Quantum Physics Lecture 3

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Quantum Physics Lecture 3"

Transcription

1 Quantum Physics Lecture 3 If light (waves) are particle-like, are particles wave-like? Electron diffraction - Davisson & Germer Experiment Particle in a box -Quantisation of energy Wave Particle?? Wave groups and velocity

2 The Story so far.. Electromagnetic radiation interacts with matter in 3 ways: Photoelectric, Compton, Pair production Relative strength depends on energy, in order as shown If light (waves) particle-like are particles wave-like?

3 Wave Properties of Particles Recall, photon has momentum: p = ω c = k = h λ or λ = h p De Broglie (1924) suggested that this relation is general: particles which have momentum have an associated (or de Broglie) wavelength: where m is relativistic mass. m~m o at non-relativistic speed. Suggested in De B. PhD thesis & implied by Bohr model of atom Direct Experimental evidence?? λ = h p = h mv N.B. h = 2π = Js Significance is for SMALL objects

4 Davisson & Germer Experiment Diffraction of Electrons by a Crystal of Nickel The Physical Review 1927 The investigation reported in this paper was begun as the result of an accident which occurred in this laboratory in April D & G had been working on electron scattering (1921) from polycrystalline nickel: during the accident the target became oxidised. After removing the oxide by heating, the scattering was dramatically altered : The target was now more crystalline: electrons were diffracted by the crystal, just like x-rays!

5 Analysis of D & G Experiment just like x-rays θ θ d crystal planes (planes drawn in blue) 2dsinθ = nλ electron energy KE = 54 ev normal incidence θ : angle with planes enhanced reflectivity at 50 d : plane separation to find θ bisect 50 ( 25 ) (Bragg) θ = = 65

6 Analysis of D & G Expt. cont. θ 2dsinθ = nλ λ = h/p θ θ = 65 crystal planes find p from KE KE = 54 ev (<< 0.51 MeV (= m o c 2 ) so non-relativistic) d KE = m o v 2 /2 = (m o v) 2 /2m o so p = m o v = (2m o KE) λ = λ = h m o v = h 2m o KE 6.63x10 34 J s ( 2) ( 9.1x10 31 kg) ( 54 ev )( 1.6x10 19 C) = 0.166nm (n=1) λ= 2dsin 65 = (2)(0.091 nm)(0.906) = nm

7 Conclude: Particles can act as if they are also waves Diffraction becomes significant if λ (= h/p) is similar in size to aperture/spacing What if the particle (wave) is confined? e.g. In a box

8 Particle in a Box confinement of moving particle implies energy quantisation Particle in a box, making elastic collisions with rigid walls. Cannot go outside box Has a kinetic energy KE (& zero potential energy change in box) Total energy (non-relativistic) E = KE = 1 2 m ( ov 2 = m v o ) 2m o OK for particle, just bounces between walls. 2 = ( h λ ) 2 2m o = h 2 2m o λ 2 L What if it s a wave? Means standing waves in box nodes at walls c.f. Guitar strings, Waves in cup, etc

9 Particle in a Box (cont.) λ 1 = 2L/1 L λ 2 = 2L/2 λ 3 = 2L/3 λ n = 2L λ 4 = 2L/4 n Where n = 1, 2, 3,. E n = h 2 2m o λ n 2 = 2m o h 2 ( ) 2 = n 2 h 2 2L 8m n o L 2 E n : quantised energy level. n is the quantum number E 0 (since v=0 implies infinite λ) E 3 E 2 E 1 So lowest energy level is E 1 called the ground state

10 Conclude: Confining a wave restricts possible wavelengths only certain λ and hence Energies allowed! Wider implication: Confining a wave (particle) restricts possible states e.g. Diffraction possible directions affected by spacing d The atom (Lecture 6) and much else.

