Frequency threshold

Wlien photons of sufiBciently high frequency v are directed onto a metal surface, electrons are emitted in a process known as photoelectron emission [ ]. The threshold frequency Vq is related to the work fimction by the expression... 

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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FIGURE 1.15 When a metal is illuminated with ultraviolet radiation, electrons are ejected, provided the frequency is above a threshold frequency that is characteristic of the metal. 

Below a characteristic threshold frequency, Vg, no electrons are observed, regardless of the light s intensity. 

Above the threshold frequency, the maximum kinetic energy of ejected electrons increases linearly with the frequency of the light, as shown in Figure 7-6. 

Above the threshold frequency, the number of emitted electrons increases with the light s intensity, but the kinetic energy per electron does not depend on the light s intensity. 

All metals exhibit the same pattern, but as Figure 7 7 shows, each metal has a different threshold frequency. 

C07-0115. The photoelectric effect for magnesium metal has a threshold frequency of 8.95 X 10 s". Can Mg be used in photoelectric devices that sense visible light Do a calculation in support of your answer. 

The incident light must have some minimum frequency (the threshold frequency) in order for electrons to be ejected. 

In the photoelectric method, the measured average work function is always less than the true since patches of high work function tend to be excluded from the emission process. Thus, the nonuniform distribution of adsorbate on a patch surface may cause a slight discrepancy in the evaluation of A. Experimentally, the photoelectric method has various limitations. Photocurrents of the order of 10 A. must be measured accurately in the region of vo, and for films of work function greater than 5 v., the threshold frequency lies in the far ultraviolet—a practical disadvantage. Furthermore, the method is inapplicable at pressures in excess of 10 mm. Hg because of ionization of the gas by collision. 

A photoelectric method was also used by Baker and Rideal (76) for studying the adsorption of Ha, CO, and CaH on evaporated metal films of Ta, Fe, Ni, and Co. Photocurrents near the threshold were too small to be measured accurately, so the threshold frequencies were obtained by in-... 

The Maxwell-Heaviside theory seen as a U(l) symmetry gauge field theory has no explanation for the photoelectric effect, which is the emission of electrons from metals on ultraviolet irradiation [39]. Above a threshold frequency, the emission is instantaneous and independent of radiation intensity. Below the threshold, there is no emission, however intense the radiation. In U(l), electrodynamics energy is proportional to intensity and there is, consequently, no possible explanation for the photoelectric effect, which is conventionally regarded as an archetypical quantum effect. In classical 0(3) electrodynamics, the effect is simply... 

Volta potential angular radiation frequency threshold frequency ( red boundary ) plasma frequency... 

The photocurrent 1 due to photoemission of electrons from simple metals into an electrolyte solution in the near-the-threshold frequency range is given by the relation (Gurevich et al., 1967)... 

First, the level F, whose position determines the thermodynamic work function wx, is located in the case of semiconductors in the forbidden band. The energy characteristics of a semiconductor-electrolyte interface under photoemission are presented in Fig. 31, which shows, in particular, that the threshold frequency is given by the relation tiw0 = Eg + where % is the difference between the potential energy level of a delocalized electron outside... 

Here and C are quantities proportional to the probabilities of indirect and direct transitions, respectively, so that C. According to the above considerations, the two threshold frequencies co0 and co 0 are given by... 

Two papers by Albert Einstein ultimately led to acceptance of the idea of quantization of energy for radiation, and were central to the development of the quantum theory (ironically, in later years Einstein became the most implacable critic of this same theory). The first of these papers, in 1905, concerned the photoelectric effect. Light ejected electrons from a metallic surface if the light had a greater frequency than some threshold frequency v0 which depended on the particular metal. The kinetic energy K of the emitted electrons was proportional to the excess frequency, v — v0 (Figure 5.4). Only the number of emitted electrons, not the kinetic energy, increased as the intensity increased. 

Accurate measurements of the electron affinity of simple Ge and Sn radicals have been obtained by threshold photodetachment experiments carried out in ion cyclotron resonance experiments183. In these experiments, measurement of the threshold frequency for removing the electron from the anion yields an upper limit for the electron affinity of the species, as shown for GeH3- in equation 28. 

Einstein s hypothesis, then, led to two definite predictions. In the first place, there should be a photoelectric threshold frequencies less than a certain limit, equal to 4>/h, should be incapable of ejecting photoelectrons from a metal. This prediction proved to be verified experimentally, and with more and more accurate determinations of work function it continues to hold true. It is interesting to see where this threshold comes in the spectrum. For this purpose, it is more convenient to find the wave length X = c/v corresponding to the frequency /h. If we express in electron volts, as is commonly done, (see Eq. (1.1), Chap. IX), we have the relation... 

The X-ray singularity problem was originally solved in the asymptotic limit and the complicated many-body problem was turned into an effective one-particle problem (219). For the X-ray photon frequency absorption spectrum g(m) for the process in which a deep, structureless core electron is excited to the conduction band by the absorption of an X-ray of frequency w is expressed by the power law... 

Studies in which the frequency of the light is varied show that no electrons are emitted by a given metal below a specific threshold frequency v0. 

For light with frequency lower than the threshold frequency, no electrons are emitted regardless of the intensity of the light. 

These observations can be explained by assuming that electromagnetic radiation is quantized (consists of photons), and that the threshold frequency represents the minimum energy required to remove the electron from the metal s surface. 

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