Molecular Energy Levels
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Rotational Motion (The Dynamics of a Rigid Body)
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 11: Rotational Motion (The Dynamics of a Rigid Body) Henry Semat City College of New York Robert Katz University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/physicskatz Part of the Physics Commons Semat, Henry and Katz, Robert, "Physics, Chapter 11: Rotational Motion (The Dynamics of a Rigid Body)" (1958). Robert Katz Publications. 141. https://digitalcommons.unl.edu/physicskatz/141 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Robert Katz Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 11 Rotational Motion (The Dynamics of a Rigid Body) 11-1 Motion about a Fixed Axis The motion of the flywheel of an engine and of a pulley on its axle are examples of an important type of motion of a rigid body, that of the motion of rotation about a fixed axis. Consider the motion of a uniform disk rotat ing about a fixed axis passing through its center of gravity C perpendicular to the face of the disk, as shown in Figure 11-1. The motion of this disk may be de scribed in terms of the motions of each of its individual particles, but a better way to describe the motion is in terms of the angle through which the disk rotates. -
Unit 1 Old Quantum Theory
UNIT 1 OLD QUANTUM THEORY Structure Introduction Objectives li;,:overy of Sub-atomic Particles Earlier Atom Models Light as clectromagnetic Wave Failures of Classical Physics Black Body Radiation '1 Heat Capacity Variation Photoelectric Effect Atomic Spectra Planck's Quantum Theory, Black Body ~diation. and Heat Capacity Variation Einstein's Theory of Photoelectric Effect Bohr Atom Model Calculation of Radius of Orbits Energy of an Electron in an Orbit Atomic Spectra and Bohr's Theory Critical Analysis of Bohr's Theory Refinements in the Atomic Spectra The61-y Summary Terminal Questions Answers 1.1 INTRODUCTION The ideas of classical mechanics developed by Galileo, Kepler and Newton, when applied to atomic and molecular systems were found to be inadequate. Need was felt for a theory to describe, correlate and predict the behaviour of the sub-atomic particles. The quantum theory, proposed by Max Planck and applied by Einstein and Bohr to explain different aspects of behaviour of matter, is an important milestone in the formulation of the modern concept of atom. In this unit, we will study how black body radiation, heat capacity variation, photoelectric effect and atomic spectra of hydrogen can be explained on the basis of theories proposed by Max Planck, Einstein and Bohr. They based their theories on the postulate that all interactions between matter and radiation occur in terms of definite packets of energy, known as quanta. Their ideas, when extended further, led to the evolution of wave mechanics, which shows the dual nature of matter -
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, . -
ROTATIONAL SPECTRA (Microwave Spectroscopy)
UNIT-1 ROTATIONAL SPECTRA (Microwave Spectroscopy) Lesson Structure 1.0 Objective 1.1 Introduction 1.2 Classification of molecules 1.3 Rotational spectra of regid diatomic molecules 1.4 Selection rules 1.5 Non-rigid rotator 1.6 Spectrum of a non-rigid rotator 1.7 Linear polyatomic molecules 1.8 Non-linear polyatomic molecules 1.9 Asymmetric top molecles 1.10. Starck effect Solved Problems Model Questions References 1.0 OBJECIVES After studyng this unit, you should be able to • Define the monent of inertia • Discuss the rotational spectra of rigid linear diatomic molecule • Spectrum of non-rigid rotator • Moment of inertia of linear polyatomic molecules Rotational Spectra (Microwave Spectroscopy) • Explain the effect of isotopic substitution and non-rigidity on the rotational spectra of a molecule. • Classify various molecules according to thier values of moment of inertia • Know the selection rule for a rigid diatomic molecule. 1.0 INTRODUCTION Spectroscopy in the microwave region is concerned with the study of pure rotational motion of molecules. The condition for a molecule to be microwave active is that the molecule must possess a permanent dipole moment, for example, HCl, CO etc. The rotating dipole then generates an electric field which may interact with the electrical component of the microwave radiation. Rotational spectra are obtained when the energy absorbed by the molecule is so low that it can cause transition only from one rotational level to another within the same vibrational level. Microwave spectroscopy is a useful technique and gives the values of molecular parameters such as bond lengths, dipole moments and nuclear spins etc. -
