DOCSLIB.ORG

Hydrogen and Deuterium Spectroscopy

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Hydrogen and Deuterium Spectroscopy Abstract: An optical spectrometer equipped with calibrated transmission 0.9 5.00E-04 Reflection Grating Calibration: Using the same mercury discharge tube as sin(theta)versus m x lambda for Hg calibration residual versus m x lambda 4.00E-04 and reflection diffraction gratings with 602.9(2) and 620.1(1) lines/mm, 0.8 of transmission grating for the transmission grating, the positions of 19 Hg emission lines were 3.00E-04 0.7 measured up to 5th order (Figure 3). Using the known wavelengths of the ) respectively, has been used to determine a value for the Rydberg constant. a 2.00E-04 t e h t ) 0.6 ( a n t 1.00E-04 mercury lines, the line density of the grating was determined to be i e Using the transmission grating, the angular positions of 7 Balmer emission s h t n ( i n l i 0.00E+00 0.5 a s u 620.1(1)lines/mm. lines from hydrogen were measured and from a least-squares fit to the data, R d i s -1.00E-04 e 7 -1 0.4 r was determined to be 1.09755(8)´10 m . Using the reflection grating, 26 -2.00E-04 0.3 Rydberg Constant of Hydrogen: Using the calibrated transmission grating, Balmer lines up to 5th order could be observed. From a least-squares fit to -3.00E-04 7 -1 0.2 -4.00E-04 the positions of the violet, green and red Balmer lines from a hydrogen their positions, R was determined to be 1.09819(14)´10 m . Using the same 3.00E-07 5.00E-07 7.00E-07 9.00E-07 1.10E-06 1.30E-06 1.50E-06 3.00E-07 5.00E-07 7.00E-07 9.00E-07 1.10E-06 1.30E-06 1.50E-06 m x lambda (m) reflection grating and a discharge tube containing both hydrogen and m x lambda (m) discharge tube were measured up to 5th order. The angular positions were deuterium, the ratio of the mass of the proton to the electron was determined Figure 1: Plot and LS fit to the calibration data for the transmission grating. The error bars are smaller measured both left and right of the zeroth order position, and, in all cases, the than the symbols used to plot the data. The right-hand graph shows a plot of the residuals from the fit. from the angular splitting of the H and D lines. The relative mass was two angles were the same to within 0.02°. After averaging the two angles, the determined to be 1200(400). wavelengths of the emission lines in each order were determined as: 5.2E+06 2.5E+03 order *1/lambda versus order *(1/4-1/n^2) for Residual in 1/lambda versus order *(1/4-1/n^2) 4.7E+06 hydrogen with reflection grating 2.0E+03 for hydrogen with reflection grating order 123 4 5 Transmission Grating Calibration: To calibrate the transmission grating, Violet 2nd order 1.5E+03 4.2E+06 ) Green 1 violet 433.6(5) 433.8(5) 433.6(3) 433.6(2) 433.73(13) - ) ^ 1 the angular positions of the four prominent emission lines from a Hg - 1.0E+03 m ^ 3.7E+06 ( m a ( d green 485.9(5) 485.5(3) 485.67(16) 485.76(11) 485.70(8) a b 5.0E+02 d m discharge tube were measured in first, second and third order both left and b 3.2E+06 a l m / a 1 l / 0.0E+00 red 655.8(5) 655.9(2) 655.58(15) 655.75(11) not obs n 1 Red i * 2.7E+06 l right of the straight-through position. The angular positions were as follows: r a e Violet u -5.0E+02 d d r s i o 2.2E+06 Green e R -1.0E+03 2 order(m) qLeft(±0.01°) qRight(±0.01°) qMean(±0.01°) Red 1.7E+06 1st order From a least squares fit of 1/l versus (1/4-1/n ), Figure 4, constraining the violet 1 15.23° 15.21° 15.22° -1.5E+03 1.2E+06 -2.0E+03 fitted line to pass through the origin, the value of R for the transmission green 1 19.23° 19.20° 19.21° 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46 