To consider the implications of the particle model, it is helpful to think about monochromatic light, many photons all with the same frequency, like light produced by a laser.
First, compare two beams of light with equal intensity but different frequencies. Thus, the high frequency beam is capable of transferring larger amounts energy into another system. But the intensities of the beams or the same, so the total energy transfered by each beam is the same. This tells us that the beam with the higher frequency has fewer photons.
But in the wave model, the same intensity of each beam means they must have the same amplitude. The energy in a wave is related to its amplitude, so it would seem both light beams must have equal ability to transfer energy. Clearly, the two models lead to different hypotheses. Next, consider the action of increasing the beams' intensity. In the particle model, we would describe this as addingmore photons to the beam, but each particular photon still only carries a certain amount of energy.
Using the particle model, we conclude that the brightness of the beam does not influence how much energy any particular photon can transfer to another system.
In the wave model, a greater brightness would indicate a larger amplitude wave; we would conclude that greater intensity waves have the ability to transfer larger amounts of energy into another system.
Again, the models make different predictions. At this point, we have two different models for light. We know that the wave model is quite able to predict the behavior of light in two-slit interference, where the particle model can not.
Yet the particle model can explain certain behaviors that the wave model cannot. One of those behaviors is exhibited as the photoelectric effect, which provides strong experimental evidence of the particle model of light. In fact, it was the photoelectric effect that first led Albert Einstein to develop the particle model of light. In the photoelectric effect , a beam of incoming light shines on a metallic surface. When the beam hits the metal, photons eject electrons from the metal and sends the electrons down a tube to a collector.
To do so, the photons must provide the electrons with enough energy to break their bonds to the metal, and sufficient kinetic energy to reach the collector. Reaching the collector requires a certain amount of minimum kinetic energy at emission, because an electric field exists between the collector and the emitter that acts to slow down the electrons on their path.
This is shown in the figure below. For now, focus your attention solely on the grayed tube at the top and ignore the portions of the circuit including the battery and ammeter. The photoelectric experiment allows us to test the wave model against the particle model, for this particular setup. As an experimenter, we have control over both the intensity of the light and the frequency of the light.
We can independently vary one or the other, and note the effect, enabling us to determine the appropriate model for this system. The photoelectric effect can be explained using the conservation of energy. Light brings in a certain amount of energy. If the energy is sufficiently high, it frees an electron from the metal.
If the incident light has less energy than the work function, the electrons remain attached to the plate. Suppose the incident light has sufficient energy to free the electron from the plate. The electron is emitted, and has a kinetic energy of at least 0 J, possibly more. The work function is fixed for a given material and doesn't change, so higher energy light results in faster moving electrons. Next, the electron travels from the emitter towards the collector. In this region, an electric field points from the emitter toward the collector.
The electric force on the electron slows it down as it travels from the emitter to the collector. Thinking about energy again, the electron gains potential energy as it loses kinetic energy. As an experimenter, we we control the strength of the electric field, and thus the amount of potential energy the particle gains as it traverses the tube.
If we stop the electron exactly as it reaches the collector, it means we transfer all of the kinetic energy to potential energy, and we can measure the kinetic energy the electron had just after emission. The potential required to do this is called the stopping potential. If we have a situation where many electrons reach the collector, we can slowly increase the voltage between the plates until we just reach the stopping potential. These results all support the particle model of light.
Beams with higher intensities contain more photons. Higher intensity beams free more electrons because more photons are present to transfer energy. However the amount of energy one photon can transfer to an electron is determined by the photon's frequency. Increasing the frequency of incoming light increases the energy transfered to the electrons, which is why higher frequency beams produce electrons with more kinetic energy.
Now that we're familiar with the concepts of light quantization, we explore these concepts to quantify them mathematically. As you read, consider how the equations reflect the concepts presented above. Our goal is to determine the energy of the incident light. There are two main processes involved in the photoelectric effect.
The first involves the light transferring energy to the electron, freeing it from the metal and giving it kinetic energy. Next, the electron travels down the tube, gaining potential energy and losing kinetic energy. As stated above, we adjust the voltage between the plates until the electron just barely stops short of the collector. First, we will look at the second process, of slowing the electron down as it traverses the tube.
The change in total energy 0 is given by the sum of the change in the kinetic and electrical potential energies:. We can rewrite our above equation as. Our goal is to relate this mathematically to the energy of the incident light. Recall that incident energy is split; it frees the electron and gives the electron kinetic energy.
Combining this with our results above, we have:. We have found an equation for the amount of energy transfered by the light for a given stopping potential. If we adjust the energy of the incoming light, we must also adjust the stopping potential. If we change some aspect of the light and find that we don't need to change the stopping potential, it means the energy transfered by the light has not changed.
This setup is useful because the wave model and particle model hypothesize different ways of adjusting the energy of the light as discussed previously in this section. To test the models, we can try each method of adjusting light energy and note whether or not we needed to change the stopping potential to compensate which would indicate different electron kinetic energy.
Experimentally, we find that adjusting the frequency of the incident light requires us to adjust the stopping potential, but adjusting the intensity does not. The answer is neither. However we should refrain from saying that light is actually this quantum stuff, because future experiments may require us to replace this model with something else.
