Thomson and Rayleigh Scattering

Save this PDF as:

Size: px
Start display at page:

Transcription

1 Thomson and Rayleigh Scattering Initial questions: What produces the shapes of emission and absorption lines? What information can we get from them regarding the environment or other conditions? In this and the next several lectures, we re going to explore in more detail some specific radiative processes. The simplest, and the first we ll do, involves scattering. There are many interesting limits of scattering, but for a start we ll treat frequency-independent nonrelativistic scattering (Thomson scattering). Suppose a lonely electron has an electromagnetic wave incident on it. The wave has a frequency ω. Ask class: what will be the response of the electron to the electric field of the wave? Since the electric field is sinusoidal, the electron will oscillate up and down at the frequency ω. Ask class: what will be the result of that acceleration? The electron will radiate. Ask class: at what frequency? It will just be at the driving frequency of the radiation, ω. Note also that the radiation is not in the original direction of polarization. Seen from the outside, this means it looks like a photon hits the electron, then scatters off in some new direction. In the limit we re considering, the new frequency is exactly the same as the old frequency. That s Thomson scattering. If we have a flux (in number per square centimeter per second) of incident particles at some target, and there is some rate of interactions (in number per second), the cross section is just the rate divided by the flux. Ask class: in this case, we have an energy flux and a power, so how do we get the cross section? Same idea: power (energy per second) divided by energy flux (energy per area per second). Therefore, to figure out the cross section, we need the radiated power for a given flux. The electric force from a linearly polarized wave is F = eˆǫe 0 sin ωt, (1) where ˆǫ is the E field direction. From Newton s second law and the definition of the dipole moment d = er, we get d = (e 2 E 0 /m)ˆǫ sin ωt d = (e 2 E 0 /mω 2 (2) )ˆǫ sin ωt. Note, by the way, a subtle but crucial difference between a single charged particle like the electron we are considering, and a target with multiple electrons that is polarizable. For something that is polarizable, an incident electric field shifts the probability distribution of the electron clouds in such a way as to induce a dipole moment that is proportional to the incident electric field. If the constant of proportionality is α p, this means that the dipole moment is d = α pˆǫe 0 sin ωt. (3)

4 less!), so we ll say that x (3) ω 2 0ẋ. Then we find ẍ + ω 2 0τẋ + ω 2 0x = 0. (10) Note that the middle term has an odd number of time derivatives. That means that it is not time reversible. That s one of the signatures of damping, which is also not time reversible. Let s add a driving force. Suppose that an external time-varying electric field is added, which contributes a force ee 0 cos ωt. This is what an incident photon would do. A common trick here is to use exp(iωt) instead of cosωt, and remember to take the real part later. We get ẍ + ω 2 0τẋ + ω 2 0x = (ee 0 /m) exp(iωt). (11) When confronted with differential equations of this type, a good approach is to try a solution of the form x = A exp(αt), then solve for A and α after substitution. When you do this, you find x = x 0 exp[i(ωt + δ)] (12) where x 0 = (ee 0 /m) (ω 2 2 iω0τ) 3 1 δ = tan 1 [ω 3 τ/(ω 2 ω0)] 2. Looking past all the various factors, what this basically says is that the electron does oscillate at the driving frequency ω, but delayed (or advanced) by the phase shift δ. We can now figure out the power radiated by getting the time average using the Larmor formula and taking the real part: (13) P = e 2 x 0 2 ω 4 /(3c 3 ) = e4 E 2 0 3m 2 c 3 ω 4 (ω 2 ω 2 0) 2 + (ω 3 0τ) 2. (14) The time-averaged flux is S = (c/8π)e 2 0, so the cross section is the power over the flux or Note that since τ is so small, τω 0 1. σ(ω) = σ T ω 4 (ω 2 ω 2 0) 2 + (ω 3 0τ) 2. (15) Ask class: what s one limit we could explore? We could look at the limit ω ω 0. Ask class: what is the answer in that limit? It s just σ T. This corresponds to our expectations. Ask class: what about when ω ω 0? Then σ(ω) = σ T (ω/ω 0 ) 4, which is what we got before for Rayleigh scattering. Now let s explore another limit in some more detail. Suppose that the frequency ω of the photon is close to the natural (or resonant) frequency ω 0 of the atom/molecule. The only subtlety here is dealing with the (ω 2 ω 2 0) 2 term in the bottom. A standard method is

