Hydrogen Atomic and Molecular Hydrogen
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CNSC Research Report 2016-17
The Science of Safety: CNSC Research Report 2016–17 © Canadian Nuclear Safety Commission (CNSC) 2018 Cat. No. CC171-24E-PDF ISSN 2369-4351 Extracts from this document may be reproduced for individual use without permission provided the source is fully acknowledged. However, reproduction in whole or in part for purposes of resale or redistribution requires prior written permission from the Canadian Nuclear Safety Commission. Également publié en français sous le titre : La science de la sûreté : Rapport de recherche de la CCSN 2016-2017 Document availability This document can be viewed on the CNSC website. To request a copy of the document in English or French, please contact: Canadian Nuclear Safety Commission 280 Slater Street P.O. Box 1046, Station B Ottawa, Ontario K1P 5S9 CANADA Tel.: 613-995-5894 or 1-800-668-5284 (in Canada only) Facsimile: 613-995-5086 Email: [email protected] Website: nuclearsafety.gc.ca Facebook: facebook.com/CanadianNuclearSafetyCommission YouTube: youtube.com/cnscccsn Twitter: @CNSC_CCSN Publishing History June 2018 Edition 1.0 Table of contents Message from the President .......................................................................................................................... 1 Introduction ................................................................................................................................................... 2 Ensuring the safety of nuclear power plants ................................................................................................. 6 Protecting -
Quantum Theory of the Hydrogen Atom
Quantum Theory of the Hydrogen Atom Chemistry 35 Fall 2000 Balmer and the Hydrogen Spectrum n 1885: Johann Balmer, a Swiss schoolteacher, empirically deduced a formula which predicted the wavelengths of emission for Hydrogen: l (in Å) = 3645.6 x n2 for n = 3, 4, 5, 6 n2 -4 •Predicts the wavelengths of the 4 visible emission lines from Hydrogen (which are called the Balmer Series) •Implies that there is some underlying order in the atom that results in this deceptively simple equation. 2 1 The Bohr Atom n 1913: Niels Bohr uses quantum theory to explain the origin of the line spectrum of hydrogen 1. The electron in a hydrogen atom can exist only in discrete orbits 2. The orbits are circular paths about the nucleus at varying radii 3. Each orbit corresponds to a particular energy 4. Orbit energies increase with increasing radii 5. The lowest energy orbit is called the ground state 6. After absorbing energy, the e- jumps to a higher energy orbit (an excited state) 7. When the e- drops down to a lower energy orbit, the energy lost can be given off as a quantum of light 8. The energy of the photon emitted is equal to the difference in energies of the two orbits involved 3 Mohr Bohr n Mathematically, Bohr equated the two forces acting on the orbiting electron: coulombic attraction = centrifugal accelleration 2 2 2 -(Z/4peo)(e /r ) = m(v /r) n Rearranging and making the wild assumption: mvr = n(h/2p) n e- angular momentum can only have certain quantified values in whole multiples of h/2p 4 2 Hydrogen Energy Levels n Based on this model, Bohr arrived at a simple equation to calculate the electron energy levels in hydrogen: 2 En = -RH(1/n ) for n = 1, 2, 3, 4, . -
Source of Atomic Hydrogen for Ion Trap Experiments: Review and Basic Properties
WDS'15 Proceedings of Contributed Papers — Physics, 155–161, 2015. ISBN 978-80-7378-311-2 © MATFYZPRESS Source of Atomic Hydrogen for Ion Trap Experiments: Review and Basic Properties A. Kovalenko, Š Roučka, S. Rednyk, T. D. Tran, D. Mulin, R. Plašil, J. Glosík Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czech Republic. Abstract. The H-atom source was used to produce atomic hydrogen for study of ion-molecule reactions relevant to astrochemistry at low temperatures. H atoms were cooled and formed into an effusive beam, passing through a 22-pole ion trap. Here we present the basic operating principles of the H-atom source and give a review of this apparatus with some calculations