11 Waves of what? everything in the future is a wave, everything in the past is a particle Light: wave of E & M fields Matter: wave of existence But: a particle is at a point, whereas a wave is extended So where is the particle? And how does a point particle interact with more than one atom at the same time to give diffraction pattern? Consider waves, groups and packets

12 General fomula for Waves 1-D wave: Simple harmonic function of time t and distance x y = Acos2π ft = Acosωt At x = 0: (amplitude A, frequency f) At general x? - travelling wave speed v wave travels a distance x in time t = x/v Amplitude at any x, at any time t, is amplitude at x = 0 but at the earlier time t - x/v y = Acos2π f t x v ( ) = Acos2π ( ft fx v) = Acos2π ( ft x λ) y = Acos ωt kx ( ) ω = 2πf k = 2π λ Also written Velocity v = f λ Is v the same as the particle velocity v p? E=hf p=mv p =h/λ v = f λ = hf λ h = E p = mc2 = c2!? mv p v p Clearly not! Wave group Superposition of many waves

13 Wave Groups The wave y = A cos (ωt - kx) cannot reasonably be associated with a particle because of its (infinite) extent. Instead, consider a wave group Simplest example of wave group is beats : 2 waves of slightly different frequencies: y 1 = Acos( ωt kx) y 2 = A cos ( ω + Δω )t ( k + Δk)x [ ] y = y 1 + y 2 (using cos a + cos b = 2cos((a+b)/2).cos((a-b)/2) y = 2Acos 1 2[ ( 2ω + Δω)t ( 2k + Δk )x ]cos 1 2 [ Δωt Δkx ] For Δω and Δk small: y = 2Acos[ ωt kx]cos[ Δω 2 t Δk 2 x ] i.e. the basic wave modulated by beat frequency Δω/2 and wavenumber Δk/2 Δω Velocity of group (beat) v g = 2 = Δω Group of many waves: Δk Δk 2 v g = dω dk

14 Group velocity and particle velocity v g = dω dk = dω dv dk dv = v Are they the same??? Now ω = E = mc2 = m 0 c 2 dω So 1 v 2 c 2 dv = m 0 v ( 1 v 2 c 2 ) 3 2 And k = p = mv = m 0 v dk So 1 v 2 c 2 dv = m 0 1 v 2 c 2 ( ) 3 2 v g = dω dv dk dv = v Group velocity equals particle velocity

15 Group velocity and dispersion v g = dω dk = v Can equate particle velocity (v) with group velocity (v g ), not with phase velocity (v p )! v p = ω k Wave group built from many individual waves; each wave has a phase velocity (v p ). If v p is independent of ω or λ (as for light in a vacuum), then cannot represent a particle! v g = dω dk = ω k = v p Corollary: it is a further requirement of de Broglie wave group that the phase velocity varies with wavelength: This dispersion has implications (later)

16 Particle versus photon General relations apply to both, some specifics do not: E 2 = m o 2 c 4 + p 2 c 2 ( ω ) 2 = m 2 o c 4 + ( k) 2 c 2 photon particle m o = 0 m o 0 ( ω ) 2 = ( k) 2 c 2 ω k = f λ = c ω k c

Wavelength of 1 ev electron

Wavelength of 1 ev electron HW8: M Chap 15: Question B, Exercises 2, 6 M Chap 16: Question B, Exercises 1 M Chap 17: Questions C, D From Last Time Essay topic and paragraph due Friday, Mar. 24 Light waves are particles and matter

More information

Physics 390: Homework set #2 Solutions

Physics 390: Homework set #2 Solutions January 6, 007 Physics 390: Homework set # Solutions Reading: Tipler & Llewellyn, Chapters 4, 5 Questions:. Suppose we cover one slit in the two-slit electron experiment with a very thin sheet of fluorescent

More information

Matter Waves. Chapter 5

Matter Waves. Chapter 5 Matter Waves Chapter 5 De Broglie pilot waves Electromagnetic waves are associated with quanta - particles called photons. Turning this fact on its head, Louis de Broglie guessed : Matter particles have

More information

Richard Feynman: Electron waves are probability waves in the ocean of uncertainty.

