Quantum Energy

10 Key excerpts on "Quantum Energy"

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  Electrons, Neutrons and Protons in Engineering

  A Study of Engineering Materials and Processes Whose Characteristics May Be Explained by Considering the Behavior of Small Particles When Grouped Into Systems Such as Nuclei, Atoms, Gases, and Crystals

  • J. R. Eaton(Author)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  CHAPTER 10 ENERGY LEVELS I N T R O D U C T I O N The quantum theory states that energy is transferred in small packets, the size of the packet being dependent on the characteristics of the system to which, or from which, the transfer takes place. It must not be inferred that the quanta of energy are of standardized size (as is the case with the electronic charge). Ac-tually quanta of every size are theoretically possible; the restrictions on size are set by the system which is asked to accept or to emit energy. In Chapter 5 the energy levels of atoms were discussed in considerable detail, with particular re-ference to the energy levels of the hydrogen atom. It was shown that the atom, the system made up of the nucleus with its complement of electrons, can accept energy from external sources only when the amount of energy supplied is equal to or greater than certain amounts characteristic of the particular element. Thus, the hydrogen atom can be excited from the ground state only when there is available a packet of energy having at least 10.19 eV of energy. In describing the behavior of energy absorption by atoms, it is stated that there are certain allowed energy levels between which are forbidden gaps. This quantization of energy levels applies not only to single atoms, but extends to the systems known as molecules and crystals. In fact the concept of energy levels becomes evident whenever two or more particles unite to form a more complicated aggregate. The study of the energy levels of groups of particles has many interesting and surprising ramifications. A knowledge of energy levels is necessary for an under-standing of such subjects as electrical conduction through gases, certain thermal properties of gases, electrical, thermal and optical properties of solids, chemical reactions, and even nuclear interactions.

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  Thermodynamics and Statistical Mechanics

  An Integrated Approach

  • M. Scott Shell(Author)
  • 2015(Publication Date)
  • Cambridge University Press

    (Publisher)

  We also do not need quantum mechanics in order to understand many molecular-level interactions. Why? Quantum effects are dominant at very small scales, typically ångström units (Å) or less. By quantum effects, we mean that the probability distribution implied by the wave- function is not sharply peaked, and uncertainties in the positions and velocities of the atoms are significant. Moreover, quantum behavior is often not as important at moderate to high temperatures because, above absolute zero, systems sit at energies that are significantly higher than their ground-state values. At these elevated energies, the energy eigenvalue spectrum becomes dense such that it appears effectively continuous rather than discrete. Figure 3.1 shows the spectrum for a particle in a box, where it is clear that the energy levels begin to look continuous at elevated energies. In addition, for systems in which electrons are localized, to a good approximation we often do not need quantum theory to describe atom–atom interactions. A quantum treatment, however, is always necessary when electron clouds are nonlocalized, as in metals, or when there is bond formation or bond breaking. That is, classical models cannot capture chemical reactions at the molecular level. When quantum effects are not important, we can model the world to a good approxi- mation using a classical description. Here, the term “classical” in the sense of a system is distinct from that of “classical thermodynamics.” Classical systems are composed of particles with definite positions and momenta, and their time evolution is governed by deterministic laws. Indeed, the classical picture forms the basis of 1 10 100 8mL 2 h 2 E Figure 3.1. The energy eigenvalue spectrum for the classic particle-in-a- box problem. Each horizontal line gives an energy eigenvalue. Notice that the energy levels appear more closely spaced together when viewed at larger energy scales. 25 3.2 The classical picture

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  Chemical Physics & Physical Chemistry

  • (Author)
  • 2014(Publication Date)
  • Library Press

    (Publisher)