of vacuum conditions and parameters of the produced H-atom beam. Introduction Hydrogen is the most abundant element in the Universe [Field et al., 1966]. It is the main component of stars, giant planets and interstellar clouds. Reactions with atomic or molecular hydrogen are important for understanding the processes which occur in the interstellar medium and during the formation of the new stars. There are three isotopes of hydrogen: protium, deuterium and tritium. The reactions of ions with H atoms have to be studied for better understanding of formation and destruction of more complex ions and molecules observed in interstellar medium. There are regions in space called H I and H II regions where hydrogen is mostly neutral in H I regions, rather than ionized or molecular in the H II regions. The atomic hydrogen plays fundamental role in many astrophysical contexts especially in formation H2 molecules [Habart et al., 2005; Sternberg et al., 2014]. -
Principal, Azimuthal and Magnetic Quantum Numbers and the Magnitude of Their Values
268 A Textbook of Physical Chemistry – Volume I Principal, Azimuthal and Magnetic Quantum Numbers and the Magnitude of Their Values The Schrodinger wave equation for hydrogen and hydrogen-like species in the polar coordinates can be written as: 1 휕 휕휓 1 휕 휕휓 1 휕2휓 8휋2휇 푍푒2 (406) [ (푟2 ) + (푆푖푛휃 ) + ] + (퐸 + ) 휓 = 0 푟2 휕푟 휕푟 푆푖푛휃 휕휃 휕휃 푆푖푛2휃 휕휙2 ℎ2 푟 After separating the variables present in the equation given above, the solution of the differential equation was found to be 휓푛,푙,푚(푟, 휃, 휙) = 푅푛,푙. 훩푙,푚. 훷푚 (407) 2푍푟 푘 (408) 3 푙 푘=푛−푙−1 (−1)푘+1[(푛 + 푙)!]2 ( ) 2푍 (푛 − 푙 − 1)! 푍푟 2푍푟 푛푎 √ 0 = ( ) [ 3] . exp (− ) . ( ) . ∑ 푛푎0 2푛{(푛 + 푙)!} 푛푎0 푛푎0 (푛 − 푙 − 1 − 푘)! (2푙 + 1 + 푘)! 푘! 푘=0 (2푙 + 1)(푙 − 푚)! 1 × √ . 푃푚(퐶표푠 휃) × √ 푒푖푚휙 2(푙 + 푚)! 푙 2휋 It is obvious that the solution of equation (406) contains three discrete (n, l, m) and three continuous (r, θ, ϕ) variables. In order to be a well-behaved function, there are some conditions over the values of discrete variables that must be followed i.e. boundary conditions. Therefore, we can conclude that principal (n), azimuthal (l) and magnetic (m) quantum numbers are obtained as a solution of the Schrodinger wave equation for hydrogen atom; and these quantum numbers are used to define various quantum mechanical states. In this section, we will discuss the properties and significance of all these three quantum numbers one by one. Principal Quantum Number The principal quantum number is denoted by the symbol n; and can have value 1, 2, 3, 4, 5…..∞. -
Crystal Chemistry of Perovskite-Type Hydride Namgh3: Implications for Hydrogen Storage
Chem. Mater. 2008, 20, 2335–2342 2335 Crystal Chemistry of Perovskite-Type Hydride NaMgH3: Implications for Hydrogen Storage Hui Wu,*,†,‡ Wei Zhou,†,‡ Terrence J. Udovic,† John J. Rush,†,‡ and Taner Yildirim†,§ NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau DriVe, MS 6102, Gaithersburg, Maryland 20899-6102, Department of Materials Science and Engineering, UniVersity of Maryland, College Park, Maryland 20742-2115, and Department of Materials Science and Engineering, UniVersity of PennsylVania, 3231 Walnut Street, Philadelphia, PennsylVania 19104-6272 ReceiVed NoVember 26, 2007. ReVised Manuscript ReceiVed January 11, 2008 The crystal structure, lattice dynamics, and local metal-hydrogen bonding of the perovskite hydride NaMgH3 were investigated using combined neutron powder diffraction, neutron vibrational spectroscopy, and first-principles calculations. NaMgH3 crystallizes in the orthorhombic GdFeO3-type perovskite structure (Pnma) with a-b+a- octahedral tilting in the temperature range of 4 to 370 K. In contrast with previous structure studies, the refined Mg-H lengths and H-Mg-H angles indicate that the MgH6 octahedra maintain a near ideal configuration, which is corroborated by bond valence methods and our DFT calculations, and is consistent with perovskite oxides with similar tolerance factor values. The temperature dependences of the lattice distortion, octahedral tilting angle, and atomic displacement of H are also consistent with the recently observed high H mobility at elevated temperature. The stability and dynamics of NaMgH3 are discussed and rationalized in terms of the details of our observed perovskite structure. Further experiments reveal that its perovskite crystal structure and associated rapid hydrogen motion can be used to improve the slow hydrogenation kinetics of some strongly bound light-metal-hydride systems such as MgH2 and possibly to design new alloy hydrides with desirable hydrogen-storage properties. -
