The Photoelectric Effect

This is the emission of electrons from metals (or metal alloys) irradiated by light of suitable wavelength. 

When the photocathode is illuminated by light of wavelength below a 

The photoelectric effect shows that the energy of light is not distributed evenly over a uniform wavefront, but is concentrated in space within the dimensions of atomic particles, in particular electrons. 

An important aspect of the photoelectric effect is that it requires a minimum frequency of light which depends on the material of the photocathode. This means that each particle of light or photon carries an energy E proportional to the frequency v E = hv. The factor h is known as Planck s constant , one of the most fundamental physical constants in all of nature. 

The kinetic energy of the photoelectron kin of mass mt and velocity v is then 

If we use the value given by Eq. (19.8) for the average energy in a mode of vibration, then multiply it by the number of modes in the wavelength range to calculate the spectral distribution, we obtain for 

Planck took the extraordinary step of setting e inversely proportional to the wavelength, recognizing that the Wien displacement law would come out of the resulting equation. Since the frequency times the wavelength is equal to the velocity, we have l/X = v/c, where v is the frequency and c the velocity. Setting e proportional to l/X is equivalent to setting it proportional to the frequency  

By properly choosing the value of the constant ft, Planck found that Eq. (19.11) agreed with the measured distribution within the experimental error To find the maximum, we set duJdX = 0 the Wien displacement law is obtained in the form 

The nature of light seemed no longer to be simple. Light was a wave motion, but with Planck s work it acquired a corpuscular aspect. The light wave contains energy in elementary discrete units, quanta. 

As may be imagined, Planck s discovery excited very little interest and no controversy. The prevailing attitude seemed to be if we ignore it, it will go away. Perhaps it might have gone away but for Einstein s interpretation of the photoelectric effect, another longstanding thorn in the side of classical physics. 

Calculate the energy (in jonles) of (a) a photon with a wavelength of 5.00 X 10 nm (infrared region) and (h) a photon with a wavelength of 5.00 X 10 nm (X ray region). 

Strategy In both (a) and (h) we are given the wavelength of a photon and asked to calcnlate its energy. We need to nse Eqnation (7.3) to calcnlate the energy. Planck s constant is given in the text and also on the hack inside cover. 

This is the energy of a single photon with a 5.00 X 10 nm wavelength. 

Check Because the energy of a photon increases with decreasing wavelength, we see that an X-ray photon is 1 X 10 , or a million times, more energetic than an infrared photon. 

Practice Exercise The energy of a photon is 5.87 X 10 ° J. What is its wavelength (in nanometers)  

This equation has the same form as Equation (7.2) because, as we will see shortly, electromagnetic radiation is emitted as well as absorbed in the form of photons. 

An apparatus for studying the photoelectric effect. Light of a certain frequency falls on a clean metal surface. Ejected electrons are attracted toward the positive electrode. The flow of electrons is registered by a detecting meter. 

This phenomenon occurs when the exposure of some material to light causes it to eject electrons. Many metals do this quite readily. A simple apparatus that could be used to study this behavior is drawn schematically in Fig. 1-8. Incident light strikes the metal dish in the evacuated chamber. If electrons are ejected, some of them will strike the collecting wire, giving rise to a deflection of the galvanometer. In this apparatus, one can vary the potential difference between the metal dish and the collecting wire, and also the intensity and frequency of the incident light. 

Suppose that the potential difference is set at zero and a current is detected when light of a certain intensity and frequency strikes the dish. This means that electrons 

The observations from experiments of this sort can be summarized as follows  

Below a certain cutoff frequency of incident light, no photoelectrons are ejected, no matter how intense the light. 

Above the cutoff frequency, the number of photoelectrons is directly proportional to the intensity of the light. 

The sensor for each pixel in a digital camera is a tiny photoelectric device. The photoelectric sensors that open some snpermarket and elevator doors also utilize this effect. 

Incandescent ( red hot or white hot ) solids, liquids, and high-pressure gases give continuous spectra. Wheu au electric current is passed through a gas in a vacuum tube at very low pressures, however, the hght that the gas emits can he dispersed hy a prism into dis- 

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The quantum behaviour of radiation was demonstrated by Einstein (1921 Nobel Prize for Physics) in his explanation of the photoelectric effect. If radiation of sufficient energy strikes a clean metal surface, electrons (photoelectrons) are emitted, one electron per quantum. The energy of the photoelectron, E, is given by the difference between the energy of the incident quantum and the work function, IV, which is the minimum ener required to cause the ionization of an electron from the metal surface  

Minimum energy required to cause ionization from the metal surface 

These experimental observations were in direct opposition to those expected for a wave theory of radiation. In wave theory, no threshold energy would be required for photoelectron release. A wave with low energy would simply operate long enough to contribute sufficient energy to cause the electron to be ionized. The kinetic energy of the photoelectrons would be expected to increase with the intensity of the radiation waves . 

Another effect that the wave theory of radiation cannot explain is the 

When Ayiv = W there is just enough oton energy to cause the release of a photoelectron v in this case is known as the threshold frequency 

There is a long list of possible interactions of photons, but only the three most important ones will be discussed here the photoelectric effect, Compton scattering, and pair production. 

