Photoelectric equation

Photoelectron spectroscopy is the study of the electron kinetic energy spectrum produced upon photoionization of molecules with monochromatic radiation. We may write the basic photoelectric equation as... 

The photovoltaic devices are the most modern. They are semi-conductor or. in other words, solid-state components, and they incorporate the principle of the conversion of radiant energy directly into usable electrical power. The photovoltaic phenomenon is founded upon the basic photoelectric equation of Albert Einstein, namely ... 

Equation (19.14) is the Einstein photoelectric equation. It is apparent from the equation that below a critical frequency, Vq, given by hvg = co, the electron does not gain sufficient energy from the light quantum to escape the metal. This explains the cut-off frequency Vq that is observed. A greater light intensity means only that more quanta are absorbed per unit time and more electrons are emitted the energies of the emitted electrons are completely independent of the intensity. 

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 ... 

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... 

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. 

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-... 

A hundred years ago it was generally supposed that all the properties of light could be explained in terms of its wave nature. A series of investigations carried out between 1900 and 1910 by Max Planck (1858-1947) (blackbody radiation) and Albert Einstein (1879-1955) (photoelectric effect) discredited that notion. Today we consider light to be generated as a stream of particles called photons, whose energy E is given by the equation... 

Absorption, equation, 15 importance in detection, 44, 45 measurements by Barkla, 11-13 of x-rays, discussion, 9-20 in detectors, 44, 45 photoelectric, 18-20 and scattering as functions of wavelength, 107... 

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. 

The photoelectric method is based on the photoelectric effect. The kinetic energy of the electrons emitted during illumination of a metal with light having a frequency v obeys the Einstein equation... 

The photoelectric effect, in which the photon is absorbed and an electron is produced with kinetic energy equal to the difference between the photon energy and the binding energy of the electron (Einstein equation). 

Schrodinger s equation is widely known as a wave equation and the quantum formalism developed on the basis thereof is called wave mechanics. This terminology reflects historical developments in the theory of matter following various conjectures and experimental demonstration that matter and radiation alike, both exhibit wave-like and particle-like behaviour under appropriate conditions. The synthesis of quantum theory and a wave model was first achieved by De Broglie. By analogy with the dual character of light as revealed by the photoelectric effect and the incoherent Compton scattering... 

The electronic interaction of the relatively large molecules of phthalocyanine shows (Fig. 30) a considerable temperature effect (77a). In an experiment demonstrating this effect, the platinum foil (B in Fig. 2) was covered by the dye molecules until the work function was lowered to 4.32 volts at room temperature. If B was cooled by pouring liquid air into the upper tube of the photocell (a in Fig. 30), the photoelectric sensitivity increased and remained constant as long as liquid air was added. If the liquid air evaporated (6 in Fig. 30), the photoemission dropped to the original value at room temperature. This effect was arbitrarily reproducible. The calculation of the work function 4> and the constant M by the curves of Fowler [see Equation (5) in section III,la] in Fig. 31 gives = 4,32 volts, log M = —12.17 at room temperature (curve I), and = 4.15 volts, log M = —12.17 at low temperature (curve II). While... 

Millikan s experiment did not prove, of course, that (he charge on the cathode ray. beta ray, photoelectric, or Zeeman particle was e. But if we call all such particles electrons, and assume that they have e/m = 1.76 x Hi" coulombs/kg. and e = 1.60 x 10" coulomb (and hence m =9.1 x 10 " kg), we find that they fit very well into Bohr s theory of the hydrogen atom and successive, more comprehensive atomic theories, into Richardson s equations for thermionic emission, into Fermi s theory of beta decay, and so on. In other words, a whole web of modem theory and experiment defines the electron. The best current value of e = (1.60206 0.00003) x 10 g coulomb. 

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