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Dec 19, 2019 0    
The photoelectric effect
This photon walks into a crystal . . .
by Xiaoshan Xu, Jocelyn Bosley

When light strikes a material, electrons may be ejected from the material. This is called the photoelectric effect (Fig. 1), and it’s the basis for many different technologies that convert light energy into electrical energy to generate current. (For details, see More Power, The Future of Solar Energy is . . . an Inkjet Printer?!, and the videos below.)

Common sense might lead us to expect that, the more intense the light, the greater the number of electrons ejected. This is not always the case, however—curiously, whether electrons can be ejected at all depends not on the intensity but on the color of the light. This fact puzzled scientists for years, until Einstein explained it by assuming that light propagates in packets called photons.

Seeing the Light

At the time, this was an unusual way to think about light, and it seemed to conflict with the familiar view of light as a wave. Like other waves, light has two important properties: wavelength (the distance between adjacent crests or troughs) and frequency (the number of waves passing a particular point each second). Since all light travels at the same speed, wavelength and frequency are inversely related: when the wavelength is long, fewer waves pass in a given interval of time, and when the wavelength is short, more waves pass during the same interval (Fig. 2). We have several light-sensitive pigments in our eyes that respond to different frequencies of light, which we in turn perceive as different colors. These pigments are sensitive only to a narrow range of light frequencies, however, which is why most light is invisible to us (Fig. 3).

Einstein suggested that, while light waves sometimes behave similarly to other waves we observe, the photoelectric effect could only be explained by considering light as individual energy packets—a kind of light “particle,” the energy of which increases with the frequency of the light wave.

We tend to think of energy as a continuous phenomenon. In the world of our everyday experience, energy is something we measure rather than count, and it can come in any quantity. By analogy, chocolate syrup is a continuous form of chocolate, which can be measured to any degree of precision your instruments allow. Hershey’s kisses, by contrast, are a discrete form of chocolate; without cutting them into pieces (in which case they are no longer Hershey’s kisses), only whole-number quantities are possible. By imagining that light comes in discrete units, more like Hershey’s kisses than like chocolate syrup, Einstein was suggesting that only certain quantities of light energy were possible. The discrete quantities of energy a photon, electron, or other subatomic particle can have are the “quanta” that give quantum mechanics its name.

When we observe the photoelectric effect, the photon provides the energy to break the bond between the electron and the host material. Einstein realized this was only possible when the energy of the photon corresponds exactly to the energy the electron needs to escape. It’s a bit like a board game in which you must roll exactly the right number of spaces in order to advance to the final square and win the game. If a photon has the right amount of energy—that is, if it has a particular frequency, or color—it liberates an electron, allowing the electron to move freely through the material. Only at these particular frequencies will more intense light (i.e., more photons) cause more electrons to be ejected. These free electrons can, in turn, be used to create an electric current.

Electrons Tell the Tale

In addition to being the foundation for solar cells and other technologies that convert light into electricity, the photoelectric effect is useful to scientists studying novel materials.

Not surprisingly, how difficult it is to eject an electron using a photon depends on how tightly the electron is bound to the material. In any given material, there are many, many electrons, and different electrons may be bound in different ways, with different strengths. Using the photoelectric effect, we can investigate patterns in the binding of electrons in different materials. These differences in binding strength turn out to be responsible for differences in many interesting and important material properties, such as color, conductivity, flexibility, etc.

Going one step further, scientists have found that, because atomic arrangements strongly affect the binding of electrons, we can use the photoelectric effect to investigate how atoms are arranged in a material.

As discussed in The Shape of the Future, the compound LuFeO3 can have two different crystal structures: orthorhombic and hexagonal. This difference in structure, shown in Fig. 4, creates different local environments for iron (Fe) atoms. This difference in the local environment affects the binding of electrons in the iron atoms. As a result, the number of electrons expelled by a certain photon energy is different for the hexagonal and orthorhombic LuFeO3. Fig. 5 shows images of LuFeO3 illuminated using two different frequencies of light, corresponding to different photon energies. When we grow crystals and want to know more about their structure, we can use this method to analyze the binding energies of electrons and infer information about the local environments of atoms in the crystal.

In the photoelectric effect, light (represented by a blue arrow) strikes a material, causing an electron (represented by a red sphere) to be ejected from the material.
Fig. 1 (Click to enlarge) In the photoelectric effect, light (represented by a blue arrow) strikes a material, causing an electron (represented by a red sphere) to be ejected from the material.
As the wavelength of a light wave decreases, its frequency increases. The red light wave has a the highest wavelength and lowest frequency of the waves shown here, while the violet light wave has the lowest wavelength and highest frequency.
Fig. 2 (Click to enlarge) As the wavelength of a light wave decreases, its frequency increases. The red light wave has a the highest wavelength and lowest frequency of the waves shown here, while the violet light wave has the lowest wavelength and highest frequency.
The electromagnetic spectrum includes all possible energies of light, from the highest energies (high frequency, low wavelength) at the left to the lowest energies (low frequency, high wavelength) at the right. Only the narrow range of energies represented by the colored lines is visible to us.
Fig. 3 (Click to enlarge) The electromagnetic spectrum includes all possible energies of light, from the highest energies (high frequency, low wavelength) at the left to the lowest energies (low frequency, high wavelength) at the right. Only the narrow range of energies represented by the colored lines is visible to us.
In the hexagonal LuFeO3 on the left, each iron atom has only five oxygen neighbors. In the orthorhombic LuFeO3 on the right, each iron atom is surrounded by six oxygen atoms. While they have the same chemical composition, these differing crystal structures affect the properties of the material.
Fig. 4 (Click to enlarge) In the hexagonal LuFeO3 on the left, each iron atom has only five oxygen neighbors. In the orthorhombic LuFeO3 on the right, each iron atom is surrounded by six oxygen atoms. While they have the same chemical composition, these differing crystal structures affect the properties of the material.
The brighter areas emit more electrons. As you can see, at one frequency, the hexagonal LuFeO3 emits more electrons, appearing brighter in the image; at the other frequency, the contrast is reversed, and the orthorhombic LuFeO3 emits more electrons. (size: 50×50 micrometers)
Fig. 5 (Click to enlarge) The brighter areas emit more electrons. As you can see, at one frequency, the hexagonal LuFeO3 emits more electrons, appearing brighter in the image; at the other frequency, the contrast is reversed, and the orthorhombic LuFeO3 emits more electrons. (size: 50×50 micrometers)
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