Richard Feynman: Electron waves are probability waves in the ocean of uncertainty. Richard Feynman: Electron waves are probability waves in the ocean of uncertainty. Last Time We Solved some of the Problems with Classical Physics Discrete Spectra? Bohr Model but not complete. Blackbody

More information

Atkins & de Paula: Atkins Physical Chemistry 9e Checklist of key ideas. Chapter 7: Quantum Theory: Introduction and Principles

Atkins & de Paula: Atkins Physical Chemistry 9e Checklist of key ideas. Chapter 7: Quantum Theory: Introduction and Principles Atkins & de Paula: Atkins Physical Chemistry 9e Checklist of key ideas Chapter 7: Quantum Theory: Introduction and Principles classical mechanics, the laws of motion introduced in the seventeenth century

More information

Physics 111 Homework Solutions Week #9 - Thursday

Physics 111 Homework Solutions Week #9 - Thursday Physics 111 Homework Solutions Week #9 - Thursday Monday, March 1, 2010 Chapter 24 241 Based on special relativity we know that as a particle with mass travels near the speed of light its mass increases

More information

Wave Phenomena Physics 15c. Lecture 11 Dispersion

Wave Phenomena Physics 15c. Lecture 11 Dispersion Wave Phenomena Physics 15c Lecture 11 Dispersion What We Did Last Time Defined Fourier transform f (t) = F(ω)e iωt dω F(ω) = 1 2π f(t) and F(w) represent a function in time and frequency domains Analyzed

More information

arxiv:physics/ v3 [physics.gen-ph] 2 Jan 2006

arxiv:physics/ v3 [physics.gen-ph] 2 Jan 2006 A Wave Interpretation of the Compton Effect As a Further Demonstration of the Postulates of de Broglie arxiv:physics/0506211v3 [physics.gen-ph] 2 Jan 2006 Ching-Chuan Su Department of Electrical Engineering

More information

5.111 Lecture Summary #4 Wednesday, September 10, 2014

5.111 Lecture Summary #4 Wednesday, September 10, 2014 5.111 Lecture Summary #4 Wednesday, September 10, 2014 Reading for today: Section 1.5 and Section 1.6. (Same sections in 5 th and 4 th editions) Read for Lecture #5: Section 1.3 Atomic Spectra, Section

More information

The Discovery of the Wave Nature of the Electron

The Discovery of the Wave Nature of the Electron The Discovery of the Wave Nature of the Electron de Broglie s Theory of Matter Waves Luis Suarez University of South Carolina Louis de Broglie 1892-1987 2 A brief history of light Is it a stream of particles

More information

Recitation on the Compton effect Solution

Recitation on the Compton effect Solution Recitation on the Compton effect Solution 1. Show that a photon cannot transfer all of its energy to a free electron. (Hint: Energy and momentum must be conserved.) Answer 1: If all the photon s energy

More information

Quantum physics. Anyone who is not shocked by the quantum theory has not understood it. Niels Bohr, Nobel Price in 1922 ( )

Quantum physics. Anyone who is not shocked by the quantum theory has not understood it. Niels Bohr, Nobel Price in 1922 ( ) Quantum physics Anyone who is not shocked by the quantum theory has not understood it. Niels Bohr, Nobel Price in 1922 (1885-1962) I can safely say that nobody understand quantum physics Richard Feynman

More information

Wave Mechanics in One Dimension

Wave Mechanics in One Dimension Wave Mechanics in One Dimension Wave-Particle Duality The wave-like nature of light had been experimentally demonstrated by Thomas Young in 1820, by observing interference through both thin slit diffraction

More information

Module 1. An Introduction to Radiation

Module 1. An Introduction to Radiation Module 1 An Introduction to Radiation General Definition of Radiation Ionizing radiation, for example, X-rays, gamma-rays, α particles Ionizing radiation is capable of removing an electron from the atom

