scholarly journals On the law and mechanism of monomolecular reaction

1926 ◽  
Vol 110 (755) ◽  
pp. 543-560 ◽  
Keyword(s):  
Chemical Reactions ◽  
Chemical Reaction ◽  
Chemical Reactivity ◽  
Thermionic Emission ◽  
Black Body ◽  
Black Body Radiation ◽  
Single Frequency ◽  
Monomolecular Reaction ◽  
Wide Range ◽  
The Law

1. The object of the present paper is to work out an expression for the rate of monomolecular reaction on the basis of the idea that radiation is the cause of such reactions. The whole position of the radiation hypothesis of chemical reactivity up till now has been fully discussed by Harned. I only wish to draw attention to the fact, as pointed out by Langmuir, and Lewis and McKeown, that a great similarity exists between photo-electric emission of electrons and photo-chemical reaction. The true analogue of the thermo-chemical reaction should be sought, however, in the phenomenon of thermionic emission of electrons. It has long been shown experimentally by Richardson and others that the thermionic emission of electrons is vastly in excess of the total photo-electric emission at any temperature T. In the same way we should expect that the amount of thermo-chemical reaction in a system at a given temperature should be greater than the total photo-chemical reaction by black body radiation at the same temperature. Becker has shown that the distribution of velocities among the photo-electrons emitted from a metal by the action of black body radiation at a temperature T is similar to that found amongst the electrons emitted thermally from the hot metal at the same temperature T. It is thus natural to assume that the thermionic emission of electrons from a hot body is really due to the radiation in equilibrium with it. Richardson║ has recently given a very interesting discussion on the photo-electric theory of thermionic emission of electrons. Owing to the well-known difficulties the old view of the freely-moving electrons in a metal has, in recent years, been replaced by that of a lattice structure— a metal being considered to be constituted of interlaced lattices of ions and electrons. Such a view of metallic electrons precludes them from sharing in kinetic energy according to the equipartition law. It is rather more rational to imagine that the metallic electrons do exist in some modified quantum orbits, and are bound to the ions by a certain potential energy. If this view of the electronic structure in metals be accepted, then we have to look to radiation as the only controlling factor in the emission of electrons from hot bodies. The writer has tried to show that the law of thermionic emission derived on the basis of radiative mechanism is in good agreement with experiment. Lewis and McKeown have pointed out that “the concept of matter and radiation being at one and the same temperature means that as a result of absorption and emission, the system as a whole maintains a certain distribution of energy among all frequencies.” If by some process a set of frequencies are removed the system tends to make good the loss by a corresponding reverse process, provided the velocity of the process be not too large to make it physically impossible to keep the system at a fixed temperature by means of a thermostat. In my view the resemblance of photo-electric emission and photo-chemical reaction with thermionic emission and thermo-chemical reaction respectively arises from both kinds of processes being due to radiation. But the distinction lies in the fact that one is due to the action of high temperature radiation on a cold system, while the other is brought about by the action of radiation in temperature equilibrium with the system itself. 2. The Range of Frequencies of Radiation capable of bringing about a Chemical Reaction . Up till now it has been usually assumed that a single frequency, or rather a narrow range of frequencies, is capable of bringing about a chemical change. But experiments have shown that photo-chemical reactions are produced by the action of light of a wide range of frequencies. The simplest of all chemical reactions is the breaking up of atoms into ions and electrons, and it is widely known that the photo-electric action in various elements, both in solid and vapour phase, are brought about by all frequencies of radiation above a certain limiting frequency. The familiar reaction of practical photography is also known to be produced by light of a great variety of wave-lengths. It is, therefore, evident that a more complete theory of chemical reactivity should involve a summation of a number of frequencies, or, what is more plausible, an integration over a whole range of frequencies above a certain limiting value.

scholarly journals The complete photo-electric emission from the alloy of sodium and potassium

1917 ◽  
Vol 93 (652) ◽  
pp. 359-372 ◽  
Keyword(s):  
Temperature Variation ◽  
Unit Area ◽  
Thermionic Emission ◽  
Black Body ◽  
External Source ◽  
Black Body Radiation ◽  
The Subject ◽  
The Law ◽  
Work Done ◽  
Sodium And Potassium

