Mean Path Length Invariance in Multiple Light Scattering
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VISCOSITY of a GAS -Dr S P Singh Department of Chemistry, a N College, Patna
Lecture Note on VISCOSITY OF A GAS -Dr S P Singh Department of Chemistry, A N College, Patna A sketchy summary of the main points Viscosity of gases, relation between mean free path and coefficient of viscosity, temperature and pressure dependence of viscosity, calculation of collision diameter from the coefficient of viscosity Viscosity is the property of a fluid which implies resistance to flow. Viscosity arises from jump of molecules from one layer to another in case of a gas. There is a transfer of momentum of molecules from faster layer to slower layer or vice-versa. Let us consider a gas having laminar flow over a horizontal surface OX with a velocity smaller than the thermal velocity of the molecule. The velocity of the gaseous layer in contact with the surface is zero which goes on increasing upon increasing the distance from OX towards OY (the direction perpendicular to OX) at a uniform rate . Suppose a layer ‘B’ of the gas is at a certain distance from the fixed surface OX having velocity ‘v’. Two layers ‘A’ and ‘C’ above and below are taken into consideration at a distance ‘l’ (mean free path of the gaseous molecules) so that the molecules moving vertically up and down can’t collide while moving between the two layers. Thus, the velocity of a gas in the layer ‘A’ ---------- (i) = + Likely, the velocity of the gas in the layer ‘C’ ---------- (ii) The gaseous molecules are moving in all directions due= to −thermal velocity; therefore, it may be supposed that of the gaseous molecules are moving along the three Cartesian coordinates each. -
Key Elements of X-Ray CT Physics Part 2: X-Ray Interactions
Key Elements of X-ray CT Physics Part 2: X-ray Interactions NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2006 Photoelectric Effect • Photoe- absorption is the preferred interaction for X-ray imging. 2 - •Rem.:Eb Z ; characteristic x-rays and/or Auger e preferredinhigh Zmaterial. • Probability of photoe- absorption Z3/E3 (Z = atomic no.) provide contrast according to different Z. • Due to the absorption of the incident x-ray without scatter, maximum subject contrast arises with a photoe- effect interaction No scattering contamination better contrast • Explains why contrast as higher energy x-rays are used in the imaging process - • Increased probability of photoe absorption just above the Eb of the inner shells cause discontinuities in the attenuation profiles (e.g., K-edge) NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2017 Photoelectric Effect NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2017 X-ray Cross Section and Linear Attenuation Coefficient • Cross section is a measure of the probability (‘apparent area’) of interaction: (E) measured in barns (10-24 cm2) • Interaction probability can also be expressed in terms of the thickness of the material – linear attenuation coefficient: (E) = fractional number of photons removed (attenuated) from the beam after traveling through a unit length in media by absorption or scattering -1 - • (E) [cm ]=Z[e /atom] · Navg [atoms/mole] · 1/A [moles/gm] · [gm/cm3] · (E) [cm2/e-] • Multiply by 100% to get % removed from the beam/cm • (E) as E , e.g., for soft tissue (30 keV) = 0.35 cm-1 and (100 keV) = 0.16 cm-1 NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2017 Calculation of the Linear Attenuation Coefficient To the extent that Compton scattered photons are completely removed from the beam, the attenuation coefficient can be approximated as The (effective) Z value of a material is particular important for determining . -
Introduction to the Ray Optics Module