  ________________________ WORLD TECHNOLOGIES ________________________ Chapter- 3 Quantum Chemistry Quantum chemistry is a branch of theoretical chemistry which applies quantum mechanics and quantum field theory to address problems in chemistry. One application of quantum chemistry is the electronic behavior of atoms and molecules relative to their chemical reactivity. Quantum chemistry lies on the border between chemistry and physics. Thus, significant contributions have been made by scientists from both fields. It has a strong and active overlap with the field of atomic physics and molecular physics, as well as physical chemistry. Quantum chemistry mathematically describes the fundamental behavior of matter at the molecular scale, but can span from elementary particles such as electrons (fermions) and photons (bosons) to the cosmos such as star-formation. It is, in principle, possible to describe all chemical systems using this theory. In practice, only the simplest chemical systems may realistically be investigated in purely quantum mechanical terms, and approximations must be made for most practical purposes. Hence a detailed under-standing of quantum mechanics is not necessary for most chemistry, as the important implications of the theory (principally the orbital approximation) can be understood and applied in simpler terms. In quantum mechanics the Hamiltonian, or the physical state, of a particle can be expressed as the sum of two operators, one corresponding to kinetic energy and the other to potential energy. The Hamiltonian in the Schrödinger wave equation used in quantum chemistry does not contain terms for the spin of the electron. Solutions of the Schrödinger equation for the hydrogen atom gives the form of the wave function for atomic orbitals, and the relative energy of the various orbitals. The orbital approximation can be used to understand the other atoms e.g.

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  Time, Emergences and Communications

  • Bernard Dugué(Author)
  • 2018(Publication Date)
  • Wiley-ISTE

    (Publisher)

  60 Time, Emergences and Communications Many sciences hide the quantum description of matter and content themselves with the representation of living materials, substances and systems as a set of components endowed with qualities, and creating systems with new properties when they combine. The questions of morphogenesis and emergence, in particular, remain unanswered. But with the new interpretation of quantum matter, it will be possible to formulate these questions in an unprecedented way. In the field of chemistry, quantum physics has been applied with remarkable success and it is this discipline, far more than thermodynamics, which offers a fine understanding of the phenomena of association, bonding and transformation. Quantum chemistry explains the structures of atomic bonds, whereas chemical thermodynamics is more interested in energy balances and reaction speeds. The central concept of quantum chemistry is the “electronic cloud”, also referred to as “electronic orbital”. In the case of hydrogen, this can be calculated mathematically by solving Schrödinger’s equation. By convention, every atom has its electrons placed on the orbitals calculated for hydrogen, and the model works fairly properly! Quantum chemistry is developed as a physics of the forms, and even a physics of communication. In general, thermochemistry tends to ignore the quantum description and uses classical state variables, H enthalpy, S entropy and G free enthalpy. The main goal of classical chemistry is to establish the possibility of reactions, associated energy exchanges and kinetics. Classical chemistry sees things on the surface, imagining atoms as the pieces of a game of Lego reacting in concert.

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  Quantum Mechanics

  A Paradigms Approach

  • David H. McIntyre(Author)
  • 2022(Publication Date)
  • Cambridge University Press

    (Publisher)

  107 C H A P T E R 5 Quantized Energies: Particle in a Box In the first part of this book we used the spin system to illustrate the basic concepts and tools of quan- tum mechanics. With a firm foundation in how quantum mechanics works, we are ready to address the central question that quantum mechanics was designed to answer: How do we explain the structure of the microscopic world? All around us are nuclei, atoms, molecules, and solids with unique properties that cannot be explained with classical physics but require quantum mechanics. For example, quantum mechanics can tell us why sodium lamps are yellow, why laser diodes have a unique color, and why uranium is radioactive. The key to understanding the structure of microscopic systems lies in the energy states that the systems are allowed to have. Each microscopic system has a unique set of energy levels that gives that system a “fingerprint” that sets it apart from other systems. With the tools of quantum mechanics, we can build a theoretical model for the system, predict that fingerprint, and compare it to the experimen- tal measurement. Our goal in this chapter and the ones that follow is to learn how to predict this energy fingerprint. In this chapter we will study a particularly simple model system that exhibits most of the important features that are shared by all microscopic systems. 5.1  SPECTROSCOPY The energy fingerprint of a system not only identifies that system uniquely, but the allowed energies determine the time evolution of the system through the Schrödinger equation, as we learned in Chapter 3. One of the primary experimental techniques for measuring the energy fingerprint of a system is spectros- copy. We saw a hint of this in the magnetic resonance example of Section 3.4: absorption and emission of photons causes transitions between quantized energy levels of the system only when the photon energy matches the spacing between the energy eigenstates.

