Wave-Particle Duality 波粒二象性
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The Balmer Series
The Balmer Series Introduction Historically, the spectral lines of hydrogen have been categorized as six distinct series. The visible portion of the hydrogen spectrum is contained in the Balmer series, named after Johann Balmer who discovered an empirical relationship for calculating its wave- lengths [2]. In 1885 Balmer discovered that by labeling the four visible lines of the hydorgen spectrum with integers n, (n = 3, 4, 5, 6) (See Table 1 and Figure 1) each wavelength λ could be calculated from the relationship n2 λ = B , (1) n2 − 4 where B = 364.56 nm. Johannes Rydberg generalized Balmer’s result to include all of the wavelengths of the hydrogen spectrum. The Balmer formula is more commonly re–expressed in the form of the Rydberg formula 1 1 1 = RH − , (2) λ 22 n2 where n =3, 4, 5 . and the Rydberg constant RH =4/B. The purpose of this experiment is to determine the wavelengths of the visible spec- tral lines of hydrogen using a spectrometer and to calculate the Balmer constant B. Procedure The spectrometer used in this experiment is shown in Fig. 1. Adjust the diffraction grating so that the normal to its plane makes a small angle α to the incident beam of light. This is shown schematically in Fig. 2. Since α u 0, the angles between the first and zeroth order intensity maxima on either side, θ and θ0 respectively, are related to the wavelength λ of the incident light according to [1] λ = d sin(φ) , (3) accurate to first order in α. Here, d is the separation between the slits of the grating, and θ0 + θ φ = (4) 2 1 Color Wavelength [nm] Integer [n] Violet2 410.2 6 Violet1 434.0 5 blue 486.1 4 red 656.3 3 Table 1: The wavelengths and integer associations of the visible spectral lines of hy- drogen shown in Fig. -
Physics of the Atom
Physics of the Atom Ernest The Nobel Prize in Chemistry 1908 Rutherford "for his investigations into the disintegration of the elements, and the chemistry of radioactive substances" Niels Bohr The Nobel Prize in Physics 1922 "for his services in the investigation of the structure of atoms and of the radiation emanating from them" W. Ubachs – Lectures MNW-1 Early models of the atom atoms : electrically neutral they can become charged positive and negative charges are around and some can be removed. popular atomic model “plum-pudding” model: W. Ubachs – Lectures MNW-1 Rutherford scattering Rutherford did an experiment that showed that the positively charged nucleus must be extremely small compared to the rest of the atom. Result from Rutherford scattering 2 dσ ⎛ 1 Zze2 ⎞ 1 = ⎜ ⎟ ⎜ ⎟ 4 dΩ ⎝ 4πε0 4K ⎠ sin ()θ / 2 Applet for doing the experiment: http://www.physics.upenn.edu/courses/gladney/phys351/classes/Scattering/Rutherford_Scattering.html W. Ubachs – Lectures MNW-1 Rutherford scattering the smallness of the nucleus the radius of the nucleus is 1/10,000 that of the atom. the atom is mostly empty space Rutherford’s atomic model W. Ubachs – Lectures MNW-1 Atomic Spectra: Key to the Structure of the Atom A very thin gas heated in a discharge tube emits light only at characteristic frequencies. W. Ubachs – Lectures MNW-1 Atomic Spectra: Key to the Structure of the Atom Line spectra: absorption and emission W. Ubachs – Lectures MNW-1 The Balmer series in atomic hydrogen The wavelengths of electrons emitted from hydrogen have a regular pattern: Johann Jakob Balmer W. Ubachs – Lectures MNW-1 Lyman, Paschen and Rydberg series the Lyman series: the Paschen series: W. -
Lecture #2: August 25, 2020 Goal Is to Define Electrons in Atoms
Lecture #2: August 25, 2020 Goal is to define electrons in atoms • Bohr Atom and Principal Energy Levels from “orbits”; Balance of electrostatic attraction and centripetal force: classical mechanics • Inability to account for emission lines => particle/wave description of atom and application of wave mechanics • Solutions of Schrodinger’s equation, Hψ = Eψ Required boundaries => quantum numbers (and the Pauli Exclusion Principle) • Electron configurations. C: 1s2 2s2 2p2 or [He]2s2 2p2 Na: 1s2 2s2 2p6 3s1 or [Ne] 3s1 => Na+: [Ne] Cl: 1s2 2s2 2p6 3s23p5 or [Ne]3s23p5 => Cl-: [Ne]3s23p6 or [Ar] What you already know: Quantum Numbers: n, l, ml , ms n is the principal quantum number, indicates the size of the orbital, has all positive integer values of 