The experimental work described in the present paper suggested itself to the writer in connection with an earlier investigation on the law governing the temperature variation of the complete photo-electric emission from a hot body, i. e . the photo-electric emission from a body in equilibrium with the full (black body) radiation corresponding to its temperature. By making use of hypotheses contained in the quantum theory, the writer obtained the following expression for the current per unit area C = AT (1+2 k T/ Ф +2 k 2 T 2 / Ф 2 ) e -Ф / k t, where Ф is the work done in removing an electron from the hot body, and is equal to hv, v being the lowest frequency of the radiation capable of producing a photo-electric emission, and h being Planck’s constant. The quantity k is the "gas constant” reckoned for one molecule, and A is a quantity independent of T, and characteristic of the substance. As the expression inside the brackets in the above formula does not differ appreciably from unity, the latter is substantially of the same type as Richardson’s equation C = AT λ e -Ф / k T , (1) for the thermionic emission. Richardson* has also shown that it follows, from thermodynamic considerations, that this law governs the complete photo-electric emission. There is reason to believe that the thermionic emission is not wholly photo-electric in origin, but it is clear that some portion of it is the complete auto-photo-electric emission of the substance concerned, and that the law governing its temperature variation should be the same as that for the whole thermionic emission. We are thus led to expect that, when a body is exposed to an external source of full radiation, the same law will govern the variation of its complete photo-electric emission with the temperature of the source of the radiation. This expectation has been confirmed by experiments on the alloy of sodium and potassium, the description of which constitutes the subject of the present paper.

2003 Alfred Bader Award LecturePredicting the rates of chemical reactions

2005 ◽  
Vol 83 (1) ◽  
pp. 1-8 ◽  
Author(s):  
J Peter Guthrie
Keyword(s):  
Computational Chemistry ◽  
Chemical Reactions ◽  
Chemical Reaction ◽  
Chemical Reactivity ◽  
Equilibrium Thermodynamics ◽  
Detailed Mechanism ◽  
Quantitative Tool

The dream of being able to predict the rate of a chemical reaction corresponding to a detailed mechanism is now almost within our grasp. No barrier theory (NBT), which makes the calculations relatively facile, is described, as are various applications of the approach to date. Illustrations are given of the use of NBT not just as a quantitative tool for predicting rates, but as a qualitative tool for thinking about which of a pair of reactions will have the higher intrinsic barrier, and thus be slower for similar thermodynamic driving force.Key words: rate, equilibrium, thermodynamics, kinetics, no barrier theory, computational chemistry, chemical reactivity.

scholarly journals Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
John H. Lienhard V
Keyword(s):  
Black Body ◽  
Black Body Radiation ◽  
Analytical Approximation ◽  
New Approach ◽  
Radiation Exchange ◽  
Wide Range ◽  
The Difference ◽  
Exact Calculations ◽  
Improved Accuracy ◽  
Fractional Function

The radiation fractional function is the fraction of black body radiation below a given value of λT. Edwards and others have distinguished between the traditional, or “external,” radiation fractional function and an “internal” radiation fractional function. The latter is used for linearization of net radiation from a nongray surface when the temperature of an effectively black environment is not far from the surface's temperature, without calculating a separate total absorptivity. This paper examines the analytical approximation involved in the internal fractional function, with results given in terms of the incomplete zeta function. A rigorous upper bound on the difference between the external and internal emissivity is obtained. Calculations using the internal emissivity are compared to exact calculations for several models and materials. A new approach to calculating the internal emissivity is developed, yielding vastly improved accuracy over a wide range of temperature differences. The internal fractional function should be used for evaluating radiation thermal resistances, in particular.

scholarly journals Non-Gray Radiation Exchange: The Internal Fractional Function Reconsidered

2018 ◽  
Author(s):  
John H. Lienhard
Keyword(s):  
Black Body ◽  
Black Body Radiation ◽  
Analytical Approximation ◽  
Radiation Exchange ◽  
Wide Range ◽  
The Difference ◽  
Exact Calculations ◽  
Simplified Calculation ◽  
Improved Accuracy ◽  
Fractional Function

