Physical Constants --- Complete Listing
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Mass Spectrometry: Quadrupole Mass Filter
Advanced Lab, Jan. 2008 Mass Spectrometry: Quadrupole Mass Filter The mass spectrometer is essentially an instrument which can be used to measure the mass, or more correctly the mass/charge ratio, of ionized atoms or other electrically charged particles. Mass spectrometers are now used in physics, geology, chemistry, biology and medicine to determine compositions, to measure isotopic ratios, for detecting leaks in vacuum systems, and in homeland security. Mass Spectrometer Designs The first mass spectrographs were invented almost 100 years ago, by A.J. Dempster, F.W. Aston and others, and have therefore been in continuous development over a very long period. However the principle of using electric and magnetic fields to accelerate and establish the trajectories of ions inside the spectrometer according to their mass/charge ratio is common to all the different designs. The following description of Dempster’s original mass spectrograph is a simple illustration of these physical principles: The magnetic sector spectrograph PUMP F DD S S3 1 r S2 Fig. 1: Dempster’s Mass Spectrograph (1918). Atoms/molecules are first ionized by electrons emitted from the hot filament (F) and then accelerated towards the entrance slit (S1). The ions then follow a semicircular trajectory established by the Lorentz force in a uniform magnetic field. The radius of the trajectory, r, is defined by three slits (S1, S2, and S3). Ions with this selected trajectory are then detected by the detector D. How the magnetic sector mass spectrograph works: Equating the Lorentz force with the centripetal force gives: qvB = mv2/r (1) where q is the charge on the ion (usually +e), B the magnetic field, m is the mass of the ion and r the radius of the ion trajectory. -
Magnetism, Magnetic Properties, Magnetochemistry
Magnetism, Magnetic Properties, Magnetochemistry 1 Magnetism All matter is electronic Positive/negative charges - bound by Coulombic forces Result of electric field E between charges, electric dipole Electric and magnetic fields = the electromagnetic interaction (Oersted, Maxwell) Electric field = electric +/ charges, electric dipole Magnetic field ??No source?? No magnetic charges, N-S No magnetic monopole Magnetic field = motion of electric charges (electric current, atomic motions) Magnetic dipole – magnetic moment = i A [A m2] 2 Electromagnetic Fields 3 Magnetism Magnetic field = motion of electric charges • Macro - electric current • Micro - spin + orbital momentum Ampère 1822 Poisson model Magnetic dipole – magnetic (dipole) moment [A m2] i A 4 Ampere model Magnetism Microscopic explanation of source of magnetism = Fundamental quantum magnets Unpaired electrons = spins (Bohr 1913) Atomic building blocks (protons, neutrons and electrons = fermions) possess an intrinsic magnetic moment Relativistic quantum theory (P. Dirac 1928) SPIN (quantum property ~ rotation of charged particles) Spin (½ for all fermions) gives rise to a magnetic moment 5 Atomic Motions of Electric Charges The origins for the magnetic moment of a free atom Motions of Electric Charges: 1) The spins of the electrons S. Unpaired spins give a paramagnetic contribution. Paired spins give a diamagnetic contribution. 2) The orbital angular momentum L of the electrons about the nucleus, degenerate orbitals, paramagnetic contribution. The change in the orbital moment -
Ph501 Electrodynamics Problem Set 8 Kirk T
Princeton University Ph501 Electrodynamics Problem Set 8 Kirk T. McDonald (2001) [email protected] http://physics.princeton.edu/~mcdonald/examples/ Princeton University 2001 Ph501 Set 8, Problem 1 1 1. Wire with a Linearly Rising Current A neutral wire along the z-axis carries current I that varies with time t according to ⎧ ⎪ ⎨ 0(t ≤ 0), I t ( )=⎪ (1) ⎩ αt (t>0),αis a constant. Deduce the time-dependence of the electric and magnetic fields, E and B,observedat apoint(r, θ =0,z = 0) in a cylindrical coordinate system about the wire. Use your expressions to discuss the fields in the two limiting cases that ct r and ct = r + , where c is the