More information

Introduction to Quantum Mechanics (Prelude to Nuclear Shell Model) Heisenberg Uncertainty Principle In the microscopic world,

Introduction to Quantum Mechanics (Prelude to Nuclear Shell Model) Heisenberg Uncertainty Principle In the microscopic world, Introduction to Quantum Mechanics (Prelude to Nuclear Shell Model) Heisenberg Uncertainty Principle In the microscopic world, x p h π If you try to specify/measure the exact position of a particle you

More information

We also find the development of famous Schrodinger equation to describe the quantization of energy levels of atoms.

We also find the development of famous Schrodinger equation to describe the quantization of energy levels of atoms. Lecture 4 TITLE: Quantization of radiation and matter: Wave-Particle duality Objectives In this lecture, we will discuss the development of quantization of matter and light. We will understand the need

More information

In the early years of the twentieth century, Max Planck, Albert Einstein, Louis de Broglie, Neils

In the early years of the twentieth century, Max Planck, Albert Einstein, Louis de Broglie, Neils Chapter 2 The Early History of Quantum Mechanics In the early years of the twentieth century, Max Planck, Albert Einstein, Louis de Broglie, Neils Bohr, Werner Heisenberg, Erwin Schrödinger, Max Born,

More information

Chapter 28: Quantum Physics. Don t Copy This. Quantum Physics 3/16/13

Chapter 28: Quantum Physics. Don t Copy This. Quantum Physics 3/16/13 Chapter 28: Quantum Physics Key Terms: Photoelectric effect Photons de Broglie wavelength Energy level diagram Wave-particle duality Don t Copy This Except for relativity, everything we have studied up

More information

De Broglie s Pilot Waves

De Broglie s Pilot Waves De Broglie s Pilot Waves Bohr s Moel of the Hyrogen tom: One way to arrive at Bohr s hypothesis is to think of the electron not as a particle but as a staning wave at raius r aroun the proton. Thus, nλ

More information

Lecture PowerPoints. Chapter 27 Physics: Principles with Applications, 7th edition Giancoli

Lecture PowerPoints. Chapter 27 Physics: Principles with Applications, 7th edition Giancoli Lecture PowerPoints Chapter 27 Physics: Principles with Applications, 7th edition Giancoli This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching

More information

QUANTUM MECHANICS Chapter 12

QUANTUM MECHANICS Chapter 12 QUANTUM MECHANICS Chapter 12 Colours which appear through the Prism are to be derived from the Light of the white one Sir Issac Newton, 1704 Electromagnetic Radiation (prelude) FIG Electromagnetic Radiation

More information

Road map (Where are we headed?)

Road map (Where are we headed?) Road map (Where are we headed?) oal: Fairly high level understanding of carrier transport and optical transitions in semiconductors Necessary Ingredients Crystal Structure Lattice Vibrations Free Electron

More information

Chapter Two. Energy Bands and Effective Mass

Chapter Two. Energy Bands and Effective Mass Chapter Two Energy Bands and Effective Mass Energy Bands Formation At Low Temperature At Room Temperature Valence Band Insulators Metals Effective Mass Energy-Momentum Diagrams Direct and Indirect Semiconduction

More information

The Wave Function. Chapter The Harmonic Wave Function

The Wave Function. Chapter The Harmonic Wave Function Chapter 3 The Wave Function On the basis of the assumption that the de Broglie relations give the frequency and wavelength of some kind of wave to be associated with a particle, plus the assumption that

More information

1.4 The Compton Effect

1.4 The Compton Effect 1.4 The Compton Effect The Nobel Prize in Physics, 1927: jointly-awarded to Arthur Holly Compton (figure 9), for his discovery of the effect named after him. Figure 9: Arthur Holly Compton (1892 1962):

More information

Lesson Plan: Introduction to Quantum Mechanics via Wave Theory and the Photoelectric Effect