Vibrational Quantum Number
Fundamentals in Biophotonics Quantum nature of atoms, molecules – matter Aleksandra Radenovic [email protected] EPFL – Ecole Polytechnique Federale de Lausanne Bioengineering Institute IBI 26. 03. 2018. Quantum numbers •The four quantum numbers-are discrete sets of integers or half- integers. –n: Principal quantum number-The first describes the electron shell, or energy level, of an atom –ℓ : Orbital angular momentum quantum number-as the angular quantum number or orbital quantum number) describes the subshell, and gives the magnitude of the orbital angular momentum through the relation Ll2 ( 1) –mℓ:Magnetic (azimuthal) quantum number (refers, to the direction of the angular momentum vector. The magnetic quantum number m does not affect the electron's energy, but it does affect the probability cloud)- magnetic quantum number determines the energy shift of an atomic orbital due to an external magnetic field-Zeeman effect -s spin- intrinsic angular momentum Spin "up" and "down" allows two electrons for each set of spatial quantum numbers. The restrictions for the quantum numbers: – n = 1, 2, 3, 4, . – ℓ = 0, 1, 2, 3, . , n − 1 – mℓ = − ℓ, − ℓ + 1, . , 0, 1, . , ℓ − 1, ℓ – –Equivalently: n > 0 The energy levels are: ℓ < n |m | ≤ ℓ ℓ E E 0 n n2 Stern-Gerlach experiment If the particles were classical spinning objects, one would expect the distribution of their spin angular momentum vectors to be random and continuous. Each particle would be deflected by a different amount, producing some density distribution on the detector screen. Instead, the particles passing through the Stern–Gerlach apparatus are deflected either up or down by a specific amount. -
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 . -
Low Power Energy Harvesting and Storage Techniques from Ambient Human Powered Energy Sources
University of Northern Iowa UNI ScholarWorks Dissertations and Theses @ UNI Student Work 2008 Low power energy harvesting and storage techniques from ambient human powered energy sources Faruk Yildiz University of Northern Iowa Copyright ©2008 Faruk Yildiz Follow this and additional works at: https://scholarworks.uni.edu/etd Part of the Power and Energy Commons Let us know how access to this document benefits ouy Recommended Citation Yildiz, Faruk, "Low power energy harvesting and storage techniques from ambient human powered energy sources" (2008). Dissertations and Theses @ UNI. 500. https://scholarworks.uni.edu/etd/500 This Open Access Dissertation is brought to you for free and open access by the Student Work at UNI ScholarWorks. It has been accepted for inclusion in Dissertations and Theses @ UNI by an authorized administrator of UNI ScholarWorks. For more information, please contact [email protected]. LOW POWER ENERGY HARVESTING AND STORAGE TECHNIQUES FROM AMBIENT HUMAN POWERED ENERGY SOURCES. A Dissertation Submitted In Partial Fulfillment of the Requirements for the Degree Doctor of Industrial Technology Approved: Dr. Mohammed Fahmy, Chair Dr. Recayi Pecen, Co-Chair Dr. Sue A Joseph, Committee Member Dr. John T. Fecik, Committee Member Dr. Andrew R Gilpin, Committee Member Dr. Ayhan Zora, Committee Member Faruk Yildiz University of Northern Iowa August 2008 UMI Number: 3321009 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. -
Energy Harvesting from Rotating Structures