1 to ∞(infinity) (Bohr’s discrete orbits) l (angular momentum) orbital 0s l is the angular momentum quantum number, 1p represents the shape of the orbital, has integer values of (n – 1) to 0 2d 3f ml is the magnetic quantum number, represents the spatial direction of the orbital, can have integer values of -l to 0 to l Other terms: electron configuration, noble gas configuration, valence shell ms is the spin quantum number, has little physical meaning, can have values of either +1/2 or -1/2 Pauli Exclusion principle: no two electrons can have all four of the same quantum numbers in the same atom (Every electron has a unique set.) Hund’s Rule: when electrons are placed in a set of degenerate orbitals, the ground state has as many electrons as possible in different orbitals, and with parallel spin. -
Charles Galton Darwin's 1922 Quantum Theory of Optical Dispersion
Eur. Phys. J. H https://doi.org/10.1140/epjh/e2020-80058-7 THE EUROPEAN PHYSICAL JOURNAL H Charles Galton Darwin's 1922 quantum theory of optical dispersion Benjamin Johnson1,2, a 1 Max Planck Institute for the History of Science Boltzmannstraße 22, 14195 Berlin, Germany 2 Fritz-Haber-Institut der Max-Planck-Gesellschaft Faradayweg 4, 14195 Berlin, Germany Received 13 October 2017 / Received in final form 4 February 2020 Published online 29 May 2020 c The Author(s) 2020. This article is published with open access at Springerlink.com Abstract. The quantum theory of dispersion was an important concep- tual advancement which led out of the crisis of the old quantum theory in the early 1920s and aided in the formulation of matrix mechanics in 1925. The theory of Charles Galton Darwin, often cited only for its reliance on the statistical conservation of energy, was a wave-based attempt to explain dispersion phenomena at a time between the the- ories of Ladenburg and Kramers. It contributed to future successes in quantum theory, such as the virtual oscillator, while revealing through its own shortcomings the limitations of the wave theory of light in the interaction of light and matter. After its publication, Darwin's theory was widely discussed amongst his colleagues as the competing inter- pretation to Compton's in X-ray scattering experiments. It also had a pronounced influence on John C. Slater, whose ideas formed the basis of the BKS theory. 1 Introduction Charles Galton Darwin mainly appears in the literature on the development of quantum mechanics in connection with his early and explicit opinions on the non- conservation (or statistical conservation) of energy and his correspondence with Niels Bohr. -
Rydberg Constant and Emission Spectra of Gases
Page 1 of 10 Rydberg constant and emission spectra of gases ONE WEIGHT RECOMMENDED READINGS 1. R. Harris. Modern Physics, 2nd Ed. (2008). Sections 4.6, 7.3, 8.9. 2. Atomic Spectra line database https://physics.nist.gov/PhysRefData/ASD/lines_form.html OBJECTIVE - Calibrating a prism spectrometer to convert the scale readings in wavelengths of the emission spectral lines. - Identifying an "unknown" gas by measuring its spectral lines wavelengths. - Calculating the Rydberg constant RH. - Finding a separation of spectral lines in the yellow doublet of the sodium lamp spectrum. INSTRUCTOR’S EXPECTATIONS In the lab report it is expected to find the following parts: - Brief overview of the Bohr’s theory of hydrogen atom and main restrictions on its application. - Description of the setup including its main parts and their functions. - Description of the experiment procedure. - Table with readings of the vernier scale of the spectrometer and corresponding wavelengths of spectral lines of hydrogen and helium. - Calibration line for the function “wavelength vs reading” with explanation of the fitting procedure and values of the parameters of the fit with their uncertainties. - Calculated Rydberg constant with its uncertainty. - Description of the procedure of identification of the unknown gas and statement about the gas. - Calculating resolution of the spectrometer with the yellow doublet of sodium spectrum. INTRODUCTION In this experiment, linear emission spectra of discharge tubes are studied. The discharge tube is an evacuated glass tube filled with a gas or a vapor. There are two conductors – anode and cathode - soldered in the ends of the tube and connected to a high-voltage power source outside the tube. -