Lesson Plan: Introduction to Quantum Mechanics via Wave Theory and the Photoelectric Effect Lesson Plan: Introduction to Quantum Mechanics via Wave Theory and the Photoelectric Effect Will Stoll, Norcross High School Problem: To understand the basic principles of Quantum Mechanics through an

More information

Unit 1 Week 1. July XX August XX, 2010

Unit 1 Week 1. July XX August XX, 2010 Unit 1 Week 1 SGTB Khalsa College University of Delhi www.sushilsingh.weebly.com July XX August XX, 2010 1 2 3 4 The phenomenon of black body radiation could not be explained within the framework of electromagnetic

More information

Chapter 38 Quantum Mechanics

Chapter 38 Quantum Mechanics Chapter 38 Quantum Mechanics Units of Chapter 38 38-1 Quantum Mechanics A New Theory 37-2 The Wave Function and Its Interpretation; the Double-Slit Experiment 38-3 The Heisenberg Uncertainty Principle

More information

September. Text: Physics: Principles & Problems, Merrill-Glencoe NYS STANDARD/KEY IDEA/PERFORMANCE INDICATOR

September. Text: Physics: Principles & Problems, Merrill-Glencoe NYS STANDARD/KEY IDEA/PERFORMANCE INDICATOR September Unit Units and Scientific Notation SI System of Units Unit Conversion Scientific Notation Significant Figures Graphical Analysis Unit Kinematics Scalar vs. vector Displacement/distance Velocity/speed

More information

Applied Nuclear Physics (Fall 2006) Lecture 19 (11/22/06) Gamma Interactions: Compton Scattering

Applied Nuclear Physics (Fall 2006) Lecture 19 (11/22/06) Gamma Interactions: Compton Scattering .101 Applied Nuclear Physics (Fall 006) Lecture 19 (11//06) Gamma Interactions: Compton Scattering References: R. D. Evans, Atomic Nucleus (McGraw-Hill New York, 1955), Chaps 3 5.. W. E. Meyerhof, Elements

More information

Explanations of quantum animations Sohrab Ismail-Beigi April 22, 2009

Explanations of quantum animations Sohrab Ismail-Beigi April 22, 2009 Explanations of quantum animations Sohrab Ismail-Beigi April 22, 2009 I ve produced a set of animations showing the time evolution of various wave functions in various potentials according to the Schrödinger

More information

Electrodynamics HW Problems 06 EM Waves

Electrodynamics HW Problems 06 EM Waves Electrodynamics HW Problems 06 EM Waves 1. Energy in a wave on a string 2. Traveling wave on a string 3. Standing wave 4. Spherical traveling wave 5. Traveling EM wave 6. 3- D electromagnetic plane wave

More information

Classical and Planck picture. Planck s constant. Question. Quantum explanation for the Wein Effect.

Classical and Planck picture. Planck s constant. Question. Quantum explanation for the Wein Effect. 6.1 Quantum Physics. Particle Nature of Light Particle nature of Light Blackbody Radiation Photoelectric Effect Properties of photons Ionizing radiation Radiation damage x-rays Compton effect X-ray diffraction

More information

Physics 342: Modern Physics

Physics 342: Modern Physics Physics 342: Modern Physics Final Exam (Practice) Relativity: 1) Two LEDs at each end of a meter stick oriented along the x -axis flash simultaneously in their rest frame A. The meter stick is traveling

More information

Experimental Determination of Crystal Structure

Experimental Determination of Crystal Structure Experimental Determination of Crystal Structure Branislav K. Nikolić Department of Physics and Astronomy, University of Delaware, U.S.A. PHYS 624: Introduction to Solid State Physics http://www.physics.udel.edu/~bnikolic/teaching/phys624/phys624.html