INTRODUCTION TO Ray Optics Module Introduction to the Ray Optics Module © 1998–2020 COMSOL Protected by patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991; 8,457,932; 9,098,106; 9,146,652; 9,323,503; 9,372,673; 9,454,625; 10,019,544; 10,650,177; and 10,776,541. Patents pending. This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the terms of the license agreement. COMSOL, the COMSOL logo, COMSOL Multiphysics, COMSOL Desktop, COMSOL Compiler, COMSOL Server, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/ trademarks. Version: COMSOL 5.6 Contact Information Visit the Contact COMSOL page at www.comsol.com/contact to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at www.comsol.com/contact/offices for address and contact information. If you need to contact Support, an online request form is located at the COMSOL Access page at www.comsol.com/support/case. Other useful links include: • Support Center: www.comsol.com/support • Product Download: www.comsol.com/product-download • Product Updates: www.comsol.com/support/updates •COMSOL Blog: www.comsol.com/blogs • Discussion Forum: www.comsol.com/community •Events: www.comsol.com/events • COMSOL Video Gallery: www.comsol.com/video • Support Knowledge Base: www.comsol.com/support/knowledgebase Part number. -
Photon Cross Sections, Attenuation Coefficients, and Energy Absorption Coefficients from 10 Kev to 100 Gev*
1 of Stanaaros National Bureau Mmin. Bids- r'' Library. Ml gEP 2 5 1969 NSRDS-NBS 29 . A111D1 ^67174 tioton Cross Sections, i NBS Attenuation Coefficients, and & TECH RTC. 1 NATL INST OF STANDARDS _nergy Absorption Coefficients From 10 keV to 100 GeV U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS T X J ". j NATIONAL BUREAU OF STANDARDS 1 The National Bureau of Standards was established by an act of Congress March 3, 1901. Today, in addition to serving as the Nation’s central measurement laboratory, the Bureau is a principal focal point in the Federal Government for assuring maximum application of the physical and engineering sciences to the advancement of technology in industry and commerce. To this end the Bureau conducts research and provides central national services in four broad program areas. These are: (1) basic measurements and standards, (2) materials measurements and standards, (3) technological measurements and standards, and (4) transfer of technology. The Bureau comprises the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Radiation Research, the Center for Computer Sciences and Technology, and the Office for Information Programs. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation’s scientific community, industry, and com- merce. The Institute consists of an Office of Measurement Services and the following technical divisions: Applied Mathematics—Electricity—Metrology—Mechanics—Heat—Atomic and Molec- ular Physics—Radio Physics -—Radio Engineering -—Time and Frequency -—Astro- physics -—Cryogenics. -
Module 5: Schlieren and Shadowgraph Lecture 26: Introduction to Schlieren and Shadowgraph
Objectives_template Module 5: Schlieren and Shadowgraph Lecture 26: Introduction to schlieren and shadowgraph The Lecture Contains: Introduction Laser Schlieren Window Correction Shadowgraph Shadowgraph Governing Equation and Approximation Numerical Solution of the Poisson Equation Ray tracing through the KDP solution: Importance of the higher-order effects Correction Factor for Refraction at the glass-air interface Methodology for determining the supersaturation at each stage of the Experiment file:///G|/optical_measurement/lecture26/26_1.htm[5/7/2012 12:34:01 PM] Objectives_template Module 5: Schlieren and Shadowgraph Lecture 26: Introduction to schlieren and shadowgraph Introduction Closely related to the method of interferometry are and that employ variation in refractive index with density (and hence, temperature and concentration) to map a thermal or a species concentration field. With some changes, the flow field can itself be mapped. While image formation in interferometry is based on changes in the the refractive index with respect to a reference domain, schlieren uses the transverse derivative for image formation. In shadowgraph, effectively the second derivative (and in effect the Laplacian ) is utilized. These two methods use only a single beam of light. They find applications in combustion problems and high-speed flows involving shocks where the gradients in the refractive index are large. The schlieren method relies on beam refraction towards zones of higher refractive index. The shadowgraph method uses the change in light intensity due to beam expansion to describe the thermal/concentration field. Before describing the two methods in further detail, a comparison of interferometry (I), schlieren (Sch) and shadowgraph (Sgh) is first presented. The basis of this comparison will become clear when further details of the measurement procedures are described. -