The radiation fractional function is the fraction of black body radiation below a given value of λT. Edwards and others have distinguished between the traditional, or “external”, radiation fractional function and an “internal” radiation fractional function. The latter is used for simplified calculation of net radiation from a non-gray surface when the temperature of an effectively black source is not far from the surface’s temperature, without calculating a separate total absorptivity. This paper examines the analytical approximation involved in the internal fractional function, with results given in terms of the incomplete zeta function. A rigorous upper bound on the difference between the external and internal emissivity is obtained. Calculations using the internal emissivity are compared to exact calculations for several models and materials. A new approach to calculating the internal emissivity is developed, yielding vastly improved accuracy over a wide range of temperature differences. The internal fractional function can be useful for certain simplified calculations.

Jeans' role in the law of black-body radiation

1980 ◽  
Vol 15 (4) ◽  
pp. 255-260 ◽  
Author(s):  
J B T McCaughan
Keyword(s):  
Black Body ◽  
Black Body Radiation ◽  
The Law

Microwaves: Application in Electron Microscopy

1990 ◽  
Vol 48 (3) ◽  
pp. 140-141
Author(s):  
Anthony S-Y Leong ◽  
David W Gove
Keyword(s):  
Electron Microscopy ◽  
Light Microscopy ◽  
Chemical Reactions ◽  
Electromagnetic Waves ◽  
Tissue Fixation ◽  
Primary Method ◽  
Dipolar Molecules ◽  
Wide Range ◽  
Time Required ◽  
Cryostat Sections

Microwaves (MW) are electromagnetic waves which are commonly generated at a frequency of 2.45 GHz. When dipolar molecules such as water, the polar side chains of proteins and other molecules with an uneven distribution of electrical charge are exposed to such non-ionizing radiation, they oscillate through 180° at a rate of 2,450 million cycles/s. This rapid kinetic movement results in accelerated chemical reactions and produces instantaneous heat. MWs have recently been applied to a wide range of procedures for light microscopy. MWs generated by domestic ovens have been used as a primary method of tissue fixation, it has been applied to the various stages of tissue processing as well as to a wide variety of staining procedures. This use of MWs has not only resulted in drastic reductions in the time required for tissue fixation, processing and staining, but have also produced better cytologic images in cryostat sections, and more importantly, have resulted in better preservation of cellular antigens.

The Physical World

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Variational Principles ◽  
Black Body ◽  
Black Body Radiation ◽  
Physical World ◽  
Atomic Scale ◽  
Solid State Physics ◽  
Least Action ◽  
Dimensional Spacetime

The book is an inspirational survey of fundamental physics, emphasizing the use of variational principles. Chapter 1 presents introductory ideas, including the principle of least action, vectors and partial differentiation. Chapter 2 covers Newtonian dynamics and the motion of mutually gravitating bodies. Chapter 3 is about electromagnetic fields as described by Maxwell’s equations. Chapter 4 is about special relativity, which unifies space and time into 4-dimensional spacetime. Chapter 5 introduces the mathematics of curved space, leading to Chapter 6 covering general relativity and its remarkable consequences, such as the existence of black holes. Chapters 7 and 8 present quantum mechanics, essential for understanding atomic-scale phenomena. Chapter 9 uses quantum mechanics to explain the fundamental principles of chemistry and solid state physics. Chapter 10 is about thermodynamics, which is built around the concepts of temperature and entropy. Various applications are discussed, including the analysis of black body radiation that led to the quantum revolution. Chapter 11 surveys the atomic nucleus, its properties and applications. Chapter 12 explores particle physics, the Standard Model and the Higgs mechanism, with a short introduction to quantum field theory. Chapter 13 is about the structure and evolution of stars and brings together material from many of the earlier chapters. Chapter 14 on cosmology describes the structure and evolution of the universe as a whole. Finally, Chapter 15 discusses remaining problems at the frontiers of physics, such as the interpretation of quantum mechanics, and the ultimate nature of particles. Some speculative ideas are explored, such as supersymmetry, solitons and string theory.

Constructing Quantum Mechanics

2019 ◽  
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Black Body ◽  
Black Body Radiation ◽  
Wave Mechanics ◽  
Specific Heats ◽  
Old Quantum Theory ◽  
Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

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