7 -1 yellow 1 1 20.36° 20.35° 20.35° order *(1/4-1/n^2) order *(1/4-1/n^2) grating was 1.09819(14)´10 m yellow2 1 20.43° 20.41° 20.42° 2 violet 2 31.68° 31.68° 31.68° Figure 2: Plot of the measured wavelengths of the H emission lines versus (1/4–1/n ). To separate the green 2 41.15° 41.17° 41.16° different orders, both x and y coordinates have been multiplied by the order of the emission line. The error Measuring m /m using a Deuterium Discharge Tube: Because of the yellow 1 2 44.04° 44.07° 44.05° bars are smaller than the symbols used to plot the data. The right-hand graph shows a plot of the residuals pe yellow2 2 44.25° 44.27° 44.26° from the fit. different masses of the hydrogen and deuterium nuclei, the Balmer emission violet 3 not obs 52.04° 52.04° lines from deuterium are at slightly shorter wavelengths than those from 1 5.E-04 sin(alpha) versus m x lambda for Hg calibration Residual in sin(alpha) versus m x lambda hydrogen. The wavelength difference is related to m /m by: 0.9 4.E-04 pe of reflection grating Using the literature values of the emission line wavelengths, a plot of sinq 0.8 3.E-04 ) 2.E-04 0.7 a æ1+ m / 2m ö against ml gave a straight line (Figure 1), the gradient of which was equal to h l R e p p D H l a ç ÷ ) 0.6 1.E-04 ( a = = »1- m / 2m n h i e p p s the line density of the grating. A least-squares fit the data using LINEST gave l 0.E+00 ç ÷ a 0.5 n ( i l R 1+ m / m l H D e p n i a è ø s -1.E-04 0.4 u d the line density as 602.9(2)lines/mm. i s 0.3 e -2.E-04 R 0.2 -3.E-04 lD - lH Dl Rydberg Constant: Using the calibrated transmission grating, the angular 0.1 -4.E-04 Hence = = -me / 2mp 0 -5.E-04 lH lH positions of the violet, green and red Balmer lines from a hydrogen emission 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 tube were measured in first and second order. The wavelengths of these lines m x lambda (m) m x lambda (m) were then determined using the diffraction equation for normal incidence Figure 3: Plot and LS fit to the calibration data for the reflection grating. The error bars are smaller than The angular splitting for 4 Balmer lines from a hydrogen/deuterium tube the symbols used to plot the data. The right-hand graph shows a plot of the residuals from the fit. ml = d sinq were measured in third, fourth and fifth order. Each line was measured both left and right of the zeroth order position, and, in all cases, the two angles 1st order 2nd order 1.30E+07 5.00E+03 order/lambda versus order*(1/4-1.n^2) for hydrogen Residual in order/lambda versus order*(1/4-1.n^2) for were the same to within 0.01°. 4.00E+03 with reflection grating hydrogen with reflection grating The measured wavelengths were violet 433.8(3)nm 433.9(2)nm 1.10E+07 3.00E+03 ) 1 - ^ green 485.9(3)nm 486.0(2)nm ) 2.00E+03 1 9.00E+06 m - ( ^ a The wavelengths of the 4 lines, and their wavelength splittings ,were: m d ( 1.00E+03 b red 655.8(3)nm 656.1(2)nm a m d a 7.00E+06 l b / r 0.00E+00 e m llDHDl d a l r 0.1 0.3 0.5 0.7 0.9 1.1 / o r e -1.00E+03 n i d 5.00E+06 r l a o red (3rd order) 655.69(11)nm 655.40(15)nm –0.29(19)nm u -2.00E+03 d The wavelengths of these lines are predicted by the Rydberg equation i s e 3.00E+06 R -3.00E+03 red (4th order) 655.74(11)nm 655.50(11)nm –0.24(15)nm 1 æ 1 1 ö -4.00E+03 1.00E+06 green (4th order) 485.68(11)nm 485.46(11)nm –0.22(16)nm = Rç - ÷ -5.00E+03 2 2 0.1 0.3 0.5 0.7 0.9 1.1 l è 2 n ø order * (1/4-1/n^2) order * (1/4-1/n^2) green (5th order) 485.73(8)nm 485.54(8)nm –0.19(12)nm 2 A plot of 1/l versus (1/4-1/n ) is shown in Figure 2.
Recommended publications
  • Quantum Theory of the Hydrogen Atom