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  Chemistry, 5th Edition

  • Allan Blackman, Steven E. Bottle, Siegbert Schmid, Mauro Mocerino, Uta Wille(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  from one bound state to another. In contrast, if an atom absorbs enough energy to remove an electron completely, the electron is no longer bound and can take on any amount of kinetic energy. Bound electrons have quantised energies; free electrons can have any amount of energy. Experimental values for the quantised energies of atomic electrons can be calculated from absorption and emission spectra. The theory of quantum mechanics provides a mathematical explanation that links quantised energies to the wave characteristics of electrons. These wave properties of atomic electrons are described by the Schrödinger equation below, where  H is the Hamiltonian operator for the system (containing terms for the kinetic and potential energy), E is the energy of the system and  is the wavefunction for the system.  H = E In particular,  is the amplitude of the electron’s matter wave. As with light, the amplitude itself does not have any physical meaning, but its square represents the electron density distribution or probability of finding an electron. A wavefunction is a mathematical function that gives us information about an electron’s position in an atom. The solution of the Schrödinger equation gives us both the energies and the associated wavefunctions of a chemical system. Despite its concise form, the Schrödinger equation can be solved exactly only for systems containing one electron. The Schrödinger equation has solutions only for specific, quantised energy values. For each quantised energy value, the Schrödinger equation generates a wavefunction that describes how the electrons are distributed in space. A one-electron wavefunction is called an atomic orbital. We will describe the properties of atomic orbitals in section 4.5. Each described property can be identified, or indexed, using a quantum number. These are numbers that specify the values of the electron’s quantised properties.

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  Basic Molecular Spectroscopy

  • P.A. Gorry(Author)
  • 2016(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  Chapter 2 The quantum treatment of molecules ESSENTIAL THEORY Understanding the spectra of atoms and molecules has been one of the great challenges, and success stories, in physical science this century. The fact that many atomic and molecular spectra consist of discrete lines is not expected on the basis of classical physics and it has been a triumph of quantum mechanics to explain this observation. Quantum mechanics places severe limitations on the allowed energy states of atomic and molecular systems and determines the allowed transitions between them. The rest of this book will examine how the principles of quantum mechanics can be used to explain molecular spectra and how this in turn leads to important structural information on the molecules involved. 2.1 The Schrödinger equation An essential prerequisite to understanding electronic, vibrational or rotational molecular spectra is to have an expression for the energy levels of the system under study. The observed spectrum is produced when the system changes between these allowed states. The energy levels are obtained by solving the time-independent Schrödinger wave equation for the molecular motions under consideration. It is best to consider the Schrödinger equation as the fundamental starting point in quantum mechanics—just as Newton's laws are in classical mechanics. We use the Schrödinger equation because it works! This chapter will present the important aspects of quantum mechanics necessary for an understanding of molecular spectroscopy. Although it is self-contained it is not intended that this chapter should provide a comprehensive account of molecular quantum theory— even at the introductory level—and little in the way of formal solutions will be provided. Those readers not familiar with the material in this chapter should consult one of References 1-3 for more detail. 14

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  Dictionary of Energy

  • Cutler J. Cleveland, Cutler J. Cleveland, Christopher G. Morris(Authors)
  • 2005(Publication Date)
  • Elsevier Science

    (Publisher)

  quantize Physics. to restrict the magnitude of a given physical quantity to that of a single member of a discrete set of values; these are typically integral multiples of some funda-mental unit, or quantum. Thus, quantiza-tion. quantum Physics. plural, quanta; the funda-mental unit of electromagnetic energy that is absorbed in integral multiples of E = hv , where h is Planck’s constant. quantum number Physics. a number indi-cating which member of an allowed set of magnitudes a quantized physical quantity possesses, usually an integer or half-integer. quantum theory Physics. a modern branch of physics based on the premise that energy and momentum exist in discrete amounts called quanta (see quantum ) and that, at the atomic and subatomic levels, the effects of this quantization are significant. This field extends or supersedes classical mechanics in certain respects, especially in descriptions of very small systems (atom size or less), and of certain phenomena (e.g., superfluidity). Also, quantum mechanics. R See below. R Q quantum theory Developed in the early 1900s by scientists such as Planck, Einstein, Bohr, Heisenberg, and Schroedinger, quantum theory is a term used to describe a physical theory that applies to systems normally at very small length scales (such as the level of the atom). Two primary motivations for this theory were the phenomena of the photoelectric effect and the spectra of light emitted by the Hydrogen atom, which before 1900 were not understood in terms of “classical” mechanics. Quantum theory was able to provide an explanation for these, but at the expense of violating many of our (classical) intui-tive beliefs. The word “quantum” itself refers to a system which can only be in certain discrete states, so in order to evolve from one state to another, the system must make a “quantum leap”.