Gamma, X-Ray and Neutron Shielding Properties of Polymer Concretes
Indian Journal of Pure & Applied Physics Vol. 56, May 2018, pp. 383-391 Gamma, X-ray and neutron shielding properties of polymer concretes L Seenappaa,d, H C Manjunathaa*, K N Sridharb & Chikka Hanumantharayappac aDepartment of Physics, Government College for Women, Kolar 563 101, India bDepartment of Physics, Government First grade College, Kolar 563 101, India cDepartment of Physics, Vivekananda Degree College, Bangalore 560 055, India dResearch and Development Centre, Bharathiar University, Coimbatore 641 046, India Received 21 June 2017; accepted 3 November 2017 We have studied the X-ray and gamma radiation shielding parameters such as mass attenuation coefficient, linear attenuation coefficient, half value layer, tenth value layer, effective atomic numbers, electron density, exposure buildup factors, relative dose, dose rate and specific gamma ray constant in some polymer based concretes such as sulfur polymer concrete, barium polymer concrete, calcium polymer concrete, flourine polymer concrete, chlorine polymer concrete and germanium polymer concrete. The neutron shielding properties such as coherent neutron scattering length, incoherent neutron scattering lengths, coherent neutron scattering cross section, incoherent neutron scattering cross sections, total neutron scattering cross section and neutron absorption cross sections in the polymer concretes have been studied. The shielding properties among the studied different polymer concretes have been compared. From the detail study, it is clear that barium polymer concrete is good absorber for X-ray, gamma radiation and neutron. The attenuation parameters for neutron are large for chlorine polymer concrete. Hence, we suggest barium polymer concrete and chlorine polymer concrete are the best shielding materials for X-ray, gamma and neutrons. Keywords: X-ray, Gamma, Mass attenuation coefficient, Polymer concrete 1 Introduction Agosteo et al.11 studied the attenuation of Concrete is used for radiation shielding. -
O10e “Michelson Interferometer”
Fakultät für Physik und Geowissenschaften Physikalisches Grundpraktikum O10e “Michelson Interferometer” Tasks 1. Adjust a Michelson interferometer and determine the wavelength of a He-Ne laser. 2. Measure the change in the length of a piezoelectric actor when a voltage is applied. Plot the length change as a function of voltage and determine the sensitivity of the sensor. 3. Measure the dependence of the refractive index of air as a function of the air pressure p. Plot Δn(p) and calculate the index of refraction n0 at standard conditions. 4. Measure the length of a ferromagnetic rod as a function of an applied magnetic field. Plot the relative length change versus the applied field. 5. Determine the relative change in the length of a metal rod as a function of temperature and calculate the linear expansion coefficient. Literature Physics, P.A. Tipler 3. Ed., Vol. 2, Chap. 33-3 University Physics, H. Benson, Chap. 37.6 Physikalisches Praktikum, 13. Auflage, Hrsg. W. Schenk, F. Kremer, Optik, 2.0.1, 2.0.2, 2.4 Accessories He-Ne laser, various optical components for the setup of a Michelson interferometer, piezoelectric actor with mirror, laboratory power supply, electromagnet, ferromagnetic rod with mirror, metal rod with heating filament and mirror, vacuum chamber with hand pump. Keywords for preparation - Interference, coherence - Basic principle of the Michelson interferometer - Generation and properties of laser light - Index of refraction, standard conditions - Piezoelectricity, magnetostriction, thermal expansion 1 In this experiment you will work with high quality optical components. Work with great care! While operating the LASER do not look directly into the laser beam or its reflections! Basics The time and position dependence of a plane wave travelling in the positive (negative) z-direction is given by ψ =+ψωϕ[] 0 expitkz (m ) , (1) where ψ might denote e.g. -