ENERGY HARVESTING FROM ROTATING STRUCTURES Tzern T. Toh, A. Bansal, G. Hong, Paul D. Mitcheson, Andrew S. Holmes, Eric M. Yeatman Department of Electrical & Electronic Engineering, Imperial College London, U.K. Abstract: In this paper, we analyze and demonstrate a novel rotational energy harvesting generator using gravitational torque. The electro-mechanical behavior of the generator is presented, alongside experimental results from an implementation based on a conventional DC motor. The off-axis performance is also modeled. Designs for adaptive power processing circuitry for optimal power harvesting are presented, using SPICE simulations. Key Words: energy-harvesting, rotational generator, adaptive generator, double pendulum 1. INTRODUCTION with ω the angular rotation rate of the host. Energy harvesting from moving structures has been a topic of much research, particularly for applications in powering wireless sensors [1]. Most motion energy harvesters are inertial, drawing power from the relative motion between an oscillating proof mass and the frame from which it is suspended [2]. For many important applications, including tire pressure sensing and condition monitoring of machinery, the host structure undergoes continuous rotation; in these Fig. 1: Schematic of the gravitational torque cases, previous energy harvesters have typically generator. IA is the armature current and KE is the been driven by the associated vibration. In this motor constant. paper we show that rotational motion can be used directly to harvest power, and that conventional Previously we reported initial experimental rotating machines can be easily adapted to this results for this device, and circuit simulations purpose. based on a buck-boost converter [3]. In this paper All mechanical to electrical transducers rely on we consider a Flyback power conversion circuit, the relative motion of two generator sections. -
Bouncing Oil Droplets, De Broglie's Quantum Thermostat And
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 28 August 2018 doi:10.20944/preprints201808.0475.v1 Peer-reviewed version available at Entropy 2018, 20, 780; doi:10.3390/e20100780 Article Bouncing oil droplets, de Broglie’s quantum thermostat and convergence to equilibrium Mohamed Hatifi 1, Ralph Willox 2, Samuel Colin 3 and Thomas Durt 4 1 Aix Marseille Université, CNRS, Centrale Marseille, Institut Fresnel UMR 7249,13013 Marseille, France; hatifi[email protected] 2 Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, 153-8914 Tokyo, Japan; [email protected] 3 Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150,22290-180, Rio de Janeiro – RJ, Brasil; [email protected] 4 Aix Marseille Université, CNRS, Centrale Marseille, Institut Fresnel UMR 7249,13013 Marseille, France; [email protected] Abstract: Recently, the properties of bouncing oil droplets, also known as ‘walkers’, have attracted much attention because they are thought to offer a gateway to a better understanding of quantum behaviour. They indeed constitute a macroscopic realization of wave-particle duality, in the sense that their trajectories are guided by a self-generated surrounding wave. The aim of this paper is to try to describe walker phenomenology in terms of de Broglie-Bohm dynamics and of a stochastic version thereof. In particular, we first study how a stochastic modification of the de Broglie pilot-wave theory, à la Nelson, affects the process of relaxation to quantum equilibrium, and we prove an H-theorem for the relaxation to quantum equilibrium under Nelson-type dynamics. -
The Quantum Mechanical Model of the Atom
The Quantum Mechanical Model of the Atom Quantum Numbers In order to describe the probable location of electrons, they are assigned four numbers called quantum numbers. The quantum numbers of an electron are kind of like the electron’s “address”. No two electrons can be described by the exact same four quantum numbers. This is called The Pauli Exclusion Principle. • Principle quantum number: The principle quantum number describes which orbit the electron is in and therefore how much energy the electron has. - it is symbolized by the letter n. - positive whole numbers are assigned (not including 0): n=1, n=2, n=3 , etc - the higher the number, the further the orbit from the nucleus - the higher the number, the more energy the electron has (this is sort of like Bohr’s energy levels) - the orbits (energy levels) are also called shells • Angular momentum (azimuthal) quantum number: The azimuthal quantum number describes the sublevels (subshells) that occur in each of the levels (shells) described above. - it is symbolized by the letter l - positive whole number values including 0 are assigned: l = 0, l = 1, l = 2, etc. - each number represents the shape of a subshell: l = 0, represents an s subshell l = 1, represents a p subshell l = 2, represents a d subshell l = 3, represents an f subshell - the higher the number, the more complex the shape of the subshell. The picture below shows the shape of the s and p subshells: (notice the electron clouds) • Magnetic quantum number: All of the subshells described above (except s) have more than one orientation. -