The photoelectric effect is an interaction between a photon and a bound atomic electron. As a result of the interaction, the photon disappears and one of the atomic electrons is ejected as a free electron, called the photoelectron (Fig. 4.16). The kinetic energy of the electron is 

The probability of this interaction occurring is called the photoelectric cross section or photoelectric coefficient. Its calculation is beyond the scope of this book, but it is important to discuss the dependence of this coefficient on parameters such as E., Z, and A. The equation giving the photoelectric coefficient may be written as 

In 1887 Heinrich Hertz, who is better known for his discovery of radio waves, noticed in his investigations of evacuated tubes that when light was shined on a piece of metal in a vacuum, various electrical effects were produced. Given that the electron was yet to be discovered, an explanation was not forthcoming. After the discovery of the electron, however, reinvestigation of this phenomenon by other scientists, especially the Hungarian-German physicist Philipp Eduard Anton von 

To observe a cosmic gamma ray, one must first devise a means to stop it (or at least to slow it down in some measurable way) within a detecting medium. In the gamma-ray regime, the primary interaction mechanisms of photons with matter are the photoelectric effect, the Compton effect, and pair production. Extensive analyses are available of these fundamental interaction processes. Here, we only briefly review their basic physical characteristics. 

Photoelectric absorption occurs when an incident photon is completely absorbed in an atomic collision with practically all of its energy transferred to an atomic electron, which is ejected. Eor photoionization to occur, the 

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We use the X or gamma rays power penetrating to detect possible heterogeneities in inspected pieces. These rays are absorbed by the matter crossed, essentially by the photoelectrical effect, (fig. 02). 

Photoelectron spectroscopy provides a direct measure of the filled density of states of a solid. The kinetic energy distribution of the electrons that are emitted via the photoelectric effect when a sample is exposed to a monocluomatic ultraviolet (UV) or x-ray beam yields a photoelectron spectrum. Photoelectron spectroscopy not only provides the atomic composition, but also infonnation conceming the chemical enviromnent of the atoms in the near-surface region. Thus, it is probably the most popular and usefiil surface analysis teclmique. There are a number of fonus of photoelectron spectroscopy in conuuon use. 

X-ray photoelectron spectroscopy (XPS) is among the most frequently used surface chemical characterization teclmiques. Several excellent books on XPS are available [1, 2, 3, 4, 5, 6 and 7], XPS is based on the photoelectric effect an atom absorbs a photon of energy hv from an x-ray source next, a core or valence electron with bindmg energy is ejected with kinetic energy (figure Bl.25.1) ... 

The final technique addressed in this chapter is the measurement of the surface work function, the energy required to remove an electron from a solid. This is one of the oldest surface characterization methods, and certainly the oldest carried out in vacuo since it was first measured by Millikan using the photoelectric effect [4]. The observation of this effect led to the proposal of the Einstein equation ... 

Another phenomenon that was inexplicable in classical terms was the photoelectric effect discovered by Hertz in f 887. When ultraviolet light falls on an alkali metal surface, electrons are ejected from the surface only when the frequency of the radiation reaches the threshold... 

The explanation of the hydrogen atom spectmm and the photoelectric effect, together with other anomalous observations such as the behaviour of the molar heat capacity Q of a solid at temperatures close to 0 K and the frequency distribution of black body radiation, originated with Planck. In 1900 he proposed that the microscopic oscillators, of which a black body is made up, have an oscillation frequency v related to the energy E of the emitted radiation by... 

Einstein, in 1906, applied this theory to the photoelectric effect and showed that... 

Photoelectron spectroscopy involves the ejection of electrons from atoms or molecules following bombardment by monochromatic photons. The ejected electrons are called photoelectrons and were mentioned, in the context of the photoelectric effect, in Section 1.2. The effect was observed originally on surfaces of easily ionizable metals, such as the alkali metals. Bombardment of the surface with photons of tunable frequency does not produce any photoelectrons until the threshold frequency is reached (see Figure 1.2). At this frequency, v, the photon energy is just sufficient to overcome the work function

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Phofoelectron spectroscopy is a simple extension of the photoelectric effect involving the use of higher-energy incident photons and applied to the study not only of solid surfaces but also of samples in the gas phase. Equations (8.1) and (8.2) still apply buf, for gas-phase measuremenfs in particular, fhe work function is usually replaced by fhe ionization energy l so fhaf Equation (8.2) becomes... 

Even though Einstein developed the theory of the photoelectric effect in 1906 photoelectron spectroscopy, as we now know it, was not developed until the early 1960s, particularly by Siegbahn, Turner and Price. 

Xps is based on the photoelectric effect when an incident x-ray causes ejection of an electron from a surface atom. Figure 7 shows a schematic of the process for a hypothetical surface atom. In this process, an incident x-ray photon of energy hv impinges on the surface atom causing ejection of an electron, usually from a core electron energy level. This primary photoelectron is detected in xps. 

Practical X-ray energies do not exceed 100 keV. The primary beam is mainly attenuated by the photoelectric effect. Scattering, both elastic (Rayleigh) and inelastic (Compton), represents a minor contribution to attenuation at energies below 100 keV. 