Further Quantum Physics
Further Quantum Physics Concepts in quantum physics and the structure of hydrogen and helium atoms Prof Andrew Steane January 18, 2005 2 Contents 1 Introduction 7 1.1 Quantum physics and atoms . 7 1.1.1 The role of classical and quantum mechanics . 9 1.2 Atomic physics—some preliminaries . .... 9 1.2.1 Textbooks...................................... 10 2 The 1-dimensional projectile: an example for revision 11 2.1 Classicaltreatment................................. ..... 11 2.2 Quantum treatment . 13 2.2.1 Mainfeatures..................................... 13 2.2.2 Precise quantum analysis . 13 3 Hydrogen 17 3.1 Some semi-classical estimates . 17 3.2 2-body system: reduced mass . 18 3.2.1 Reduced mass in quantum 2-body problem . 19 3.3 Solution of Schr¨odinger equation for hydrogen . ..... 20 3.3.1 General features of the radial solution . 21 3.3.2 Precisesolution.................................. 21 3.3.3 Meanradius...................................... 25 3.3.4 How to remember hydrogen . 25 3.3.5 Mainpoints.................................... 25 3.3.6 Appendix on series solution of hydrogen equation, off syllabus . 26 3 4 CONTENTS 4 Hydrogen-like systems and spectra 27 4.1 Hydrogen-like systems . 27 4.2 Spectroscopy ........................................ 29 4.2.1 Main points for use of grating spectrograph . ...... 29 4.2.2 Resolution...................................... 30 4.2.3 Usefulness of both emission and absorption methods . 30 4.3 The spectrum for hydrogen . 31 5 Introduction to fine structure and spin 33 5.1 Experimental observation of fine structure . ..... 33 5.2 TheDiracresult ..................................... 34 5.3 Schr¨odinger method to account for fine structure . 35 5.4 Physical nature of orbital and spin angular momenta . -
Highly Conductive Antiperovskites with Soft Anion Lattices 12 January 2021, by I
Highly conductive antiperovskites with soft anion lattices 12 January 2021, by I. Mindy Takamiya, Mari Toyama 'cation." They also have numerous intriguing properties, including superconductivity and, in contrast to most materials, contraction upon heating. Lithium- and sodium-rich antiperovskites, such as Li3OCl and Na3OCl, have been attracting much attention due to their high ionic conductivity and alkali metal concentration, making them promising candidates to replace liquid electrolytes used in lithium ion batteries. "But achieving a comparable lithium ion conductivity in solid materials has been challenging," explains iCeMS solid-state chemist Hiroshi Kageyama, who led the study. Soft anions, like sulfur ions (S2-), provide an ideal conduction path for sodium (Na+) and lithium (Li+) ions, Kageyama and his team synthesized a new family with the hydride ions (H-) helping to stabilize the of lithium- and sodium-rich antiperovskites that compound's structure. Credit: Mindy Takamiya/Kyoto begins to overcome this issue. Instead of 'hard' University iCeMS oxygen and halogen anions, their antiperovskites contain a hydrogen anion, called a hydride, and 'soft' chalcogen anions like sulfur. A new structural arrangement of atoms shows The scientists conducted a wide range of promise for developing safer batteries made with theoretical and experimental investigations on solid materials. Scientists at Kyoto University's these antiperovskites, and found that the soft anion Institute for Integrated Cell-Material Sciences lattice provides an ideal conduction path for lithium (iCeMS) designed a new type of 'antiperovskite' and sodium ions, which can be further enhanced by that could help efforts to replace the flammable chemical substitutions. organic electrolytes currently used in lithium ion batteries. -