Rotational Piezoelectric Energy Harvesting: a Comprehensive Review on Excitation Elements, Designs, and Performances
energies Review Rotational Piezoelectric Energy Harvesting: A Comprehensive Review on Excitation Elements, Designs, and Performances Haider Jaafar Chilabi 1,2,* , Hanim Salleh 3, Waleed Al-Ashtari 4, E. E. Supeni 1,* , Luqman Chuah Abdullah 1 , Azizan B. As’arry 1, Khairil Anas Md Rezali 1 and Mohammad Khairul Azwan 5 1 Department of Mechanical and Manufacturing, Faculty of Engineering, Universiti Putra Malaysia, Serdang 43400, Malaysia; [email protected] (L.C.A.); [email protected] (A.B.A.); [email protected] (K.A.M.R.) 2 Midland Refineries Company (MRC), Ministry of Oil, Baghdad 10022, Iraq 3 Institute of Sustainable Energy, Universiti Tenaga Nasional, Jalan Ikram-Uniten, Kajang 43000, Malaysia; [email protected] 4 Mechanical Engineering Department, College of Engineering University of Baghdad, Baghdad 10022, Iraq; [email protected] 5 Department of Mechanical Engineering, College of Engineering, Universiti Tenaga Nasional, Jalan Ikram-15 Uniten, Kajang 43000, Malaysia; [email protected] * Correspondence: [email protected] (H.J.C.); [email protected] (E.E.S.) Abstract: Rotational Piezoelectric Energy Harvesting (RPZTEH) is widely used due to mechanical rotational input power availability in industrial and natural environments. This paper reviews the recent studies and research in RPZTEH based on its excitation elements and design and their influence on performance. It presents different groups for comparison according to their mechanical Citation: Chilabi, H.J.; Salleh, H.; inputs and applications, such as fluid (air or water) movement, human motion, rotational vehicle tires, Al-Ashtari, W.; Supeni, E.E.; and other rotational operational principal including gears. The work emphasises the discussion of Abdullah, L.C.; As’arry, A.B.; Rezali, K.A.M.; Azwan, M.K. -
4 Nuclear Magnetic Resonance
Chapter 4, page 1 4 Nuclear Magnetic Resonance Pieter Zeeman observed in 1896 the splitting of optical spectral lines in the field of an electromagnet. Since then, the splitting of energy levels proportional to an external magnetic field has been called the "Zeeman effect". The "Zeeman resonance effect" causes magnetic resonances which are classified under radio frequency spectroscopy (rf spectroscopy). In these resonances, the transitions between two branches of a single energy level split in an external magnetic field are measured in the megahertz and gigahertz range. In 1944, Jevgeni Konstantinovitch Savoiski discovered electron paramagnetic resonance. Shortly thereafter in 1945, nuclear magnetic resonance was demonstrated almost simultaneously in Boston by Edward Mills Purcell and in Stanford by Felix Bloch. Nuclear magnetic resonance was sometimes called nuclear induction or paramagnetic nuclear resonance. It is generally abbreviated to NMR. So as not to scare prospective patients in medicine, reference to the "nuclear" character of NMR is dropped and the magnetic resonance based imaging systems (scanner) found in hospitals are simply referred to as "magnetic resonance imaging" (MRI). 4.1 The Nuclear Resonance Effect Many atomic nuclei have spin, characterized by the nuclear spin quantum number I. The absolute value of the spin angular momentum is L =+h II(1). (4.01) The component in the direction of an applied field is Lz = Iz h ≡ m h. (4.02) The external field is usually defined along the z-direction. The magnetic quantum number is symbolized by Iz or m and can have 2I +1 values: Iz ≡ m = −I, −I+1, ..., I−1, I.