More information

The Schrödinger Equation in One Dimension

The Schrödinger Equation in One Dimension The Schrödinger Equation in One Dimension Introduction We have defined a comple wave function Ψ(, t) for a particle and interpreted it such that Ψ ( r, t d gives the probability that the particle is at

More information

PHYSICS 149: Lecture 24

PHYSICS 149: Lecture 24 PHYSICS 149: Lecture 24 Chapter 11: Waves 11.8 Reflection and Refraction 11.10 Standing Waves Chapter 12: Sound 12.1 Sound Waves 12.4 Standing Sound Waves Lecture 24 Purdue University, Physics 149 1 ILQ

More information

12 - DUAL NATURE OF RADIATION AND MATTER Page 1

12 - DUAL NATURE OF RADIATION AND MATTER Page 1 1 - DUAL NATURE OF RADIATION AND MATTER Page 1 1.1 Birth of Modern Physics By 1880, most physicists thought that important laws in physics were already discovered and all that remained was their refined

More information

FI 3103 Quantum Physics

FI 3103 Quantum Physics FI 3103 Quantum Physics Alexander A. Iskandar Physics of Magnetism and Photonics Research Group Institut Teknologi Bandung General Information Lecture schedule 17 18 9136 51 5 91 Tutorial Teaching Assistant

More information

Waves and the Schroedinger Equation

Waves and the Schroedinger Equation Waves and the Schroedinger Equation 5 april 010 1 The Wave Equation We have seen from previous discussions that the wave-particle duality of matter requires we describe entities through some wave-form

More information

Experiment 12 ELECTRON DIFFRACTION. Diffraction by Graphite 1. Diffraction by Aluminum 3. The Electron Diffraction Apparatus 5

Experiment 12 ELECTRON DIFFRACTION. Diffraction by Graphite 1. Diffraction by Aluminum 3. The Electron Diffraction Apparatus 5 1-i Experiment 1 ELECTRON DIFFRACTION Introduction 1 Diffraction by Graphite 1 Diffraction by Aluminum 3 The Electron Diffraction Apparatus 5 Procedure and Analysis 6 References 7 Prelab Problems 8 Appendix

More information

The Basic Properties of Surface Waves

The Basic Properties of Surface Waves The Basic Properties of Surface Waves Lapo Boschi lapo@erdw.ethz.ch April 24, 202 Love and Rayleigh Waves Whenever an elastic medium is bounded by a free surface, coherent waves arise that travel along

More information

Physics 43 Chapter 41 Homework #11 Key

Physics 43 Chapter 41 Homework #11 Key Physics 43 Chapter 4 Homework # Key π sin. A particle in an infinitely deep square well has a wave function given by ( ) for and zero otherwise. Determine the epectation value of. Determine the probability

More information

The Bohr Model of Hydrogen

The Bohr Model of Hydrogen The Bohr Model of Hydrogen Suppose you wanted to identify and measure the energy high energy photons. One way to do this is to make a calorimeter. The CMS experiment s electromagnetic calorimeter is made

More information

Modern Physics for Scientists and Engineers International Edition, 4th Edition

Modern Physics for Scientists and Engineers International Edition, 4th Edition Modern Physics for Scientists and Engineers International Edition, 4th Edition http://optics.hanyang.ac.kr/~shsong Review: 1. THE BIRTH OF MODERN PHYSICS 2. SPECIAL THEORY OF RELATIVITY 3. THE EXPERIMENTAL

More information

A) n L < 1.0 B) n L > 1.1 C) n L > 1.3 D) n L < 1.1 E) n L < 1.3

A) n L < 1.0 B) n L > 1.1 C) n L > 1.3 D) n L < 1.1 E) n L < 1.3 1. A beam of light passes from air into water. Which is necessarily true? A) The frequency is unchanged and the wavelength increases. B) The frequency is unchanged and the wavelength decreases. C) The