5 to retain factors such as ω ω 0, but otherwise set ω to ω 0. Then we get σ(ω) = πσ T 2τ = πσ T 2τ = 2π2 e 2 mc ω0 2τ/2π (ω ω 0 ) 2 +(ω0 2τ/2)2 Γ/2π (16) (ω ω 0 ) 2 +(Γ/2) 2 Γ/2π (ω ω 0 ) 2 +(Γ/2) 2 where Γ = ω 2 0τ is the natural width of the resonance and we have used τ = 2e 2 /3mc 3 from Lecture 11 and σ T = (8π/3)e 4 /m 2 c 4 from earlier in this lecture. This profile is known as a Lorentz profile for a spectral line. Incidentally, near the resonance the shape of the cross section is the same as the shape of a line from free oscillations of the atom. That s not accidental; one could excite the free oscillations by having a pulse of radiation near ω 0 hit the atom, then ring down freely. This whole approach has interest in part because it provides the only classical description of a spectral line. Often when one gets the correct quantum result, one refers the cross section to the classical result to get a ratio. For example, let s integrate that line over angular frequency ω or the cycle frequency ν: 0 σ(ω)dω = 2π 2 e 2 /(mc) 0 σ(ν)dν = πe 2 (17) /(mc). But wait, didn t we cheat? We found that at high frequencies the cross section approaches a constant value (the cross section σ T of Thomson scattering). This would mean that the total integral is infinite! Oops. This type of situation is encountered in a number of places in physics; the formal integral is infinite, but you know that physically it must be finite. One way to deal with this is to impose a cutoff on the integral, and (1) show that this is justified physically, and (2) show that the precise value of the cutoff doesn t make much difference. Ask class: in this case, what cutoff can we make and how can we justify it? We know that the radiation reaction formula is only valid if ωτ 1, so if ω gets too large, all bets are off. Now, does the frequency at which we cut off the integral make a difference? The integral of just the Thomson cross section is ω max 0 σ T dω = σ T ω max. We know that ω max 1/τ, so σ T ω max σ T /τ = 4πe 2 /mc, so the precise value can t matter much. Therefore, our little swindle above was okay. The preceding was a classical attempt to model a spectral line of an atom. In the quantum theory one does things differently, but it is still convenient to define the oscillator strength f nn of a transition from state n to n by σ(ν)dν = πe2 0 mc f nn. (18) Recommended Rybicki and Lightman problem: 3.5

Thomson and Rayleigh Scattering

Thomson and Rayleigh Scattering In this and the next several lectures, we re going to explore in more detail some specific radiative processes. The simplest, and the first we ll do, involves scattering.

Absorption and Addition of Opacities Initial questions: Why does the spectrum of the Sun show dark lines? Are there circumstances in which the spectrum of something should be a featureless continuum? What

1. Photons in a vacuum

Radiative Processes Ask class: most of our information about the universe comes from photons. What are the reasons for this? Let s compare them with other possible messengers, specifically massive particles,

We consider a hydrogen atom in the ground state in the uniform electric field

Lecture 13 Page 1 Lectures 13-14 Hydrogen atom in electric field. Quadratic Stark effect. Atomic polarizability. Emission and Absorption of Electromagnetic Radiation by Atoms Transition probabilities and

Quantum Mechanics I Physics 325. Importance of Hydrogen Atom

Quantum Mechanics I Physics 35 Atomic spectra and Atom Models Importance of Hydrogen Atom Hydrogen is the simplest atom The quantum numbers used to characterize the allowed states of hydrogen can also

Physics 53. Wave Motion 1

Physics 53 Wave Motion 1 It's just a job. Grass grows, waves pound the sand, I beat people up. Muhammad Ali Overview To transport energy, momentum or angular momentum from one place to another, one can