speed of light and r. The related, but more intricate case of a solenoid with a linearly rising current is considered in http://physics.princeton.edu/~mcdonald/examples/solenoid.pdf Princeton University 2001 Ph501 Set 8, Problem 2 2 2. Harmonic Multipole Expansion A common alternative to the multipole expansion of electromagnetic radiation given in the Notes assumes from the beginning that the motion of the charges is oscillatory with angular frequency ω. However, we still use the essence of the Hertz method wherein the current density is related to the time derivative of a polarization:1 J = p˙ . (2) The radiation fields will be deduced from the retarded vector potential, 1 [J] d 1 [p˙ ] d , A = c r Vol = c r Vol (3) which is a solution of the (Lorenz gauge) wave equation 1 ∂2A 4π ∇2A − = − J. (4) c2 ∂t2 c Suppose that the Hertz polarization vector p has oscillatory time dependence, −iωt p(x,t)=pω(x)e . -
An Introduction to Hartree-Fock Molecular Orbital Theory
An Introduction to Hartree-Fock Molecular Orbital Theory C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology June 2000 1 Introduction Hartree-Fock theory is fundamental to much of electronic structure theory. It is the basis of molecular orbital (MO) theory, which posits that each electron's motion can be described by a single-particle function (orbital) which does not depend explicitly on the instantaneous motions of the other electrons. Many of you have probably learned about (and maybe even solved prob- lems with) HucÄ kel MO theory, which takes Hartree-Fock MO theory as an implicit foundation and throws away most of the terms to make it tractable for simple calculations. The ubiquity of orbital concepts in chemistry is a testimony to the predictive power and intuitive appeal of Hartree-Fock MO theory. However, it is important to remember that these orbitals are mathematical constructs which only approximate reality. Only for the hydrogen atom (or other one-electron systems, like He+) are orbitals exact eigenfunctions of the full electronic Hamiltonian. As long as we are content to consider molecules near their equilibrium geometry, Hartree-Fock theory often provides a good starting point for more elaborate theoretical methods which are better approximations to the elec- tronic SchrÄodinger equation (e.g., many-body perturbation theory, single-reference con¯guration interaction). So...how do we calculate molecular orbitals using Hartree-Fock theory? That is the subject of these notes; we will explain Hartree-Fock theory at an introductory level. 2 What Problem Are We Solving? It is always important to remember the context of a theory. -
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. -
Operating Instructions Ac Snap-Around Volt-Ohm
4.5) HOW TO USE POINTER LOCK & RANGE FINDER LIFETIME LIMITED WARRANTY 05/06 From #174-1 SYMBOLS The attention to detail of this fine snap-around instrument is further enhanced by OPERATING INSTRUCTIONS (1) Slide the pointer lock button to the left. This allows easy readings in dimly lit the application of Sperry's unmatched service and concern for detail and or crowded cable areas (Fig.8). reliability. AC SNAP-AROUND VOLT-OHM-AMMETER (2) For quick and easy identification the dial drum is marked with the symbols as These Sperry snap-arounds are internationally accepted by craftsman and illustrated below (Fig.9). servicemen for their unmatched performance. All Sperry's snap-around MODEL SPR-300 PLUS & SPR-300 PLUS A instruments are unconditionally warranted against defects in material and Pointer Ampere Higher workmanship under normal conditions of use and service; our obligations under Lock range range to the to the this warranty being limited to repairing or replacing, free of charge, at Sperry's right. right. sole option, any such Sperry snap-around instrument that malfunctions under normal operating conditions at rated use. 1 Lower Lower range range to the to the left. left. REPLACEMENT PROCEDURE Fig.8 Fig.9 Securely wrap the instrument and its accessories in a box or mailing bag and ship prepaid to the address below. Be sure to include your name and address, as 5) BATTERY & FUSE REPLACEMENT well as the name of the distributor, with a copy of your invoice from whom the (1) Remove the screw on the back of the case for battery and fuse replacement unit was purchased, clearly identifying the model number and date of purchase. -