    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, .
  • Rydberg Constant and Emission Spectra of Gases

    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.
  • Deuterium – Tritium Pulse Propulsion with Hydrogen As Propellant and the Entire Space-Craft As a Gigavolt Capacitor for Ignition

    Deuterium – Tritium Pulse Propulsion with Hydrogen As Propellant and the Entire Space-Craft As a Gigavolt Capacitor for Ignition

    Deuterium – Tritium pulse propulsion with hydrogen as propellant and the entire space-craft as a gigavolt capacitor for ignition. By F. Winterberg University of Nevada, Reno Abstract A deuterium-tritium (DT) nuclear pulse propulsion concept for fast interplanetary transport is proposed utilizing almost all the energy for thrust and without the need for a large radiator: 1. By letting the thermonuclear micro-explosion take place in the center of a liquid hydrogen sphere with the radius of the sphere large enough to slow down and absorb the neutrons of the DT fusion reaction, heating the hydrogen to a fully ionized plasma at a temperature of ~ 105 K. 2. By using the entire spacecraft as a magnetically insulated gigavolt capacitor, igniting the DT micro-explosion with an intense GeV ion beam discharging the gigavolt capacitor, possible if the space craft has the topology of a torus. 1. Introduction The idea to use the 80% of the neutron energy released in the DT fusion reaction for nuclear micro-bomb rocket propulsion, by surrounding the micro-explosion with a thick layer of liquid hydrogen heated up to 105 K thereby becoming part of the exhaust, was first proposed by the author in 1971 [1]. Unlike the Orion pusher plate concept, the fire ball of the fully ionized hydrogen plasma can here be reflected by a magnetic mirror. The 80% of the energy released into 14MeV neutrons cannot be reflected by a magnetic mirror for thermonuclear micro-bomb propulsion. This was the reason why for the Project Daedalus interstellar probe study of the British Interplanetary Society [2], the neutron poor deuterium-helium 3 (DHe3) reaction was chosen.
  • Improving the Accuracy of the Numerical Values of the Estimates Some Fundamental Physical Constants

    Improving the Accuracy of the Numerical Values of the Estimates Some Fundamental Physical Constants

    Improving the accuracy of the numerical values of the estimates some fundamental physical constants. Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev To cite this version: Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev. Improving the accuracy of the numerical values of the estimates some fundamental physical constants.. Digital Technologies, Odessa National Academy of Telecommunications, 2019, 25, pp.23 - 39. hal-02117148 HAL Id: hal-02117148 https://hal.archives-ouvertes.fr/hal-02117148 Submitted on 2 May 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Improving the accuracy of the numerical values of the estimates some fundamental physical constants. Valery F. Timkov1*, Serg V. Timkov2, Vladimir A. Zhukov2, Konstantin E. Afanasiev2 1Institute of Telecommunications and Global Geoinformation Space of the National Academy of Sciences of Ukraine, Senior Researcher, Ukraine. 2Research and Production Enterprise «TZHK», Researcher, Ukraine. *Email: [email protected] The list of designations in the text: l
  • Investigation of the Use of Deuterium and Oxygen in Illicit Fentanyl Analysis Author(S): John F

    Investigation of the Use of Deuterium and Oxygen in Illicit Fentanyl Analysis Author(S): John F

    The author(s) shown below used Federal funding provided by the U.S. Department of Justice to prepare the following resource: Document Title: Investigation of the Use of Deuterium and Oxygen in Illicit Fentanyl Analysis Author(s): John F. Casale, Mike Lott, Jennifer R. Mallette Document Number: 255103 Date Received: August 2020 Award Number: NIJ-ONDCP IAA: 2017 DEA contract research task This resource has not been published by the U.S. Department of Justice. This resource is being made publically available through the Office of Justice Programs’ National Criminal Justice Reference Service. Opinions or points of view expressed are those of the author(s) and do not necessarily reflect the official position or policies of the U.S. Department of Justice. Investigation of the Use of Deuterium and Oxygen in Illicit Fentanyl Analysis John F. Casalea, Mike Lottb, and Jennifer R. Mallettea aU.S. Drug Enforcement Administration Special Testing and Research Laboratory Dulles, VA bIsoForensics, Inc. Salt Lake City, UT 84108 This work was conducted through an Inter-Agency Agreement dated June 28, 2017, between the Office of National Drug Control Policy (ONDCP) and the National Institute of Justice (NIJ), under DEA Contract number 15DDHQ18P00000344 with funding from the NIJ, Office of Justice Programs, U.S. Department of Justice. The opinions, findings, and conclusions or recommendations expressed in this publication/program/exhibition are those of the authors, and do not necessarily reflect those of the Department of Justice or ONDCP. This resource was prepared by the author(s) using Federal funds provided by the U.S. Department of Justice.
  • Isotopic Fractionation of Carbon, Deuterium, and Nitrogen: a Full Chemical Study?