Bohr's Theory and Spectra of Hydrogen And
____________________________________________________________________________________________________ Subject Chemistry Paper No and Title 8 and Physical Spectroscopy Module No and Title 7 and Bohr’s theory and spectra of hydrogen and hydrogen- like ions. Module Tag CHE_P8_M7 CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 7 (BOHR’S THEORY AND SPECTRA OF HYDROGEN AND HYDROGEN-LIKE IONS) ____________________________________________________________________________________________________ TABLE OF CONTENTS 1. Learning Outcomes 2. What is a Spectrum? 2.1 Introduction 2.2 Atomic Spectra 2.3 Hydrogen Spectrum 2.4 Balmer Series 2.5 The Rydberg Formula 3. Bohr’s Theory 3.1 Bohr Model 3.2 Line Spectra 3.3 Multi-electron Atoms 4. Summary CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 7 (BOHR’S THEORY AND SPECTRA OF HYDROGEN AND HYDROGEN-LIKE IONS) ____________________________________________________________________________________________________ 1. Learning Outcomes After studying this module, you should be able to grasp the important ideas of Bohr’s Theory of the structure of atomic hydrogen. We will first review the experimental observations of the atomic spectrum of hydrogen, which led to the birth of quantum mechanics. 2. What is a Spectrum? 2.1 Introduction In spectroscopy, we are interested in the absorption and emission of radiation by matter and its consequences. A spectrum is the distribution of photon energies coming from a light source: • How many photons of each energy are emitted by the light source? Spectra are observed by passing light through a spectrograph: • Breaks the light into its component wavelengths and spreads them apart (dispersion). • Uses either prisms or diffraction gratings. The absorption and emission of photons are governed by the Bohr condition ΔE = hν. -
Rydberg Excitation of Single Atoms for Applications in Quantum Information and Metrology Aaron Hankin
University of New Mexico UNM Digital Repository Physics & Astronomy ETDs Electronic Theses and Dissertations 1-28-2015 Rydberg Excitation of Single Atoms for Applications in Quantum Information and Metrology Aaron Hankin Follow this and additional works at: https://digitalrepository.unm.edu/phyc_etds Recommended Citation Hankin, Aaron. "Rydberg Excitation of Single Atoms for Applications in Quantum Information and Metrology." (2015). https://digitalrepository.unm.edu/phyc_etds/23 This Dissertation is brought to you for free and open access by the Electronic Theses and Dissertations at UNM Digital Repository. It has been accepted for inclusion in Physics & Astronomy ETDs by an authorized administrator of UNM Digital Repository. For more information, please contact [email protected]. Aaron Hankin Candidate Physics and Astronomy Department This dissertation is approved, and it is acceptable in quality and form for publication: Approved by the Dissertation Committee: Ivan Deutsch , Chairperson Carlton Caves Keith Lidke Grant Biedermann Rydberg Excitation of Single Atoms for Applications in Quantum Information and Metrology by Aaron Michael Hankin B.A., Physics, North Central College, 2007 M.S., Physics, Central Michigan Univeristy, 2009 DISSERATION Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Physics The University of New Mexico Albuquerque, New Mexico December 2014 iii c 2014, Aaron Michael Hankin iv Dedication To Maiko and our unborn daughter. \There are wonders enough out there without our inventing any." { Carl Sagan v Acknowledgments The experiment detailed in this manuscript evolved rapidly from an empty lab nearly four years ago to its current state. Needless to say, this is not something a graduate student could have accomplished so quickly by him or herself. -
23-Chapt-6-Quantum2