Experiment QM2: NMR Measurement of Nuclear Magnetic Moments
Physics 440 Spring (3) 2018 Experiment QM2: NMR Measurement of Nuclear Magnetic Moments Theoretical Background: Elementary particles are characterized by a set of properties including mass m, electric charge q, and magnetic moment µ. These same properties are also used to characterize bound collections of elementary particles such as the proton and neutron (which are built from quarks) and atomic nuclei (which are built from protons and neutrons). A particle's magnetic moment can be written in terms of spin as µ = g (q/2m) S where g is the "g-factor" for the particle and S is the particle spin. [Note 2 that for a classical rotating ball of charge S = (2mR /5) ω and g = 1]. For a nucleus, it is conventional to express the magnetic moment as µ A = gA µN IA /! where IA is the "spin", gA is the nuclear g-factor of nucleus A, and the constant µN = e!/2mp (where mp= proton mass) is known as the nuclear magneton. In a magnetic field (oriented in the z-direction) a spin-I nucleus can take on 2I+1 orientations with Iz = mI! where –I ≤ mI ≤ I. Such a nucleus experiences an orientation- dependent interaction energy of VB = –µ A•B = –(gA µN mI)Bz. Note that for a nucleus with positive g- factor the low energy state is the one in which the spin is aligned parallel to the magnetic field. For a spin-1/2 nucleus there are two allowed spin orientations, denoted spin-up and spin-down, and the up down energy difference between these states is simply given by |ΔVB| = VB −VB = 2µABz. -
Lord Kelvin and the Age of the Earth.Pdf
ME201/MTH281/ME400/CHE400 Lord Kelvin and the Age of the Earth Lord Kelvin (1824 - 1907) 1. About Lord Kelvin Lord Kelvin was born William Thomson in Belfast Ireland in 1824. He attended Glasgow University from the age of 10, and later took his BA at Cambridge. He was appointed Professor of Natural Philosophy at Glasgow in 1846, a position he retained the rest of his life. He worked on a broad range of topics in physics, including thermody- namics, electricity and magnetism, hydrodynamics, atomic physics, and earth science. He also had a strong interest in practical problems, and in 1866 he was knighted for his work on the transtlantic cable. In 1892 he became Baron Kelvin, and this name survives as the name of the absolute temperature scale which he proposed in 1848. During his long career, Kelvin published more than 600 papers. He was elected to the Royal Society in 1851, and served as president of that organization from 1890 to 1895. The information in this section and the picture above were taken from a very useful web site called the MacTu- tor History of Mathematics Archive, sponsored by St. Andrews University. The web address is http://www-history.mcs.st-and.ac.uk/~history/ 2 kelvin.nb 2. The Age of the Earth The earth shows it age in many ways. Some techniques for estimating this age require us to observe the present state of a time-dependent process, and from that observation infer the time at which the process started. If we believe that the process started when the earth was formed, we get an estimate of the earth's age. -
Units and Magnitudes (Lecture Notes)
physics 8.701 topic 2 Frank Wilczek Units and Magnitudes (lecture notes) This lecture has two parts. The first part is mainly a practical guide to the measurement units that dominate the particle physics literature, and culture. The second part is a quasi-philosophical discussion of deep issues around unit systems, including a comparison of atomic, particle ("strong") and Planck units. For a more extended, profound treatment of the second part issues, see arxiv.org/pdf/0708.4361v1.pdf . Because special relativity and quantum mechanics permeate modern particle physics, it is useful to employ units so that c = ħ = 1. In other words, we report velocities as multiples the speed of light c, and actions (or equivalently angular momenta) as multiples of the rationalized Planck's constant