    Isotopic Fractionation of Carbon, Deuterium, and Nitrogen: a Full Chemical Study?

    A&A 576, A99 (2015) Astronomy DOI: 10.1051/0004-6361/201425113 & c ESO 2015 Astrophysics Isotopic fractionation of carbon, deuterium, and nitrogen: a full chemical study? E. Roueff1;2, J. C. Loison3, and K. M. Hickson3 1 LERMA, Observatoire de Paris, PSL Research University, CNRS, UMR8112, Place Janssen, 92190 Meudon Cedex, France e-mail: [email protected] 2 Sorbonne Universités, UPMC Univ. Paris 6, 4 Place Jussieu, 75005 Paris, France 3 ISM, Université de Bordeaux – CNRS, UMR 5255, 351 cours de la Libération, 33405 Talence Cedex, France e-mail: [email protected] Received 6 October 2014 / Accepted 5 January 2015 ABSTRACT Context. The increased sensitivity and high spectral resolution of millimeter telescopes allow the detection of an increasing number of isotopically substituted molecules in the interstellar medium. The 14N/15N ratio is difficult to measure directly for molecules con- taining carbon. Aims. Using a time-dependent gas-phase chemical model, we check the underlying hypothesis that the 13C/12C ratio of nitriles and isonitriles is equal to the elemental value. Methods. We built a chemical network that contains D, 13C, and 15N molecular species after a careful check of the possible fraction- ation reactions at work in the gas phase. Results. Model results obtained for two different physical conditions that correspond to a moderately dense cloud in an early evolu- tionary stage and a dense, depleted prestellar core tend to show that ammonia and its singly deuterated form are somewhat enriched 15 14 15 + in N, which agrees with observations. The N/ N ratio in N2H is found to be close to the elemental value, in contrast to previous 15 + models that obtain a significant enrichment, because we found that the fractionation reaction between N and N2H has a barrier in + 15 + + 15 + the entrance channel.
  • Chapter 09584

    Chapter 09584

    Author's personal copy Excitons in Magnetic Fields Kankan Cong, G Timothy Noe II, and Junichiro Kono, Rice University, Houston, TX, United States r 2018 Elsevier Ltd. All rights reserved. Introduction When a photon of energy greater than the band gap is absorbed by a semiconductor, a negatively charged electron is excited from the valence band into the conduction band, leaving behind a positively charged hole. The electron can be attracted to the hole via the Coulomb interaction, lowering the energy of the electron-hole (e-h) pair by a characteristic binding energy, Eb. The bound e-h pair is referred to as an exciton, and it is analogous to the hydrogen atom, but with a larger Bohr radius and a smaller binding energy, ranging from 1 to 100 meV, due to the small reduced mass of the exciton and screening of the Coulomb interaction by the dielectric environment. Like the hydrogen atom, there exists a series of excitonic bound states, which modify the near-band-edge optical response of semiconductors, especially when the binding energy is greater than the thermal energy and any relevant scattering rates. When the e-h pair has an energy greater than the binding energy, the electron and hole are no longer bound to one another (ionized), although they are still correlated. The nature of the optical transitions for both excitons and unbound e-h pairs depends on the dimensionality of the e-h system. Furthermore, an exciton is a composite boson having integer spin that obeys Bose-Einstein statistics rather than fermions that obey Fermi-Dirac statistics as in the case of either the electrons or holes by themselves.
  • 1. Physical Constants 1 1

    1. Physical Constants 1 1

    1. Physical constants 1 1. PHYSICAL CONSTANTS Table 1.1. Reviewed 1998 by B.N. Taylor (NIST). Based mainly on the “1986 Adjustment of the Fundamental Physical Constants” by E.R. Cohen and B.N. Taylor, Rev. Mod. Phys. 59, 1121 (1987). The last group of constants (beginning with the Fermi coupling constant) comes from the Particle Data Group. The figures in parentheses after the values give the 1-standard- deviation uncertainties in the last digits; the corresponding uncertainties in parts per million (ppm) are given in the last column. This set of constants (aside from the last group) is recommended for international use by CODATA (the Committee on Data for Science and Technology). Since the 1986 adjustment, new experiments have yielded improved values for a number of constants, including the Rydberg constant R∞, the Planck constant h, the fine- structure constant α, and the molar gas constant R,and hence also for constants directly derived from these, such as the Boltzmann constant k and Stefan-Boltzmann constant σ. The new results and their impact on the 1986 recommended values are discussed extensively in “Recommended Values of the Fundamental Physical Constants: A Status Report,” B.N. Taylor and E.R. Cohen, J. Res. Natl. Inst. Stand. Technol. 95, 497 (1990); see also E.R. Cohen and B.N. Taylor, “The Fundamental Physical Constants,” Phys. Today, August 1997 Part 2, BG7. In general, the new results give uncertainties for the affected constants that are 5 to 7 times smaller than the 1986 uncertainties, but the changes in the values themselves are smaller than twice the 1986 uncertainties.
  • And Tissue Perfusion Employing 2H20 As a Freely Diffusible Tracer (Rat Liver/Surface Coil/Spin-Lattice Relaxation/Heavy Water) JOSEPH J