Solved Problems on Quantum Mechanics in One Dimension

Solved Problems on Quantum Mechanics in One Dimension Charles Asman, Adam Monahan and Malcolm McMillan Department of Physics and Astronomy University of British Columbia, Vancouver, British Columbia, Canada

Electromagnetic Radiation Wave - a traveling disturbance, e.g., displacement of water surface (water waves), string (waves on a string), or position of air molecules (sound waves). [ π λ ] h = h sin (

EUF. Joint Entrance Examination for Postgraduate Courses in Physics

EUF Joint Entrance Examination for Postgraduate Courses in Physics For the second semester 204 23 April 204 Part Instructions Do not write your name on the test. It should be identified only by your candidate

Waves I: Generalities, Superposition & Standing Waves

Chapter 5 Waves I: Generalities, Superposition & Standing Waves 5.1 The Important Stuff 5.1.1 Wave Motion Wave motion occurs when the mass elements of a medium such as a taut string or the surface of a

CHAPTER 4 Structure of the Atom

CHAPTER 4 Structure of the Atom 4.1 The Atomic Models of Thomson and Rutherford 4.2 Rutherford Scattering 4.3 The Classic Atomic Model 4.4 The Bohr Model of the Hydrogen Atom 4.5 Successes and Failures

Class 26: Rutherford-Bohr atom

Class 6: Rutherford-Bohr atom Atomic structure After the discovery of the electron in 1897 by J. J. Thomson, Thomson and others developed models for the structure of atoms. It was known that atoms contained

Specific Intensity. I ν =

Specific Intensity Initial question: A number of active galactic nuclei display jets, that is, long, nearly linear, structures that can extend for hundreds of kiloparsecs. Many have two oppositely-directed

On the Linkage between Planck s Quantum and Maxwell s Equations

The Finnish Society for Natural Philosophy 25 Years K.V. Laurikainen Honorary Symposium 2013 On the Linkage between Planck s Quantum and Maxwell s Equations Tuomo Suntola Physics Foundations Society E-mail:

Chapter 24. Wave Optics

Chapter 24 Wave Optics Wave Optics The wave nature of light is needed to explain various phenomena. Interference Diffraction Polarization The particle nature of light was the basis for ray (geometric)

Physics 2101 Section 3 Apr 14th Announcements: Quiz Friday Midterm #4, April Midterm #4,

Physics 2101 Section 3 Apr 14 th Announcements: Quiz Friday Midterm #4, April 28 th Final: May 11 th-7:30am Class Website: 6 pm Make up Final: May 15 th -7:30am http://www.phys.lsu.edu/classes/spring2010/phys2101

Notes on wavefunctions III: time dependence and the Schrödinger equation

Notes on wavefunctions III: time dependence and the Schrödinger equation We now understand that the wavefunctions for traveling particles with momentum p look like wavepackets with wavelength λ = h/p,

1. Radiative Transfer Virtually all the exchanges of energy between the earth-atmosphere system and the rest of the universe take place by radiative transfer. The earth and its atmosphere are constantly

Chapter 21 Electric Charge and the Electric Field

Chapter 21 Electric Charge and the Electric Field 1 Electric Charge Electrostatics is the study of charges when they are stationery. Figure 1: This is Fig. 21.1 and it shows how negatively charged objects

1 Monday, November 28: Comptonization

1 Monday, November 28: Comptonization When photons and electrons coexist in the same volume of space, their scattering interactions can transfer energy from photons to electrons (Compton scattering) or

Today s lecture: Radioactivity radioactive decay mean life half life decay modes branching ratio sequential decay measurement of the transition rate radioactive dating techniques Radioactive decay spontaneous

Spectroscopic Notation

Spectroscopic Notation Most of the information we have about the universe comes to us via emission lines. However, before we can begin to understand how emission lines are formed and what they tell us,

Problem Set 1 Solutions

Chemistry 36 Dr. Jean M. Standard Problem Set Solutions. The first 4 lines in the visible region of atomic line spectrum of hydrogen atom occur at wavelengths of 656., 486., 434.0, and 40. nm (this is