GASEOUS STATE SESSION 8: Collision Parameters
COURSE TITLE : PHYSICAL CHEMISTRY I COURSE CODE : 15U5CRCHE07 UNIT 1 : GASEOUS STATE SESSION 8: Collision Parameters Collision Diameter, • The distance between the centres of two gas molecules at the point of closest approach to each other is called the collision diameter. • Two molecules come within a distance of - Collision occurs 0 0 0 • H2 - 2.74 A N2 - 3.75 A O2 - 3.61 A Collision Number, Z • The average number of collisions suffered by a single molecule per unit time per unit volume of a gas is called collision number. Z = 22 N = Number Density () – Number of Gas Molecules per Unit Volume V Unit of Z = ms-1 m2 m-3 = s-1 Collision Frequency, Z11 • The total number of collisions between the molecules of a gas per unit time per unit volume is called collision frequency. Collision Frequency, Z11 = Collision Number Total Number of molecules ퟐ Collision Frequency, Z11 = ퟐ흅흂흈 흆 흆 Considering collision between like molecules ퟏ Collision Frequency, Z = ½ ퟐ흅흂흈ퟐ흆 흆 = 흅흂흈ퟐ흆ퟐ 11 ퟐ -1 -3 Unit of Z11 = s m The number of bimolecular collisions in a gas at ordinary T and P – 1034 s-1 m-3 Influence of T and P ퟏ Z = 흅흂흈ퟐ흆ퟐ 11 ퟐ RT Z = 222 11 M ZT11 at a given P 2 Z11 at a given T 2 ZP11 at a given T 2 at a given T , P Z11 For collisions between two different types of molecules. 1 Z = 2 2 2 2 122 1 2 MEAN FREE PATH, FREE PATH – The distance travelled by a molecule between two successive collisions. -
Simulation of Electron Spectra for Surface Analysis (SESSA) Version 2.1 User's Guide
NIST NSRDS 100 Simulation of Electron Spectra for Surface Analysis (SESSA) Version 2.1 User’s Guide W.S.M. Werner W. Smekal C.J. Powell This publication is available free of charge from: https://doi.org/10.6028/NIST.NSRDS.100-2017 NIST NSRDS 100 Simulation of Electron Spectra for Surface Analysis (SESSA) Version 2.1 User’s Guide W.S.M. Werner W. Smekal Institute of Applied Physics Vienna University of Technology, Vienna, Austria C.J. Powell Materials Measurement Science Division Material Measurement Laboratory This publication is available free of charge from: https://doi.org/10.6028/NIST.NSRDS.100-2017 December 2017 U.S. Department of Commerce Wilbur L. Ross, Jr., Secretary National Institute of Standards and Technology Walter Copan, NIST Director and Under Secretary of Commerce for Standards and Technology This publication is available free of charge from https://doi.org/10.6028/NIST.NSRDS.100-2017 Disclaimer The National Institute of Standards and Technology (NIST) uses its best efforts to deliver a high-quality copy of the database and to verify that the data contained therein have been selected on the basis of sound scientifc judgement. However, NIST makes no warranties to that effect, and NIST shall not be liable for any damage that may result from errors or omissions in the database. For a literature citation, the database should be viewed as a book published by NIST. The citation would therefore be: W.S.M. Werner, W. Smekal and C. J. Powell, Simulation of Electron Spectra for Surface Analysis (SESSA) - Version 2.1 National Institute of Standards and Technology, Gaithersburg, MD (2016). -
TIE-25: Striae in Optical Glass
DATE June 2006 PAGE 1/20 . TIE-25: Striae in optical glass 0. Introduction Optical glasses from SCHOTT are well-known for their very low striae content. Even in raw production formats, such as blocks or strips, requirements for the most demanding optical systems are met. Striae intensity is thickness dependent. Hence, in finished lenses or prisms with short optical path lengths, the striae effects will decrease to levels where they can be neglected completely, i.e. they become much smaller than 10 nm optical path distortion. Striae with intensities equal and below 30 nm do not have any significant negative influence on the image quality as Modulation Transfer Function (MTF) and Point Spread Function (PSF) analyses have shown (refer to Chapter 7). In addition, questions such as how to specify raw glass or blanks for optical elements frequently arise, especially with reference to the regulations of ISO 10110 Part 4 “Inhomogeneities and Striae”. Based on the progress that has been made in the last years regarding measurement, classification and assessment of striae, this technical information shall help the customer find the right specification. 