    And Tissue Perfusion Employing 2H20 As a Freely Diffusible Tracer (Rat Liver/Surface Coil/Spin-Lattice Relaxation/Heavy Water) JOSEPH J

    Proc. Natl. Acad. Sci. USA Vol. 84, pp. 4099-4102, June 1987 Biophysics Deuterium nuclear magnetic resonance measurements of blood flow and tissue perfusion employing 2H20 as a freely diffusible tracer (rat liver/surface coil/spin-lattice relaxation/heavy water) JOSEPH J. H. ACKERMAN*t, COLEEN S. EwY*, NANCY N. BECKER*, AND ROBERT A. SHALWITZtt *Department of Pediatrics, Washington University School of Medicine, St. Louis, MO 63110; and *Department of Chemistry, Washington University, St. Louis, MO 63130 Communicated by William D. Phillips, January 28, 1987 ABSTRACT The use of deuterium oxide (21120) is pro- We propose herein the analogous use of 2H20 as a posed as a freely diffusible nuclear magnetic resonance (NMR) diffusible blood-flow and tissue-perfusion tracer where deu- blood flow and tissue perfusion tracer of potential clinical terium NMR is used to monitor label intensity as a function utility. Deuterium is a stable, nonradiative isotope commer- of time. Deuterium is a nonradiative, naturally abundant cially available as 2H20 at enrichment levels of essentially (0.0156%), quadrupole nuclide with only 0.01 the sensitivity 100%-i.e., 110 molar equivalent deuterium. This high con- of 'H. Nevertheless, the combination of an efficient centration, together with the short relaxation time of the spin quadrupole relaxation mechanism and the commercial avail- 1 (quadrupole) deuterium nuclide, provides substantial sensi- ability of 2H20, essentially 100% enriched to ca. 110 molar tivity for NMR spectroscopy. As a result, when 2H20 is equivalent deuterium, can provide substantial NMR signal- administered in a bolus fashion to a specific tissue or organ in to-noise in the intact subject.
  • Compton Wavelength, Bohr Radius, Balmer's Formula and G-Factors

    Compton Wavelength, Bohr Radius, Balmer's Formula and G-Factors

    Compton wavelength, Bohr radius, Balmer's formula and g-factors Raji Heyrovska J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejškova 3, 182 23 Prague 8, Czech Republic. [email protected] Abstract. The Balmer formula for the spectrum of atomic hydrogen is shown to be analogous to that in Compton effect and is written in terms of the difference between the absorbed and emitted wavelengths. The g-factors come into play when the atom is subjected to disturbances (like changes in the magnetic and electric fields), and the electron and proton get displaced from their fixed positions giving rise to Zeeman effect, Stark effect, etc. The Bohr radius (aB) of the ground state of a hydrogen atom, the ionization energy (EH) and the Compton wavelengths, λC,e (= h/mec = 2πre) and λC,p (= h/mpc = 2πrp) of the electron and proton respectively, (see [1] for an introduction and literature), are related by the following equations, 2 EH = (1/2)(hc/λH) = (1/2)(e /κ)/aB (1) 2 2 (λC,e + λC,p) = α2πaB = α λH = α /2RH (2) (λC,e + λC,p) = (λout - λin)C,e + (λout - λin)C,p (3) α = vω/c = (re + rp)/aB = 2πaB/λH (4) aB = (αλH/2π) = c(re + rp)/vω = c(τe + τp) = cτB (5) where λH is the wavelength of the ionizing radiation, κ = 4πεo, εo is 2 the electrical permittivity of vacuum, h (= 2πħ = e /2εoαc) is the 2 Planck constant, ħ (= e /κvω) is the angular momentum of spin, α (= vω/c) is the fine structure constant, vω is the velocity of spin [2], re ( = ħ/mec) and rp ( = ħ/mpc) are the radii of the electron and
  • Deuterium Concentration by Chemically-Refluxed Ammonia-Hydrogen Exchange