CHAPTER 5 THE HARMONIC OSCILLATOR

CHAPTER 5 THE HARMONIC OSCILLATOR The harmonic oscillator is a model which has several important applications in both classical and quantum mechanics. It serves as a prototype in the mathematical treatment

COLLEGE PHYSICS. Chapter 29 INTRODUCTION TO QUANTUM PHYSICS

COLLEGE PHYSICS Chapter 29 INTRODUCTION TO QUANTUM PHYSICS Quantization: Planck s Hypothesis An ideal blackbody absorbs all incoming radiation and re-emits it in a spectrum that depends only on temperature.

Relativity II. Selected Problems

Chapter Relativity II. Selected Problems.1 Problem.5 (In the text book) Recall that the magnetic force on a charge q moving with velocity v in a magnetic field B is equal to qv B. If a charged particle

Today in Physics 218: dispersion

Today in Physics 18: dispersion Motion of bound electrons in matter, and the frequency dependence of the dielectric constant Dispersion relations Ordinary and anomalous dispersion The world s largest-selling

Chapter 13. Mechanical Waves

Chapter 13 Mechanical Waves A harmonic oscillator is a wiggle in time. The oscillating object will move back and forth between +A and A forever. If a harmonic oscillator now moves through space, we create

MODERN PHYSICS. CET questions from Bohr s atom model, Lasers and Scattering

MODERN PHYSICS CET questions from Bohr s atom model, Lasers and Scattering 1. For the electron to revolve around the atomic nucleus without radiating energy, the electronic orbit should be : (1) Circular

Spectroscopy. Ron Robertson

Spectroscopy Ron Robertson Molecular Energy The energy of a molecule is divided into several parts: Type D E (ev) Type of Radiation Translation 10-18 Rotation 5 x 10-4 Microwaves Vibration 0.3 Infrared

21 The Nature of Electromagnetic Waves

21 The Nature of Electromagnetic Waves When we left off talking about the following circuit: I E v = c B we had recently closed the switch and the wire was creating a magnetic field which was expanding

The Role of Electric Polarization in Nonlinear optics

The Role of Electric Polarization in Nonlinear optics Sumith Doluweera Department of Physics University of Cincinnati Cincinnati, Ohio 45221 Abstract Nonlinear optics became a very active field of research

Subatomic Physics: Particle Physics Lecture 4. Quantum Electro-Dynamics & Feynman Diagrams. Antimatter. Virtual Particles. Yukawa Potential for QED

Ψ e (r, t) exp i/ (E)(t) (p) (r) Subatomic Physics: Particle Physics Lecture Quantum ElectroDynamics & Feynman Diagrams Antimatter Feynman Diagram and Feynman Rules Quantum description of electromagnetism

Lecture 11 Chapter 16 Waves I

Lecture 11 Chapter 16 Waves I Forced oscillator from last time Slinky example Coiled wire Rope Transverse Waves demonstrator Longitudinal Waves magnetic balls Standing Waves machine Damped simple harmonic

Hooke s Law. Spring. Simple Harmonic Motion. Energy. 12/9/09 Physics 201, UW-Madison 1

Hooke s Law Spring Simple Harmonic Motion Energy 12/9/09 Physics 201, UW-Madison 1 relaxed position F X = -kx > 0 F X = 0 x apple 0 x=0 x > 0 x=0 F X = - kx < 0 x 12/9/09 Physics 201, UW-Madison 2 We know

Wave Motion (Chapter 15)

Wave Motion (Chapter 15) Waves are moving oscillations. They transport energy and momentum through space without transporting matter. In mechanical waves this happens via a disturbance in a medium. Transverse

Physics 53. Oscillations. You've got to be very careful if you don't know where you're going, because you might not get there.