1.2 Formulation of the Schrödinger Equation for the Hydrogen Atom
2 1 Hydrogen orbitals 1.2 Formulation of the Schrodinger¨ equation for the hydrogen atom In this initial treatment, we will make some practical approximations and simplifi- cations. Since we are for the moment only trying to establish the general form of the hydrogenic wave functions, this will suffice. To start with, we will assume that the nucleus has zero extension. We place the origin at its position, and we ignore the centre-of-mass motion. This reduces the two-body problem to a single particle, the electron, moving in a central-field potential. To take the finite mass of the nu- cleus into account, we replace the electron mass with the reduced mass, m, of the two-body problem. Moreover, we will in this chapter ignore the effect on the wave function of relativistic effects, which automatically implies that we ignore the spins of the electron and of the nucleus. This makes us ready to formulate the Hamilto- nian. The potential is the classical Coulomb interaction between two particles of op- posite charges. With spherical coordinates, and with r as the radial distance of the electron from the origin, this is: Ze2 V(r) = − ; (1.1) 4pe0 r with Z being the charge state of the nucleus. The Schrodinger¨ equation is: h¯ 2 − ∇2y(r) +V(r)y = Ey(r) ; (1.2) 2m where the Laplacian in spherical coordinates is: 1 ¶ ¶ 1 ¶ ¶ 1 ¶ 2 ∇2 = r2 + sinq + : (1.3) r2 ¶r ¶r r2 sinq ¶q ¶q r2 sin2 q ¶j2 Since the potential is purely central, the solution to (1.2) can be factorised into a radial and an angular part, y(r;q;j) = R(r)Y(q;j). -
The Principal Quantum Number the Azimuthal Quantum Number The
To completely describe an electron in an atom, four quantum numbers are needed: energy (n), angular momentum (ℓ), magnetic moment (mℓ), and spin (ms). The Principal Quantum Number This quantum number describes the electron shell or energy level of an atom. The value of n ranges from 1 to the shell containing the outermost electron of that atom. For example, in caesium (Cs), the outermost valence electron is in the shell with energy level 6, so an electron incaesium can have an n value from 1 to 6. For particles in a time-independent potential, as per the Schrödinger equation, it also labels the nth eigen value of Hamiltonian (H). This number has a dependence only on the distance between the electron and the nucleus (i.e. the radial coordinate r). The average distance increases with n, thus quantum states with different principal quantum numbers are said to belong to different shells. The Azimuthal Quantum Number The angular or orbital quantum number, describes the sub-shell and gives the magnitude of the orbital angular momentum through the relation. ℓ = 0 is called an s orbital, ℓ = 1 a p orbital, ℓ = 2 a d orbital, and ℓ = 3 an f orbital. The value of ℓ ranges from 0 to n − 1 because the first p orbital (ℓ = 1) appears in the second electron shell (n = 2), the first d orbital (ℓ = 2) appears in the third shell (n = 3), and so on. This quantum number specifies the shape of an atomic orbital and strongly influences chemical bonds and bond angles. -
Importance of Hydrogen Atom
Hydrogen Atom Dragica Vasileska Arizona State University Importance of Hydrogen Atom • Hydrogen is the simplest atom • The quantum numbers used to characterize the allowed states of hydrogen can also be used to describe (approximately) the allowed states of more complex atoms – This enables us to understand the periodic table • The hydrogen atom is an ideal system for performing precise comparisons of theory and experiment – Also for improving our understanding of atomic structure • Much of what we know about the hydrogen atom can be extended to other single-electron ions – For example, He+ and Li2+ Early Models of the Atom • ’ J.J. Thomson s model of the atom – A volume of positive charge – Electrons embedded throughout the volume • ’ A change from Newton s model of the atom as a tiny, hard, indestructible sphere “ ” watermelon model Experimental tests Expect: 1. Mostly small angle scattering 2. No backward scattering events Results: 1. Mostly small scattering events 2. Several backward scatterings!!! Early