If neither model of light is correct, why do we teach them? Ultimately the full quantum model is just too difficult to explore in Physics 7. We have a good quantum model for light and electrons, and even whole atoms ; in some situations we can simplify this and use the wave model, while in others we can use the particle model.
In other situations the quantum model does not fit into either a wave or particle description. Light and other microscopic phenomena often behave in unfamiliar ways completely outside human experience.
Even if we cannot shoehorn quantum mechanics into our regular familiar notions of "particles" and "waves," this does not mean quantum mechanics is contradictory; it just means that the microscopic world is highly counter-intuitive.
Arguments about whether light is really a particle or a wave are a waste of oxygen, or worse yet, trees. Light can be modeled as particles when it behaves as such and it can be modeled as a wave likewise. We use these models when more complicated behaviors of light can be ignored or simplified, and we recognize that each model has limits and only applies under specific conditions. People who argue about whether light is a particle or a wave do not understand the concept of modeling and making approximations, and you should be hesitant to accept their advice about physics.
The Energy Spectrum Energy Levels When we describe the energy of a particle as quantized, we mean that only certain values of energy are allowed. Potential Determines the Energy Spectrum The collection of allowed energies a system may have is called the energy spectrum of that system.
Exercise In the example mentioned in the text where the particle can have 1 J, 4 J, 9 J, or 16 J of energy, what is the energy spectrum? Light is Quantized Just as we can think of ordinary matter being quantized as illustrated by the example with water , we also find that light comes in indivisible quanta that we refer to as photons. We know from earlier that the frequency is what determines the type of light we're discussing. The photons of different colors or different types of light have different frequencies and therefore have different energies.
At a particular frequency, one photon is the smallest amount of light that can exist. Three Potentials and Their Energy Spectra Gaining a better understanding of three important energy spectra will help us learn about a large variety of phenomena.
The Infinite Potential Well The infinite potential well is a system where a particle is trapped in a one-dimensional box of fixed size, but is completely free within the box. Example 2 Suppose you have a particle in the ground state of the infinite square well potential. Example 3 The protons and neutrons of an atom are confined to the nucleus.
Figure 3 shows how this applies to the ground state of hydrogen. If you try to follow the electron in some well-defined orbit using a probe that has a small enough wavelength to get some details, you will instead knock the electron out of its orbit.
Repeated measurements reveal a cloud of probability like that in the figure, with each speck the location determined by a single measurement. There is not a well-defined, circular-orbit type of distribution. Nature again proves to be different on a small scale than on a macroscopic scale.
There are many examples in which the wave nature of matter causes quantization in bound systems such as the atom. Whenever a particle is confined or bound to a small space, its allowed wavelengths are those which fit into that space. For example, the particle in a box model describes a particle free to move in a small space surrounded by impenetrable barriers. This is true in blackbody radiators atoms and molecules as well as in atomic and molecular spectra.
Various atoms and molecules will have different sets of electron orbits, depending on the size and complexity of the system. When a system is large, such as a grain of sand, the tiny particle waves in it can fit in so many ways that it becomes impossible to see that the allowed states are discrete. Thus the correspondence principle is satisfied. As systems become large, they gradually look less grainy, and quantization becomes less evident.
Unbound systems small or not , such as an electron freed from an atom, do not have quantized energies, since their wavelengths are not constrained to fit in a certain volume.
When do photons, electrons, and atoms behave like particles and when do they behave like waves? Watch waves spread out and interfere as they pass through a double slit, then get detected on a screen as tiny dots. Use quantum detectors to explore how measurements change the waves and the patterns they produce on the screen.
Skip to main content. When a metal is struck by light with energy above the threshold energy E o , the number of emitted electrons is proportional to the intensity of the light beam, which corresponds to the number of photons per square centimeter, but the kinetic energy of the emitted electrons is proportional to the frequency of the light.
Thus Einstein showed that the energy of the emitted electrons depended on the frequency of the light, contrary to the prediction of classical physics. Moreover, the idea that light could behave not only as a wave but as a particle in the form of photons suggested that matter and energy might not be such unrelated phenomena after all. In , Einstein was working in the Swiss patent office in Bern. He was born in Germany and throughout his childhood his parents and teachers had worried that he might be developmentally disabled.
The patent office job was a low-level civil service position that was not very demanding, but it did allow Einstein to spend a great deal of time reading and thinking about physics. In , his "miracle year" he published four papers that revolutionized physics.
One was on the special theory of relativity, a second on the equivalence of mass and energy, a third on Brownian motion, and the fourth on the photoelectric effect, for which he received the Nobel Prize in , the theory of relativity and energy-matter equivalence being still controversial at the time.
Both theories are based on the existence of simple building blocks, atoms in one case and quanta of energy in the other. The work of Planck and Einstein thus suggested a connection between the quantized nature of energy and the properties of individual atoms. A ruby laser, a device that produces light in a narrow range of wavelengths emits red light at a wavelength of What is the energy in joules of a single photon?
An x-ray generator, such as those used in hospitals, emits radiation with a wavelength of 1. The fundamental building blocks of energy are quanta and of matter are atoms. The properties of blackbody radiation , the radiation emitted by hot objects, could not be explained with classical physics.
Max Planck postulated that energy was quantized and could be emitted or absorbed only in integral multiples of a small unit of energy, known as a quantum. Both energy and matter have fundamental building blocks: quanta and atoms, respectively. Modified by Joshua Halpern Howard University.
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