When Max Planck wrote his remarkable paper of 1901, and introduced what Stehle (1994) calls his time bomb of an equation, e = / v , it took a number of years before anyone seriously paid attention to the revolutionary concept of the quantisation of energy the response was as sluggish as that, a few years later, whieh greeted X-ray diffraction from crystals. It was not until Einstein, in 1905, used Planck s concepts to interpret the photoelectric effect (the work for which Einstein was actually awarded his Nobel Prize) that physicists began to sit up and take notice. Niels Bohr s thesis of 1911 which introduced the concept of the quantisation of electronic energy levels in the free atom, though in a purely empirical manner, did not consider the behaviour of atoms assembled in solids. 

A. Einstein (Berlin) services to theoretical physics, especially discovery of the law of the photoelectric effect. 

None of Einstein s first four papers published between 1901 and 1904 foreshadowed his explosive creativity of 1905, his annus mirabilis, in which he produced in March, his proposal of the existence of light quanta and the photoelectric effect, work for which in 1922 he received the Nobel Prize in April, a paper on the determination of molecular dimensions, which earned him his Ph.D. m Zurich m May, his theory of special relativity in September, a sequel to the preceding paper containing the relation E = mc. Any one of these papers would have made him greatly renowned their totality made him immortal. 

In the course of his research on electromagnetic waves Hertz discovered the photoelectric effect. He showed that for the metals he used as targets, incident radiation in the ultraviolet was required to release negative charges from the metal. Research by Philipp Lenard, Wilhelm Hallwachs, J. J. Thomson, and other physicists finally led Albert Einstein to his famous 1905 equation for the photoelectric effect, which includes the idea that electromagnetic energy is quantized in units of hv, where h is Planck s con-... 

The photoelectric effect (the creation of an electrical current when light shines on a photosensitive material connected m an electrical circuit) was first obseiwed in 1839 by the French scientist Edward Becqiierel. More than one hundred years went by before researchers in the United States Bell Laboratories developed the first modern PV cell in 1954. Four years later, PV was used to power a satellite in space and has provided reliable electric power for space exploration ever since. 

Many elements were found to experience the photoelectric effect. Germanium, copper, selenium, and cuprous oxide comprised many of the early experimental cells. In 1953 Bell Laboratories scientists Calvin Fuller and Gerald Pearson were conducting... 

German physicists Julius Elster and Hans F. Geitel invent the first photoelectric cell as a result of studying the photoelectric effect. The first hydroelectric generator at Niagara Falls, New York, produces alternating current from a Nikola Tesla design. 

To achieve this successful theory, Planck had discarded classical physics, which puts no restriction on how small an amount of energy may be transferred from one object to another. He had proposed instead that energy is transferred in discrete packets. To justify such a dramatic revolution, more evidence was needed. That evidence came from the photoelectric effect, the ejection of electrons from a metal when its surface is exposed to ultraviolet radiation (Fig. 1.15). The experimental observations were as follows ... 

We can now interpret the experimental observations of the photoelectric effect in light of Einstein s theory ... 

Studies of black-body radiation led to Planck s hypothesis of the quantization of electromagnetic radiation. The photoelectric effect provides evidence of the particulate nature of electromagnetic radiation. 

You can appreciate why scientists were puzzled The results of some experiments (the photoelectric effect) compelled them to the view that electromagnetic radiation is particlelike. The results of other experiments (diffraction) compelled them equally firmly to the view that electromagnetic radiation is wavelike. Thus we are brought to the heart of modern physics. Experiments oblige us to accept the wave-particle duality of electromagnetic radiation, in which the concepts of waves and particles blend together. In the wave model, the intensity of the radiation is proportional to the square of the amplitude of the wave. In the particle model, intensity is proportional to the number of photons present at each instant. 

One of the most direct methods is photoelectron spectroscopy (PES), an adaptation of the photoelectric effect (Section 1.2). A photoelectron spectrometer (see illustration below) contains a source of high-frequency, short-wavelength radiation. Ultraviolet radiation is used most often for molecules, but x-rays are used to explore orbitals buried deeply inside solids. Photons in both frequency ranges have so much energy that they can eject electrons from the molecular orbitals they occupy. 

The new delightful book by Greenstein and Zajonc(9) contains several examples where the outcome of experiments was not what physicists expected. Careful analysis of the Schrddinger equation revealed what the intuitive argument had overlooked and showed that QM is correct. In Chapter 2, Photons , they tell the story that Einstein got the Nobel Prize in 1922 for the explaining the photoelectric effect with the concept of particle-like photons. In 1969 Crisp and Jaynes(IO) and Lamb and Scullyfl I) showed that the quantum nature of the photoelectric effect can be explained with a classical radiation field and a quantum description for the atom. Photons do exist, but they only show up when the EM field is in a state that is an eigenstate of the number operator, and they do not reveal themselves in the photoelectric effect. 

A detailed study of the photoelectric effect reveals how the behavior of the electrons is related to the characteristics of the light ... 

The photoelectric effect is the basis for many light-sensing devices, such as automatic door openers and camera exposure... 

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