Physics 53 Oscillations You've got to be very careful if you don't know where you're going, because you might not get there. Yogi Berra Overview Many natural phenomena exhibit motion in which particles

THE DOUBLE SLIT INTERFERENCE OF THE PHOTON-SOLITONS

Bulg. J. Phys. 29 (2002 97 108 THE DOUBLE SLIT INTERFERENCE OF THE PHOTON-SOLITONS P. KAMENOV, B. SLAVOV Faculty of Physics, University of Sofia, 1126 Sofia, Bulgaria Abstract. It is shown that a solitary

Blackbody radiation derivation of Planck s radiation low 1 Classical theories of Lorentz and Debye: Lorentz (oscillator model): Electrons and ions of matter were treated as a simple harmonic oscillators

Spectral Line Shapes. Line Contributions

Spectral Line Shapes Line Contributions The spectral line is termed optically thin because there is no wavelength at which the radiant flux has been completely blocked. The opacity of the stellar material

Chapter 35. Electromagnetic Fields and Waves

Chapter 35. Electromagnetic Fields and Waves To understand a laser beam, we need to know how electric and magnetic fields change with time. Examples of timedependent electromagnetic phenomena include highspeed

Ch 24 Wave Optics. concept questions #8, 11 problems #1, 3, 9, 15, 19, 31, 45, 48, 53

Ch 24 Wave Optics concept questions #8, 11 problems #1, 3, 9, 15, 19, 31, 45, 48, 53 Light is a wave so interference can occur. Interference effects for light are not easy to observe because of the short

Symbols, conversions, and atomic units

Appendix C Symbols, conversions, and atomic units This appendix provides a tabulation of all symbols used throughout this thesis, as well as conversion units that may useful for reference while comparing

Lecture 14. More on rotation. Rotational Kinematics. Rolling Motion. Torque. Cutnell+Johnson: , 9.1. More on rotation

Lecture 14 More on rotation Rotational Kinematics Rolling Motion Torque Cutnell+Johnson: 8.1-8.6, 9.1 More on rotation We ve done a little on rotation, discussing objects moving in a circle at constant

Lecture 1. The nature of electromagnetic radiation.

Lecture 1. The nature of electromagnetic radiation. 1. Basic introduction to the electromagnetic field: Dual nature of electromagnetic radiation Electromagnetic spectrum. Basic radiometric quantities:

Chapter 9. Gamma Decay

Chapter 9 Gamma Decay As we have seen γ-decay is often observed in conjunction with α- or β-decay when the daughter nucleus is formed in an excited state and then makes one or more transitions to its ground

Two mass-three spring system. Math 216 Differential Equations. Forces on mass m 1. Forces on mass m 2. Kenneth Harris

Two mass-three spring system Math 6 Differential Equations Kenneth Harris kaharri@umich.edu m, m > 0, two masses k, k, k 3 > 0, spring elasticity t), t), displacement of m, m from equilibrium. Positive

6.1 Electromagnetic Waves

6.1 Electromagnetic Waves electromagnetic radiation can be described as a harmonic wave in either time or distance waves are characterized by their period, frequency, wavelength and wave number Planck's

2. The graph shows how the displacement varies with time for an object undergoing simple harmonic motion.

Practice Test: 29 marks (37 minutes) Additional Problem: 31 marks (45 minutes) 1. A transverse wave travels from left to right. The diagram on the right shows how, at a particular instant of time, the

Atomic Structure. AGEN-689: Advances in Food Engineering

Atomic Structure AGEN-689: Advances in Food Engineering Ionian scholars- 15 th century Some ancient Greek philosophers speculated that everything might be made of little chunks they called "atoms." The

THE NATURE OF THE ATOM

CHAPTER 30 THE NATURE OF THE ATOM CONCEPTUAL QUESTIONS 1. REASONING AND SOLUTION A tube is filled with atomic hydrogen at room temperature. Electromagnetic radiation with a continuous spectrum of wavelengths,

Chem 81 Fall, Exam 2 Solutions

Chem 81 Fall, 1 Exam Solutions 1. (15 points) Consider the boron atom. (a) What is the ground state electron configuration for B? (If you don t remember where B is in the periodic table, ask me. I ll tell

People s Physics book

The Big Idea Quantum Mechanics, discovered early in the 20th century, completely shook the way physicists think. Quantum Mechanics is the description of how the universe works on the very small scale.

