The Path to the Quantum Atom John Heilbron Describes the Route That Led Niels Bohr to Quantize Electron Orbits a Century Ago
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Hendrik Antoon Lorentz's Struggle with Quantum Theory A. J
Hendrik Antoon Lorentz’s struggle with quantum theory A. J. Kox Archive for History of Exact Sciences ISSN 0003-9519 Volume 67 Number 2 Arch. Hist. Exact Sci. (2013) 67:149-170 DOI 10.1007/s00407-012-0107-8 1 23 Your article is published under the Creative Commons Attribution license which allows users to read, copy, distribute and make derivative works, as long as the author of the original work is cited. You may self- archive this article on your own website, an institutional repository or funder’s repository and make it publicly available immediately. 1 23 Arch. Hist. Exact Sci. (2013) 67:149–170 DOI 10.1007/s00407-012-0107-8 Hendrik Antoon Lorentz’s struggle with quantum theory A. J. Kox Received: 15 June 2012 / Published online: 24 July 2012 © The Author(s) 2012. This article is published with open access at Springerlink.com Abstract A historical overview is given of the contributions of Hendrik Antoon Lorentz in quantum theory. Although especially his early work is valuable, the main importance of Lorentz’s work lies in the conceptual clarifications he provided and in his critique of the foundations of quantum theory. 1 Introduction The Dutch physicist Hendrik Antoon Lorentz (1853–1928) is generally viewed as an icon of classical, nineteenth-century physics—indeed, as one of the last masters of that era. Thus, it may come as a bit of a surprise that he also made important contribu- tions to quantum theory, the quintessential non-classical twentieth-century develop- ment in physics. The importance of Lorentz’s work lies not so much in his concrete contributions to the actual physics—although some of his early work was ground- breaking—but rather in the conceptual clarifications he provided and his critique of the foundations and interpretations of the new ideas. -
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, . -
Quantum Field Theory*
Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement. -
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. -
Einstein's Mistakes
Einstein’s Mistakes Einstein was the greatest genius of the Twentieth Century, but his discoveries were blighted with mistakes. The Human Failing of Genius. 1 PART 1 An evaluation of the man Here, Einstein grows up, his thinking evolves, and many quotations from him are listed. Albert Einstein (1879-1955) Einstein at 14 Einstein at 26 Einstein at 42 3 Albert Einstein (1879-1955) Einstein at age 61 (1940) 4 Albert Einstein (1879-1955) Born in Ulm, Swabian region of Southern Germany. From a Jewish merchant family. Had a sister Maja. Family rejected Jewish customs. Did not inherit any mathematical talent. Inherited stubbornness, Inherited a roguish sense of humor, An inclination to mysticism, And a habit of grüblen or protracted, agonizing “brooding” over whatever was on its mind. Leading to the thought experiment. 5 Portrait in 1947 – age 68, and his habit of agonizing brooding over whatever was on its mind. He was in Princeton, NJ, USA. 6 Einstein the mystic •“Everyone who is seriously involved in pursuit of science becomes convinced that a spirit is manifest in the laws of the universe, one that is vastly superior to that of man..” •“When I assess a theory, I ask myself, if I was God, would I have arranged the universe that way?” •His roguish sense of humor was always there. •When asked what will be his reactions to observational evidence against the bending of light predicted by his general theory of relativity, he said: •”Then I would feel sorry for the Good Lord. The theory is correct anyway.” 7 Einstein: Mathematics •More quotations from Einstein: •“How it is possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” •Questions asked by many people and Einstein: •“Is God a mathematician?” •His conclusion: •“ The Lord is cunning, but not malicious.” 8 Einstein the Stubborn Mystic “What interests me is whether God had any choice in the creation of the world” Some broadcasters expunged the comment from the soundtrack because they thought it was blasphemous. -
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. -
An Atomic Physics Perspective on the New Kilogram Defined by Planck's Constant