More information

CHAPTER 27 Quantum Physics

CHAPTER 27 Quantum Physics CHAPTER 27 Quantum Physics Units Discovery and Properties of the Electron Planck s Quantum Hypothesis; Blackbody Radiation Photon Theory of Light and the Photoelectric Effect Energy, Mass, and Momentum

More information

Chapter 1. Introduction

Chapter 1. Introduction I. Classical Physics Chater 1. Introduction Classical Mechanics (Newton): It redicts the motion of classical articles with elegance and accuracy. d F ma, mv F: force a: acceleration : momentum q: osition

More information

Conservation of Momentum and Energy

Conservation of Momentum and Energy ASU University Physics Labs - Mechanics Lab 5 p. 1 Conservation of Momentum and Energy As you work through the steps in the lab procedure, record your experimental values and the results on this worksheet.

More information

Chapter 22 Quantum Mechanics & Atomic Structure 22.1 Photon Theory of Light and The Photoelectric Effect Homework # 170

Chapter 22 Quantum Mechanics & Atomic Structure 22.1 Photon Theory of Light and The Photoelectric Effect Homework # 170 22.1 Photon Theory of Light and The Photoelectric Effect Homework # 170 See Homework #95 in "Chapter 12-Electrostatics" for the table of "Useful nformation" on atomic particles. 01. What is the energy

More information

Chapter 7 Atomic Structure and Orbitals

Chapter 7 Atomic Structure and Orbitals Chapter 7 Atomic Structure and Orbitals Alpha Scattering Experiment: Rutherford s observations Light as Waves or Particles Wavelength (λ) is the distance between any two identical points in consecutive

More information

Standing Waves If the same type of waves move through a common region and their frequencies, f, are the same then so are their wavelengths, λ.

Standing Waves If the same type of waves move through a common region and their frequencies, f, are the same then so are their wavelengths, λ. Standing Waves I the same type o waves move through a common region and their requencies,, are the same then so are their wavelengths,. This ollows rom: v=. Since the waves move through a common region,

More information

WAVE NATURE OF LIGHT

WAVE NATURE OF LIGHT WAVE NATURE OF LIGHT Light is electromagnetic radiation, a type of energy composed of oscillating electric and magnetic fields. The fields oscillate perpendicular to each other. In vacuum, these waves

More information

General Physics I. Lecture 14: Sinusoidal Waves. Prof. WAN, Xin ( 万歆 )

General Physics I. Lecture 14: Sinusoidal Waves. Prof. WAN, Xin ( 万歆 ) General Physics I Lecture 14: Sinusoidal Waves Prof. WAN, Xin ( 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Motivation When analyzing a linear medium that is, one in which the restoring force

More information

Final Exam: Tuesday, May 8, 2012 Starting at 8:30 a.m., Hoyt Hall.

Final Exam: Tuesday, May 8, 2012 Starting at 8:30 a.m., Hoyt Hall. Final Exam: Tuesday, May 8, 2012 Starting at 8:30 a.m., Hoyt Hall. Chapter 38 Quantum Mechanics Units of Chapter 38 38-1 Quantum Mechanics A New Theory 37-2 The Wave Function and Its Interpretation; the

More information

Physics 228. Momentum and Force Kinetic Energy Relativistic Mass and Rest Mass Photoelectric Effect Energy and Momentum of Photons

Physics 228. Momentum and Force Kinetic Energy Relativistic Mass and Rest Mass Photoelectric Effect Energy and Momentum of Photons Physics 228 Momentum and Force Kinetic Energy Relativistic Mass and Rest Mass Photoelectric Effect Energy and Momentum of Photons Lorentz Transformations vs. Rotations The Lorentz transform is similar

More information

BASIC WAVE CONCEPTS. Reading: Main 9.0, 9.1, 9.3 GEM 9.1.1, Giancoli?