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  Basic Physical Chemistry

  The Route to Understanding

  • E Brian Smith(Author)
  • 2012(Publication Date)
  • ICP

    (Publisher)

  A most important difference between the new and the old physics is the recognition that energy is not continuous. 3.2 Basic ideas of quantum mechanics It was found that many of the failures of classical physics described above could be explained if the following bold assumption was made: energy comes in discrete packets and is not continuous . Max Planck, in 1900, first introduced this radical new idea, quantisation , to explain the colour of hot objects (black-body radiation). Albert Einstein extended its application to electromagnetic radiation by suggesting that the radiation itself consisted of small packets of energy, photons , with energy related to their frequency, ν , by E = hν, where h is Planck’s constant, 6 . 62 × 10 − 34 J s. Red light consists of low energy photons whereas blue or ultraviolet radiation is comprised of photons of higher energy. This idea provides a direct explanation of the photoelectronic effect. If the radiation is of too low a frequency, each photon has insufficient energy to dislodge electrons from the metal. A critical minimum energy, and a related frequency, ν c , given by E c = hν c , is necessary. The photons that comprise electromagnetic radiation in the blue or ultraviolet part of the electromagnetic spectrum correspond to radiation with a frequency on the order of magnitude 10 15 s − 1 . Their energy is E = hν = 6 . 62 × 10 − 34 J s × 10 15 s − 1 . The energy transferred if a mole of photons of this frequency is absorbed by a material is E = 6 . 62 × 10 − 19 J × 6 . 02 × 10 23 mol − 1 = 399 kJ mol − 1 . Electromagnetic radiation of this frequency can be absorbed by electrons in atoms or molecules and the energy absorbed is comparable with the strength of many chemical bonds. Ultraviolet light is often used to dissociate molecules and initiate chemical reactions. The new assumptions provided an explanation of the spectra of atoms.

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  Foundations for Teaching Chemistry

  Chemical Knowledge for Teaching

  • Keith S. Taber(Author)
  • 2019(Publication Date)
  • Routledge

    (Publisher)

  10 Energy in chemistry and chemical bonding

  This chapter discusses one of the key topics in the chemistry curriculum, chemical bonding. This is a highly abstract concept area where a range of models and simplifications are taught. It is also an area where students commonly develop tenacious alternative conceptions (Taber, 2013a), and thus where the teaching approach can be very important in channelling student thinking towards scientific models. One particular feature of many students’ thinking is that they learn about chemistry topics such as bonding with no cognisance of the basic physical principles they have been taught elsewhere in science. Yet if students are to develop scientific understandings of chemistry, they need to appreciate where key concepts from physics, such as force and energy, are applied. This chapter reflects this imperative by first considering the role of the energy concept in understanding school chemistry before specifically addressing chemical bonding concepts.

  Appreciating the physicists’ concept of energy and how this applies in chemistry

  Energy is one of the most fundamental and ubiquitous concepts in science. It is also one of the most abstract. It is closely associated with another abstract concept – force. The primary responsibility for teaching these ideas falls upon the physics teacher. There are, however, consequences here for the teacher of chemistry:

  1. To avoid the potential of confusing students, the science department as a whole should have a common way of talking about energy and force so the ideas are used consistently across different topics and science subjects.
  2. As energy is an important concept in chemistry, the teacher of chemistry has to rely on what has been taught and how it has been taught in another subject.
  3. The teacher of chemistry not only relies on what has been taught in physics but on whether students can transfer their learning in physics to other subjects.

  The latter consideration is not insignificant. The question of transfer of learning, applying what has been learnt beyond the original context, is seen as a major issue in education (Lobato, 2006) because students often struggle to apply what they have learned in one context in other relevant situations. This is an example of a ‘fragmentation’ learning impediment (see Figure 3.1 ), as the learner does not make intended links with prior learning (see Figure 10.1

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