The Nature of Energy • For atoms and molecules, one does not observe a continuous spectrum, as one gets from a ? white light source. • Only a line spectrum of discrete wavelengths is Electronic Structure observed. of Atoms © 2012 Pearson Education, Inc. The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell Neils Bohr Explained the emission spectrum of the hydrogen atom on basis of quantization of electron energy. Neils Bohr Explained the emission spectrum of the hydrogen atom on basis of quantization of electron energy. Emission spectrum Emitted light is separated into component frequencies when passed through a prism. 397 410 434 486 656 wavelenth in nm Hydrogen, the simplest atom, produces the simplest emission spectrum. In the late 19th century a mathematical relationship was found between the visible spectral lines of hydrogen the group of hydrogen lines in the visible range is called the Balmer series 1 1 1 = R – λ ( 22 n2 ) Rydberg 1.0968 x 107m–1 Constant Johannes Rydberg Bohr Solution the electron circles nucleus in a circular orbit imposed quantum condition on electron energy only certain “orbits” allowed energy emitted is when electron moves from higher energy state (excited state) to lower energy state the lowest electron energy state is ground state ground state of hydrogen atom n = 5 n = 4 n = 3 n = 2 n = 1 e- excited state of hydrogen atom n = 5 n = 4 n = 3 e- n = 2 n = 1 hν excited state of hydrogen atom n = 5 n = 4 n = 3 n = 2 e- n = 1 hν excited state of hydrogen atom n = 5 n = 4 n = 3 e- n = 2 n = 1 hν Emission spectrum Emitted light is separated into component frequencies when passed through a prism. -
A History of Astronomy, Astrophysics and Cosmology - Malcolm Longair
ASTRONOMY AND ASTROPHYSICS - A History of Astronomy, Astrophysics and Cosmology - Malcolm Longair A HISTORY OF ASTRONOMY, ASTROPHYSICS AND COSMOLOGY Malcolm Longair Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE Keywords: History, Astronomy, Astrophysics, Cosmology, Telescopes, Astronomical Technology, Electromagnetic Spectrum, Ancient Astronomy, Copernican Revolution, Stars and Stellar Evolution, Interstellar Medium, Galaxies, Clusters of Galaxies, Large- scale Structure of the Universe, Active Galaxies, General Relativity, Black Holes, Classical Cosmology, Cosmological Models, Cosmological Evolution, Origin of Galaxies, Very Early Universe Contents 1. Introduction 2. Prehistoric, Ancient and Mediaeval Astronomy up to the Time of Copernicus 3. The Copernican, Galilean and Newtonian Revolutions 4. From Astronomy to Astrophysics – the Development of Astronomical Techniques in the 19th Century 5. The Classification of the Stars – the Harvard Spectral Sequence 6. Stellar Structure and Evolution to 1939 7. The Galaxy and the Nature of the Spiral Nebulae 8. The Origins of Astrophysical Cosmology – Einstein, Friedman, Hubble, Lemaître, Eddington 9. The Opening Up of the Electromagnetic Spectrum and the New Astronomies 10. Stellar Evolution after 1945 11. The Interstellar Medium 12. Galaxies, Clusters Of Galaxies and the Large Scale Structure of the Universe 13. Active Galaxies, General Relativity and Black Holes 14. Classical Cosmology since 1945 15. The Evolution of Galaxies and Active Galaxies with Cosmic Epoch 16. The Origin of Galaxies and the Large-Scale Structure of The Universe 17. The VeryUNESCO Early Universe – EOLSS Acknowledgements Glossary Bibliography Biographical SketchSAMPLE CHAPTERS Summary This chapter describes the history of the development of astronomy, astrophysics and cosmology from the earliest times to the first decade of the 21st century. -
Physiker-Entdeckungen Und Erdzeiten Hans Ulrich Stalder 31.1.2019
Physiker-Entdeckungen und Erdzeiten Hans Ulrich Stalder 31.1.2019 Haftungsausschluss / Disclaimer / Hyperlinks Für fehlerhafte Angaben und deren Folgen kann weder eine juristische Verantwortung noch irgendeine Haftung übernommen werden. Änderungen vorbehalten. Ich distanziere mich hiermit ausdrücklich von allen Inhalten aller verlinkten Seiten und mache mir diese Inhalte nicht zu eigen. Erdzeiten Erdzeit beginnt vor x-Millionen Jahren Quartär 2,588 Neogen 23,03 (erste Menschen vor zirka 4 Millionen Jahren) Paläogen 66 Kreide 145 (Dinosaurier) Jura 201,3 Trias 252,2 Perm 298,9 Karbon 358,9 Devon 419,2 Silur 443,4 Ordovizium 485,4 Kambrium 541 Ediacarium 635 Cryogenium 850 Tonium 1000 Stenium 1200 Ectasium 1400 Calymmium 1600 Statherium 1800 Orosirium 2050 Rhyacium 2300 Siderium 2500 Physiker Entdeckungen Jahr 0800 v. Chr.: Den Babyloniern sind Sonnenfinsterniszyklen mit der Sarosperiode (rund 18 Jahre) bekannt. Jahr 0580 v. Chr.: Die Erde wird nach einer Theorie von Anaximander als Kugel beschrieben. Jahr 0550 v. Chr.: Die Entdeckung von ganzzahligen Frequenzverhältnissen bei konsonanten Klängen (Pythagoras in der Schmiede) führt zur ersten überlieferten und zutreffenden quantitativen Beschreibung eines physikalischen Sachverhalts. © Hans Ulrich Stalder, Switzerland Jahr 0500 v. Chr.: Demokrit postuliert, dass die Natur aus Atomen zusammengesetzt sei. Jahr 0450 v. Chr.: Vier-Elemente-Lehre von Empedokles. Jahr 0300 v. Chr.: Euklid begründet anhand der Reflexion die geometrische Optik. Jahr 0265 v. Chr.: Zum ersten Mal wird die Theorie des Heliozentrischen Weltbildes mit geometrischen Berechnungen von Aristarchos von Samos belegt. Jahr 0250 v. Chr.: Archimedes entdeckt das Hebelgesetz und die statische Auftriebskraft in Flüssigkeiten, Archimedisches Prinzip. Jahr 0240 v. Chr.: Eratosthenes bestimmt den Erdumfang mit einer Gradmessung zwischen Alexandria und Syene. -