    Deuterium Concentration by Chemically-Refluxed Ammonia-Hydrogen Exchange

    MIT-D15 DEUTERIUM CONCENTRATION BY CHEMICALLY-REFLUXED AMMONIA-HYDROGEN EXCHANGE SUPPLEMENTARY REPORTS by M. Benedict, E.A. Mason, E.R. Chow, J.S. Baron June 1969 FOR E.I. DUPONT DE NEMOURS & COMPANY UNDER U.S. ATOMIC ENERGY COMMISSION SUBCONTRACT AX-210280 Department of Nuclear Engineering Massachusetts Institute of Technology Cambridge, Massachusetts 02139 (MITNE-103) AECL PROPRIETARY DOCUMENT Notice: This document contains information obtained from Atomic Energy of Canada Limited, designated AECL PROPRIETARY. Documents so designated are made available to the USAEC pursuant to the Memorandum of Understanding executed June 7, 1960, for distribution restricted to the USAEC or its contractors. No other distribution is to be made without permission of AECL which may be secured by requesting specific clearance from the Scientific Representative, USAEC, Chalk River Liaison Office, Chalk River, Ontario. MIT-Dl5 DEUTERIUM CONCENTRATION BY CHEMICALLY-REFLUXED AMMONIA-HYDROGEN EXCHANGE SUPPLEMENTARY REPORTS by M. Benedict, E.A. Mason, E.R. Chow, J.S. Baron June 1969 for E.I. duPont de Nemours & Company under U.S. Atomic Energy Commission Subcontract AX-210280 (MIT DSR-70672) Department of Nuclear Engineering Massachusetts Institute of Technology Cambridge, Massachusetts 02139 (MITNE-103) Table of Contents Page Introductory Note I-1 Supplement A Liquid-Vapor Equilibrium in the System NH 3-H 2-N2 1. Introduction A-1 2. Results 2.1 Liquid Phase A-1 2.2 Vapor Phase A-2 3. Sources of Data A-3 4. Procedure for Correlating Data 4.1 Henry's Law Constants A-4 4.2 Ammonia Content of Vapor A-5 5. Bibliography A-19 Supplement B Enthalpies of Hydrogen, Nitrogen, and Ammonia to 14000 F and from 0 to 200 Atmospheres 1.
  • The Fine Structure Constant, the Rydberg Constant and the Planck

    The Fine Structure Constant, the Rydberg Constant and the Planck

    Perspective iMedPub Journals Polymer Sciences 2017 www.imedpub.com ISSN 2471-9935 Vol.3 No.2:13 DOI: 10.4172/2471-9935.100028 The Fine Structure Constant, the Rydberg YinYue Sha* Constant and the Planck Constant Dongling Engineering Center, Ningbo Institute of Technology, Zhejiang University, PR China Abstract *Corresponding author: YinYue Sha So let's say that the electron is orbiting the proton in the innermost orbital, and then, according to the equilibrium relationship of forces, there's the following [email protected] formula: F=K × Qp × Qe/(Rb × Rb)=Me × Ve × Ve/Rb (1) Dongling Engineering Center, Ningbo The K is the electromagnetic constant; Qp is the charge of proton; Qe is the charge Institute of Technology, Zhejiang University, of electron; Rb is the Bohr atom radius; Me is the mass of the electron; Ve is the PR China. speed of electrons. Tel: +86 574 8822 9048 Keywords: Protons; Electronic; Mass; Charge; Bohr atom radius; Fine structure constant; The Rydberg constant; Planck constant Citation: Sha YY (2017) The Fine Structure Received: July 12, 2017; Accepted: September 20, 2017; Published: September 30, Constant, the Rydberg Constant and the 2017 Planck Constant. Polym Sci Vol.3 No.2:13 One, the fine structure constant and the Bohr atomic radius. Three, The kinetic energy of the ground state electron and the Planck constant From the formula (1), we can obtain the formula for calculating the basic radius of the hydrogen atom: The kinetic energy of the ground state electron: Rb=K × Qp × Qe/(Me × Ve2) (2) Eb=1/2 × Me × Ve2=2.1798719696853