An atomic physics perspective on the new kilogram defined by Planck’s constant (Wolfgang Ketterle and Alan O. Jamison, MIT) (Manuscript submitted to Physics Today) On May 20, the kilogram will no longer be defined by the artefact in Paris, but through the definition1 of Planck’s constant h=6.626 070 15*10-34 kg m2/s. This is the result of advances in metrology: The best two measurements of h, the Watt balance and the silicon spheres, have now reached an accuracy similar to the mass drift of the ur-kilogram in Paris over 130 years. At this point, the General Conference on Weights and Measures decided to use the precisely measured numerical value of h as the definition of h, which then defines the unit of the kilogram. But how can we now explain in simple terms what exactly one kilogram is? How do fixed numerical values of h, the speed of light c and the Cs hyperfine frequency νCs define the kilogram? In this article we give a simple conceptual picture of the new kilogram and relate it to the practical realizations of the kilogram. A similar change occurred in 1983 for the definition of the meter when the speed of light was defined to be 299 792 458 m/s. Since the second was the time required for 9 192 631 770 oscillations of hyperfine radiation from a cesium atom, defining the speed of light defined the meter as the distance travelled by light in 1/9192631770 of a second, or equivalently, as 9192631770/299792458 times the wavelength of the cesium hyperfine radiation. -
Non-Einsteinian Interpretations of the Photoelectric Effect
NON-EINSTEINIAN INTERPRETATIONS ------ROGER H. STUEWER------ serveq spectral distribution for black-body radiation, and it led inexorably ~o _the ~latantl~ f::se conclusion that the total radiant energy in a cavity is mfimte. (This ultra-violet catastrophe," as Ehrenfest later termed it, was point~d out independently and virtually simultaneously, though not Non-Einsteinian Interpretations of the as emphatically, by Lord Rayleigh.2) Photoelectric Effect Einstein developed his positive argument in two stages. First, he derived an expression for the entropy of black-body radiation in the Wien's law spectral region (the high-frequency, low-temperature region) and used this expression to evaluate the difference in entropy associated with a chan.ge in volume v - Vo of the radiation, at constant energy. Secondly, he Few, if any, ideas in the history of recent physics were greeted with ~o~s1dere? the case of n particles freely and independently moving around skepticism as universal and prolonged as was Einstein's light quantum ms1d: a given v~lume Vo _and determined the change in entropy of the sys hypothesis.1 The period of transition between rejection and acceptance tem if all n particles accidentally found themselves in a given subvolume spanned almost two decades and would undoubtedly have been longer if v ~ta r~ndomly chosen instant of time. To evaluate this change in entropy, Arthur Compton's experiments had been less striking. Why was Einstein's Emstem used the statistical version of the second law of thermodynamics hypothesis not accepted much earlier? Was there no experimental evi in _c?njunction with his own strongly physical interpretation of the prob dence that suggested, even demanded, Einstein's hypothesis? If so, why ~b1ht~. -
Wolfgang Pauli Niels Bohr Paul Dirac Max Planck Richard Feynman
Wolfgang Pauli Niels Bohr Paul Dirac Max Planck Richard Feynman Louis de Broglie Norman Ramsey Willis Lamb Otto Stern Werner Heisenberg Walther Gerlach Ernest Rutherford Satyendranath Bose Max Born Erwin Schrödinger Eugene Wigner Arnold Sommerfeld Julian Schwinger David Bohm Enrico Fermi Albert Einstein Where discovery meets practice Center for Integrated Quantum Science and Technology IQ ST in Baden-Württemberg . Introduction “But I do not wish to be forced into abandoning strict These two quotes by Albert Einstein not only express his well more securely, develop new types of computer or construct highly causality without having defended it quite differently known aversion to quantum theory, they also come from two quite accurate measuring equipment. than I have so far. The idea that an electron exposed to a different periods of his life. The first is from a letter dated 19 April Thus quantum theory extends beyond the field of physics into other 1924 to Max Born regarding the latter’s statistical interpretation of areas, e.g. mathematics, engineering, chemistry, and even biology. beam freely chooses the moment and direction in which quantum mechanics. The second is from Einstein’s last lecture as Let us look at a few examples which illustrate this. The field of crypt it wants to move is unbearable to me. If that is the case, part of a series of classes by the American physicist John Archibald ography uses number theory, which constitutes a subdiscipline of then I would rather be a cobbler or a casino employee Wheeler in 1954 at Princeton. pure mathematics. Producing a quantum computer with new types than a physicist.” The realization that, in the quantum world, objects only exist when of gates on the basis of the superposition principle from quantum they are measured – and this is what is behind the moon/mouse mechanics requires the involvement of engineering. -
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.