Physics 30 Lesson 31 the Bohr Model of the Atom I
Physics 30 Lesson 31 The Bohr Model of the Atom I. Planetary models of the atom After Rutherford’s gold foil scattering experiment, all models of the atom featured a nuclear model with electrons moving around a tiny, massive nucleus. A simple way to visualise the nuclear model was as planets orbiting a central Sun. As the Sun of our solar system attracted the planets, the positive nucleus of the atom would attract the negative electrons. While the Sun and planets involve gravitation, the nucleus and electrons involve electrostatic forces. Planet Nucleus Sun electron Gravitational Attraction Planetary Model of Atom The nuclear atom was a nice combination of gravitational ideas and sub atomic particles, but it had several major flaws: 1. Did all of the electrons travel in the same orbit? Why did they not bump into one another? What was the electron structure? 2. From the known bonding characteristics of different chemical compounds, how are the electrons involved in the bonding process? 3. Why do the positive protons stay together in the nucleus? Their strong mutual repulsion should tear the nucleus apart. 4. The final, and most important flaw, concerned the nature of accelerating charges. James Maxwell had shown that accelerating electric charges radiate EM radiation (Lesson 24). If the electrons were in circular orbits, they would continually experience a centripetal acceleration and should continually radiate energy in the form of electromagnetic waves. Further, since their kinetic energy is being converted into radiant energy, the electrons should spiral into the nucleus. From observation, we know that atoms have stable structures for long periods of time and they do not radiate energy on their own. -
Quantum Theory
Repositorium für die Medienwissenschaft Arianna Borrelli Quantum Theory. A Media-Archaeological Perspective 2017 https://doi.org/10.25969/mediarep/2243 Veröffentlichungsversion / published version Sammelbandbeitrag / collection article Empfohlene Zitierung / Suggested Citation: Borrelli, Arianna: Quantum Theory. A Media-Archaeological Perspective. In: Anne Dippel, Martin Warnke (Hg.): Interferences and Events. On Epistemic Shifts in Physics through Computer Simulations. Lüneburg: meson press 2017, S. 95–121. DOI: https://doi.org/10.25969/mediarep/2243. Nutzungsbedingungen: Terms of use: Dieser Text wird unter einer Creative Commons - This document is made available under a creative commons - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 Attribution - Share Alike 4.0 License. For more information see: Lizenz zur Verfügung gestellt. Nähere Auskünfte zu dieser Lizenz https://creativecommons.org/licenses/by-sa/4.0 finden Sie hier: https://creativecommons.org/licenses/by-sa/4.0 [6] Quantum Theory: A Media-Archaeological Perspective Arianna Borrelli Introduction: Computer Simulations as a Complement to Quantum Theory? In this paper I will provide some historical perspectives on the question at the core of this workshop, namely the many ways in which computer simulations may be contributing to reshape science in general and quantum physics in particular. More specifically, I would like to focus on the issue of whether computer simulations may be regarded as offering an alternative, or perhaps a complementary, version of quantum theory. I will not be looking at the way in which computer simulations are used in quantum physics today, since this task has been outstandingly fulfilled by other contributions to this workshop. Instead, I will present a few episodes from the history of quantum theory in such a way as to make it plausible that simulations might indeed provide the next phase of historical development.