PHYS 1444 Section 003. Lecture #6. Chapter 21. Chapter 22 Gauss s Law. Electric Dipoles. Electric Flux. Thursday, Sept. 8, 2011 Dr.

PHYS 1444 Section 003 Chapter 21 Lecture #6 Dr. Jaehoon Electric Dipoles Chapter 22 Gauss s Law Electric Flux 1 Quiz #2 Thursday, Sept. 15 Beginning of the class Announcements Covers: CH21.1 through what

Rotational and Vibrational Transitions

Rotational and Vibrational Transitions Initial questions: How can different molecules affect how interstellar gas cools? What implications might this have for star formation now versus star formation before

Module17:Coherence Lecture 17: Coherence

Module7:Coherence Lecture 7: Coherence We shall separately discuss spatial coherence and temporal coherence. 7. Spatial Coherence The Young s double slit experiment (Figure 7.) essentially measures the

HW 7 Q 14,20,20,23 P 3,4,8,6,8. Chapter 7. Rotational Motion of the Object. Dr. Armen Kocharian

HW 7 Q 14,20,20,23 P 3,4,8,6,8 Chapter 7 Rotational Motion of the Object Dr. Armen Kocharian Axis of Rotation The radian is a unit of angular measure The radian can be defined as the arc length s along

Physics Notes for Class 12 Chapter 5 Magnetrism And Matter

1 P a g e Physics Notes for Class 12 Chapter 5 Magnetrism And Matter The property of any object by virtue of which it can attract a piece of iron or steel is called magnetism. Natural Magnet A natural

PHYS-2020: General Physics II Course Lecture Notes Section XIII

PHYS-2020: General Physics II Course Lecture Notes Section XIII Dr. Donald G. Luttermoser East Tennessee State University Edition 4.0 Abstract These class notes are designed for use of the instructor and

The data were explained by making the following assumptions.

Chapter Rutherford Scattering Let usstart fromtheoneofthefirst steps which was donetowards understanding thedeepest structure of matter. In 1911, Rutherford discovered the nucleus by analysing the data

Chapter 35: Quantum Physics

Newton himself was better aware of the weakness inherent in his intellectual edifice than the generations which followed him. This fact has always aroused my admiration. Albert Einstein 35.1 The Particle

Chapter 7. Plane Electromagnetic Waves and Wave Propagation

Chapter 7. Plane Electromagnetic Waves and Wave Propagation 7.1 Plane Monochromatic Waves in Nonconducting Media One of the most important consequences of the Maxwell equations is the equations for electromagnetic

From Einstein to Klein-Gordon Quantum Mechanics and Relativity

From Einstein to Klein-Gordon Quantum Mechanics and Relativity Aline Ribeiro Department of Mathematics University of Toronto March 24, 2002 Abstract We study the development from Einstein s relativistic

Assessment Plan for Learning Outcomes for BA/BS in Physics

Department of Physics and Astronomy Goals and Learning Outcomes 1. Students know basic physics principles [BS, BA, MS] 1.1 Students can demonstrate an understanding of Newton s laws 1.2 Students can demonstrate

Chapter 27 Early Quantum Physics and the Photon

Chapter 27 Early Quantum Physics and the Photon 1. A problem with the classical theory for radiation from a blackbody was that the theory predicted too much radiation in the wavelengths. A. ultraviolet

Chapter 25 Electromagnetic Waves

Chapter 25 Electromagnetic Waves Units of Chapter 25 The Production of Electromagnetic Waves The Propagation of Electromagnetic Waves The Electromagnetic Spectrum Energy and Momentum in Electromagnetic

Models of an atom and old quantum theory

Models of an atom and old quantum theory Classical models of atoms Thompson's model Chemical elements dier by the number Z of electrons in their atoms. Atoms are electrically neutral, so that the charge

Today in Physics 218: dispersion in conducting media

Today in Physics 18: dispersion in conducting media Semiclassical theory of conductivity Conductivity and dispersion in metals and in very dilute conductors Light propagation in very dilute conductors:

Scattering and Random Walks

Mention: programming, probably second homework Initial question: Suppose that my boy Lord Voldemort waved his wand and stopped all fusion in the Sun. How long would it take before we noticed the Sun s

The Electronic Structures of Atoms Electromagnetic Radiation

The Electronic Structures of Atoms Electromagnetic Radiation The wavelength of electromagnetic radiation has the symbol λ. Wavelength is the distance from the top (crest) of one wave to the top of the

NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY

NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY PRINCIPLE AND APPLICATION IN STRUCTURE ELUCIDATION Professor S. SANKARARAMAN Department of Chemistry Indian Institute of Technology Madras Chennai 600 036 sanka@iitm.ac.in

Constructive vs. destructive interference; Coherent vs. incoherent interference

Constructive vs. destructive interference; Coherent vs. incoherent interference Waves that combine in phase add up to relatively high irradiance. = Constructive interference (coherent) Waves that combine

Rutherford scattering: a simple model

Rutherford scattering: a simple model Scott D. Morrison MIT Department of Physics (Dated: December 10, 2008) We performed a Rutherford scattering experiment with gold foil and alpha particles emitted by

Lecture 13. Magnetic Field, Magnetic Forces on Moving Charges. Outline:

Lecture 13. Magnetic Field, Magnetic Forces on Moving Charges. Outline: Intro to Magnetostatics. Magnetic Field Flux, Absence of Magnetic Monopoles. Force on charges moving in magnetic field. 1 Intro to

4.5 Orbits, Tides, and the Acceleration of Gravity

4.5 Orbits, Tides, and the Acceleration of Gravity Our goals for learning: How do gravity and energy together allow us to understand orbits? How does gravity cause tides? Why do all objects fall at the

CHAPTER 12 ATOMS ONE MARK QUESTIONS WITH ANSWER. Ans: Electrons were discovered by J.J Thomason in the year 1897.

CHAPTER 12 ATOMS ONE MARK QUESTIONS WITH ANSWER 1. Who discovered electrons? Ans: Electrons were discovered by J.J Thomason in the year 1897. 2. What is the electric charge on an atom? Ans: At atom of

Laws of Motion and Conservation Laws

Laws of Motion and Conservation Laws The first astrophysics we ll consider will be gravity, which we ll address in the next class. First, though, we need to set the stage by talking about some of the basic

5.2 Rotational Kinematics, Moment of Inertia

5 ANGULAR MOTION 5.2 Rotational Kinematics, Moment of Inertia Name: 5.2 Rotational Kinematics, Moment of Inertia 5.2.1 Rotational Kinematics In (translational) kinematics, we started out with the position

Periodic Motion or Oscillations. Physics 232 Lecture 01 1

Periodic Motion or Oscillations Physics 3 Lecture 01 1 Periodic Motion Periodic Motion is motion that repeats about a point of stable equilibrium Stable Equilibrium Unstable Equilibrium A necessary requirement

CAN PLASMA SCATTERING MIMIC A COSMOLOGICAL RED SHIFT?

CAN PLASMA SCATTERING MIMIC A COSMOLOGICAL RED SHIFT? S. SCHRAMM* AND S. E. KOONIN W. K. Kellogg Radiation Laboratory California Institute of Technology, Pasadena, CA 91125 ABSTRACT We investigate the

CHEM344 HW#7 Due: Fri, Mar BEFORE CLASS!

CHEM344 HW#7 Due: Fri, Mar 14@2pm BEFORE CLASS! HW to be handed in: Atkins Chapter 8: Exercises: 8.11(b), 8.16(b), 8.19(b), Problems: 8.2, 8.4, 8.12, 8.34, Chapter 9: Exercises: 9.5(b), 9.7(b), Extra (do

( ) = Aexp( iωt ) will look like: = c n R. = ω k R. v p

Phase Velocity vs. Group Velocity We should perhaps be (at least) a little bit disturbed that the real part of the index of refraction can be less than 1 for some frequencies. When we re working with just

HW5 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.