ħ, which is the original Planck constant h divided by 2π. 27 August 2013 physics 8.701 topic 2 Frank Wilczek In classical physics one usually keeps separate units for mass, length and time. I invite you to think about why! (I'll give you my take on it later.) To bring out the "dimensional" features of particle physics units without excess baggage, it is helpful to keep track of powers of mass M, length L, and time T without regard to magnitudes, in the form When these are both set equal to 1, the M, L, T system collapses to just one independent dimension. So we can - and usually do - consider everything as having the units of some power of mass. Thus for energy we have while for momentum 27 August 2013 physics 8.701 topic 2 Frank Wilczek and for length so that energy and momentum have the units of mass, while length has the units of inverse mass. -
Lecture #4, Matter/Energy Interactions, Emissions Spectra, Quantum Numbers
Welcome to 3.091 Lecture 4 September 16, 2009 Matter/Energy Interactions: Atomic Spectra 3.091 Periodic Table Quiz 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 Name Grade /10 Image by MIT OpenCourseWare. Rutherford-Geiger-Marsden experiment Image by MIT OpenCourseWare. Bohr Postulates for the Hydrogen Atom 1. Rutherford atom is correct 2. Classical EM theory not applicable to orbiting e- 3. Newtonian mechanics applicable to orbiting e- 4. Eelectron = Ekinetic + Epotential 5. e- energy quantized through its angular momentum: L = mvr = nh/2π, n = 1, 2, 3,… 6. Planck-Einstein relation applies to e- transitions: ΔE = Ef - Ei = hν = hc/λ c = νλ _ _ 24 1 18 Bohr magneton µΒ = eh/2me 9.274 015 4(31) X 10 J T 0.34 _ _ 27 1 19 Nuclear magneton µΝ = eh/2mp 5.050 786 6(17) X 10 J T 0.34 _ 2 3 20 Fine structure constant α = µ0ce /2h 7.297 353 08(33) X 10 0.045 21 Inverse fine structure constant 1/α 137.035 989 5(61) 0.045 _ 2 1 22 Rydberg constant R¥ = mecα /2h 10 973 731.534(13) m 0.0012 23 Rydberg constant in eV R¥ hc/{e} 13.605 698 1(40) eV 0.30 _ 10 24 Bohr radius a0 = a/4πR¥ 0.529 177 249(24) X 10 m 0.045 _ _ 4 2 1 25 Quantum of circulation h/2me 3.636 948 07(33) X 10 m s 0.089 _ 11 1 26 Electron specific charge -e/me -1.758 819 62(53) X 10 C kg 0.30 _ 12 27 Electron Compton wavelength λC = h/mec 2.426 310 58(22) X 10 m 0.089 _ 2 15 28 Electron classical radius re = α a0 2.817 940 92(38) X 10 m 0.13 _ _ 26 1 29 Electron magnetic moment` µe 928.477 01(31) X 10 J T 0.34 _ _ 3 30 Electron mag. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
Physical Chemistry LD
Physical Chemistry LD Electrochemistry Chemistry Electrolysis Leaflets C4.4.5.2 Determining the Faraday constant Aims of the experiment To perform an electrolysis. To understand redox reactions in practice. To work with a Hoffman electrolysis apparatus. To understand Faraday’s laws. To understand the ideal gas equation. The second law is somewhat more complex. It states that the Principles mass m of an element that is precipitated by a specific When a voltage is applied to a salt or acid solution, material amount of charge Q is proportional to the atomic mass, and is migration occurs at the electrodes. Thus, a chemical reaction inversely proportional to its valence. Stated more simply, the is forced to occur through the flow of electric current. This same amount of charge Q from different electrolytes always process is called electrolysis. precipitates the same equivalent mass Me. The equivalent mass Me is equal to the molecular mass of an element divid- Michael Faraday had already made these observations in the ed by its valence z. 1830s. He coined the terms electrolyte, electrode, anode and cathode, and formulated Faraday's laws in 1834. These count M M = as some of the foundational laws of electrochemistry and e z describe the relationships between material conversions In order to precipitate this equivalent mass, 96,500 Cou- during electrochemical reactions and electrical charge. The lombs/mole are always needed. This number is the Faraday first of Faraday’s laws states that the amount of moles n, that constant, which is a natural constant based on this invariabil- are precipitated at an electrode is proportional to the charge ity.