1. Definition of Striae An important property of processed optical glass is the excellent spatial homogeneity of the refractive index of the material. In general, one can distinguish between global or long range homogeneity of refractive index in the material and short range deviations from glass homogeneity. Striae are spatially short range variations of the homogeneity in a glass. Short range variations are variations over a distance of about 0.1 mm up to 2 mm, whereas the spatially long range global homogeneity of refractive index ranges covers the complete glass piece (see TIE-26/2003 for more information on homogeneity). -
Chapter 2 Laser Schlieren and Shadowgraph
Chapter 2 Laser Schlieren and Shadowgraph Keywords Knife-edge · Gray-scale filter · Cross-correlation · Background oriented schlieren. 2.1 Introduction Schlieren and shadowgraph techniques are introduced in the present chapter. Topics including optical arrangement, principle of operation, and data analysis are discussed. Being refractive index-based techniques, schlieren and shadowgraph are to be com- pared with interferometry, discussed in Chap. 1. Interferometry assumes the passage of the light beam through the test section to be straight and measurement is based on phase difference, created by the density field, between the test beam and the refer- ence beam. Beam bending owing to refraction is neglected in interferometry and is a source of error. Schlieren and shadowgraph dispense with the reference beam, sim- plifying the measurement process. They exploit refraction effects of the light beam in the test section. Schlieren image analysis is based on beam deflection (but not displacement) while shadowgraph accounts for beam deflection as well as displace- ment [3, 8, 10]. In its original form, shadowgraph traces the path of the light beam through the test section and can be considered the most general approach among the three. Quantitative analysis of shadowgraph images can be tedious and, in this respect, schlieren has emerged as the most popular refractive index-based technique, combining ease of instrumentation with simplicity of analysis. P. K. Panigrahi and K. Muralidhar, Schlieren and Shadowgraph Methods in Heat 23 and Mass Transfer, SpringerBriefs in Thermal Engineering and Applied Science, DOI: 10.1007/978-1-4614-4535-7_2, © The Author(s) 2012 24 2 Laser Schlieren and Shadowgraph 2.2 Laser Schlieren A basic schlieren setup using concave mirrors that form the letter Z is shown in Fig. -
Gamma-Ray Interactions with Matter
2 Gamma-Ray Interactions with Matter G. Nelson and D. ReWy 2.1 INTRODUCTION A knowledge of gamma-ray interactions is important to the nondestructive assayist in order to understand gamma-ray detection and attenuation. A gamma ray must interact with a detector in order to be “seen.” Although the major isotopes of uranium and plutonium emit gamma rays at fixed energies and rates, the gamma-ray intensity measured outside a sample is always attenuated because of gamma-ray interactions with the sample. This attenuation must be carefully considered when using gamma-ray NDA instruments. This chapter discusses the exponential attenuation of gamma rays in bulk mater- ials and describes the major gamma-ray interactions, gamma-ray shielding, filtering, and collimation. The treatment given here is necessarily brief. For a more detailed discussion, see Refs. 1 and 2. 2.2 EXPONENTIAL A~ATION Gamma rays were first identified in 1900 by Becquerel and VMard as a component of the radiation from uranium and radium that had much higher penetrability than alpha and beta particles. In 1909, Soddy and Russell found that gamma-ray attenuation followed an exponential law and that the ratio of the attenuation coefficient to the density of the attenuating material was nearly constant for all materials. 2.2.1 The Fundamental Law of Gamma-Ray Attenuation Figure 2.1 illustrates a simple attenuation experiment. When gamma radiation of intensity IO is incident on an absorber of thickness L, the emerging intensity (I) transmitted by the absorber is given by the exponential expression (2-i) 27 28 G.