HW5 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 21.P.018 Estimate the force required to bind the two protons

Chapter 18: The Structure of the Atom

Chapter 18: The Structure of the Atom 1. For most elements, an atom has A. no neutrons in the nucleus. B. more protons than electrons. C. less neutrons than electrons. D. just as many electrons as protons.

1 CHAPTER 5 ABSORPTION, SCATTERING, EXTINCTION AND THE EQUATION OF TRANSFER

1 CHAPTER 5 ABSORPTION, SCATTERING, EXTINCTION AND THE EQUATION OF TRANSFER 5.1 Introduction As radiation struggles to make its way upwards through a stellar atmosphere, it may be weakened by absorption

PHY4604 Introduction to Quantum Mechanics Fall 2004 Practice Exam Solutions Dec. 13, 2004

PHY4604 Introduction to Quantum Mechanics Fall 2004 Practice Exam Solutions Dec. 1, 2004 No materials allowed. If you can t remember a formula, ask and I might help. If you can t do one part of a problem,

Eksamination in FY2450 Astrophysics Wednesday June 8, 2016 Solutions

Eksamination in FY2450 Astrophysics Wednesday June 8, 2016 Solutions 1a) Table 1 gives the spectral class and luminosity class of each of the 20 stars. The luminosity class of a star can (at least in principle)

6. What is the approximate angular diameter of the Sun in arcseconds? (d) 1860

ASTR 1020 Stellar and Galactic Astronomy Professor Caillault Fall 2009 Semester Exam 1 Multiple Choice Answers (Each multiple choice question is worth 1.5 points) 1. The number of degrees in a full circle

The Evolution of the Atom

The Evolution of the Atom 1808: Dalton s model of the atom was the billiard ball model. He thought the atom was a solid, indivisible sphere. Atoms of each element were identical in mass and their properties.

Lecture 13. Magnetic Field, Magnetic Forces on Moving Charges. Outline:

Lecture 13. Magnetic Field, Magnetic Forces on Moving Charges. Outline: Intro to Magnetostatics. Magnetic Field Flux, Absence of Magnetic Monopoles. Force on charges moving in magnetic field. 1 Structure

Lab M1: The Simple Pendulum

Lab M1: The Simple Pendulum Introduction. The simple pendulum is a favorite introductory exercise because Galileo's experiments on pendulums in the early 1600s are usually regarded as the beginning of

The Bohr atom and the Uncertainty Principle

The Bohr atom and the Uncertainty Principle Previous Lecture: Matter waves and De Broglie wavelength The Bohr atom This Lecture: More on the Bohr Atom The H atom emission and absorption spectra Uncertainty

Electromagnetic Waves and Polarization

Electromagnetic Waves and Polarization Physics 2415 Lecture 30 Michael Fowler, UVa Today s Topics Measuring the speed of light Wave energy and power: the Poynting vector Light momentum and radiation pressure

linearly polarized with polarization axis parallel to the transmission axis of the polarizer.

Polarization Light is a transverse wave: the electric and magnetic fields both oscillate along axes that are perpendicular to the direction of wave motion. The simplest kind of radiation is said to be

5. The Nature of Light. Does Light Travel Infinitely Fast? EMR Travels At Finite Speed. EMR: Electric & Magnetic Waves

5. The Nature of Light Light travels in vacuum at 3.0. 10 8 m/s Light is one form of electromagnetic radiation Continuous radiation: Based on temperature Wien s Law & the Stefan-Boltzmann Law Light has

Lecture 15. Torque. Center of Gravity. Rotational Equilibrium. Cutnell+Johnson:

Lecture 15 Torque Center of Gravity Rotational Equilibrium Cutnell+Johnson: 9.1-9.3 Last time we saw that describing circular motion and linear motion is very similar. For linear motion, we have position

A given Nucleus has the following particles Total number of nucleons : atomic mass number, A Proton number: atomic number, Z Neutron number: N = A Z

Chapter 30 Nuclear Physics and Radioactivity Units of Chapter 30 Structure and Properties of the Nucleus Binding Energy and Nuclear Forces Radioactivity Alpha Decay Beta Decay Gamma Decay Conservation