panels. These cells are made of semiconductor materials, which produce electricity when illuminated by sunlight.

## Exercises on the photoelectric effect

Question 1) (UEMG) Read the following excerpt:

The photoelectric effect was discovered in 1886 by the German physicist Heinrich Hertz (1857-1894). At the time, Hertz realized that the incidence of ultraviolet light on metal sheets helped to produce sparks. The theoretical explanation for the photoelectric effect, however, was only presented by the German physicist Albert Einstein in 1905.

The doubt that existed at the time was related to the kinetic energy of the electrons that were ejected from the metal: this magnitude did not depend on the __________ of the incident light. Einstein realized that the agent responsible for ejecting each electron was a single photon, a particle of light that transferred some of its energy to the electrons, ejecting it from the material, provided its __________ was large enough to do so.

Available at: https://brasilescola.uol.com.br/o-que-e/fisica/o-que-e-efeito-fotoeletrico.htm. Access: 11 Dec. 2018. (Fragment: Adapted).

Choose the alternative that CORRECTLY fills in the blanks:

a) frequency – wavelength

b) wavelength – intensity

c) intensity – frequency

d) wavelength – frequency

Template: Letter C

Resolution:

In the photoelectric effect, the intensity of light does not affect the kinetic energy of the ejected electrons, in addition, these particles are only ejected from the material if the incident light has a minimum frequency to overcome the work function of the material, so the correct alternative is letter C.

Question 2) (UFU) The nature of light is a subject that has been present in the discussions of scientists and philosophers for centuries, mainly from the possibility of applying luminous phenomena through both wave and corpuscular behaviors. According to the principle of complementarity, proposed by Niels Bohr in 1928, the wave description of light is complementary to the corpuscular description, but the two descriptions are not used simultaneously to describe a particular luminous phenomenon. In this way, luminous phenomena involving the propagation, emission and absorption of light are explained sometimes considering the wave nature, sometimes considering the corpuscular nature.

Mark the alternative that presents a luminous phenomenon that is better explained, considering the corpuscular nature of light:

a) Scattering of light when passing through a narrow slit.

b) Light interference when light beams from different sources meet.

c) Change of direction of propagation of light when passing from one transparent medium to another.

d) Absorption of light with emission of electrons by a metal plate.

Template: Letter D

Resolution:

The photoelectric effect occurs when a photon has a minimum frequency, and therefore a minimum energy, required to knock electrons off a metal plate. Thus, the alternative that describes a light corpuscular phenomenon is the letter D.