Models of the Atom • ’ Rutherford s model – Planetary model – Based on results of thin foil experiments – Positive charge is concentrated in the center of the atom, called the nucleus – Electrons orbit the nucleus like planets orbit the sun ’ Problem: Rutherford s model “ ” ’ × – The size of the atom in Rutherford s model is about 1.0 10 10 m. (a) Determine the attractive electrical force between an electron and a proton separated by this distance. (b) Determine (in eV) the electrical potential energy of the atom. “ ” ’ × – The size of the atom in Rutherford s model is about 1.0 10 10 m. (a) Determine the attractive electrical force between an electron and a proton separated by this distance. -
The Hydrogen Atom: Consideration of the Electron Self-Field Arxiv
The hydrogen atom: consideration of the electron self-field Biguaa L.V ∗ Kassandrov V.V † ∗ Quantum technology center Moscow State University y Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia January 8, 2021 Keywords: Spinor electrodynamics. Dirac-Maxwell system of equations. Solitonlike solu- tions. Spectrum of characteristics. “Bohrian” law for binding energies PACS: 03.50.-z; 03.65.-w; 03.65.-Pm 1 THE HYDROGEN ATOM AND CLASSICAL FIELD MODELS OF ELEMENTARY PARTICLES It is well known that the successful description of the hydrogen atom, first in Bohr’s theory, and then via solutions to the Schr¨odinger equation was one of the main motivations for the development of quantum theory. Later, Dirac described almost perfectly the observed hydrogen spectrum using his relativistic generalization of the Schr¨odingerequation. A slight deviation from experiment (the Lamb shift between 2s1=2 and 2p1=2 levels in the hydrogen atom) arXiv:2101.02202v1 [quant-ph] 5 Jan 2021 discovered later was interpreted as the effect of electron interaction with vacuum fluctuations of electromagnetic field and explained in the framework of quantum electrodynamics (QED) using second quantization. Nonetheless, the problem of the description of the hydrogen atom still attracts attention of researchers, and, in some sense, is a “touchstone” for many new theoretical developments. In particular, it is possible to obtain the energy spectrum via purely algebraic methods [1]. Theories of the ”supersymmetric” hydrogen atom are also widespread [2]. In the framework of the classical ideas, the spectrum can be explained by the absence of radiation for the electron ∗E-mail: [email protected] †E-mail: [email protected] 1 motion along certain “stable” orbits. -
The Hydrogen Atom
Quantum Mechanics: The Hydrogen Atom 13th April 2011 I. The Hydrogen Atom In this next section, we will tie together the elements of the last several sections to arrive at a complete description of the hydrogen atom. This will cul- minate in the definition of the hydrogen-atom orbitals and associated energies. From these functions, taken as a complete basis, we will be able to construct approximations to more complex wave functions for more complex molecules. Thus, the work of the last few lectures has fundamentally been aimed at estab- lishing a foundation for more complex problems in terms of exact solutions for smaller, model problems. II. The Radial Function We will start by reiterating the Schrodinger equation in 3D spherical coordi- nates as (refer to any standard text to get the transformation from Cartesian to spherical coordinate reference systems). Here, we have not placed the constraint of a constant distance separting the masses of the rigid rotor (refer to last lec- ture); furthermore, we will keep in the formulation the potential V (r; θ; φ) for generality. Thus, in spherical polar coordinates, H^ (r; θ; φ) (r; θ; φ) = E (r; θ; φ) be- comes: E (r; θ; φ) = −h¯2 1 @ @ 1 @ @ 1 @2 r2 + sinθ + + V (r; θ; φ) (r; θ; φ) 2µ r2 @r @r r2sinθ @θ @θ r2sin2θ @φ2 Now, for the hydrogen atom, with one electron found in "orbits" (note the quotes!) around the nucleus of charge +1, we can include an electrostatic poten- tial which is essentially the Coulomb potential between a positive and negative charge: −Ze2 V (jrj) = V (r) = 4πor where Z is the nuclear charge (i.e, +1 for the nucleus of a hydrogen atom).