BASIC WAVE CONCEPTS. Reading: Main 9.0, 9.1, 9.3 GEM 9.1.1, Giancoli? 1 BASIC WAVE CONCEPTS Reading: Main 9.0, 9.1, 9.3 GEM 9.1.1, 9.1.2 Giancoli? REVIEW SINGLE OSCILLATOR: The oscillation functions you re used to describe how one quantity (position, charge, electric field,

More information

Electron Diffraction

Electron Diffraction Electron iffraction o moving electrons display wave nature? To answer this question you will direct a beam of electrons through a thin layer of carbon and analyze the resulting pattern. Theory Louis de

More information

The Hydrogen Atom According to Bohr

The Hydrogen Atom According to Bohr The Hydrogen Atom According to Bohr The atom We ve already talked about how tiny systems behave in strange ways. Now let s s talk about how a more complicated system behaves. The atom! Physics 9 4 Early

More information

Clicker Question. Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no

Clicker Question. Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no Is the following

More information

Physics 2D Lecture Slides Lecture 10. Jan.25, 2010

Physics 2D Lecture Slides Lecture 10. Jan.25, 2010 Physics 2D Lecture Slides Lecture 10 Jan.25, 2010 Radiation from A Blackbody (a) Intensity of Radiation I =! R (#) d# " T 4 I =! T 4 (Area under curve) Stephan-Boltzmann Constant σ = 5.67 10-8 W / m 2

More information

CHAPTER 12 TEST REVIEW

CHAPTER 12 TEST REVIEW IB PHYSICS Name: Period: Date: # Marks: 76 Raw Score: IB Curve: DEVIL PHYSICS BADDEST CLASS ON CAMPUS CHAPTER 12 TEST REVIEW 1. An alpha particle is accelerated through a potential difference of 10 kv.

More information

Understand the basic principles of spectroscopy using selection rules and the energy levels. Derive Hund s Rule from the symmetrization postulate.

Understand the basic principles of spectroscopy using selection rules and the energy levels. Derive Hund s Rule from the symmetrization postulate. CHEM 5314: Advanced Physical Chemistry Overall Goals: Use quantum mechanics to understand that molecules have quantized translational, rotational, vibrational, and electronic energy levels. In a large

More information

Atomic Structure and Periodicity. AP Chemistry Ms. Grobsky

Atomic Structure and Periodicity. AP Chemistry Ms. Grobsky Atomic Structure and Periodicity AP Chemistry Ms. Grobsky Food For Thought Rutherford s model became known as the planetary model The sun was the positivelycharged dense nucleus and the negatively-charged

More information

Radiation - Electromagnetic Waves (EMR): wave consisting of oscillating electric and magnetic fields that move at the speed of light through space.

Radiation - Electromagnetic Waves (EMR): wave consisting of oscillating electric and magnetic fields that move at the speed of light through space. Radiation - Electromagnetic Waves (EMR): wave consisting of oscillating electric and magnetic fields that move at the speed of light through space. Photon: a quantum of light or electromagnetic wave. Quantum:

More information

Photoelectric Effect & Bohr Atom

Photoelectric Effect & Bohr Atom PH0008 Quantum Mechanics and Special Relativity Lecture 03 (Quantum Mechanics) 020405v2 Photoelectric Effect & Bohr Atom Prof Department of Physics Brown University Main source at Brown Course Publisher

More information

Chapter 5 Particles and Waves. Particle wave dualism for objects primarily known as particles Introduction to Schrödinger equation

Chapter 5 Particles and Waves. Particle wave dualism for objects primarily known as particles Introduction to Schrödinger equation Chapter 5 Particles and Waves Particle wave dualism for objects primarily known as particles Introduction to Schrödinger equation Recall: Summary wave particle dualism Electromagnetic waves have particle

More information

Paper 2 Mark scheme. (Total for Multiple Choice Questions = 10 marks) Acceptable answers Additional guidance Mark. Question. Number 10 D 1 6 B 1 2 C 1

Paper 2 Mark scheme. (Total for Multiple Choice Questions = 10 marks) Acceptable answers Additional guidance Mark. Question. Number 10 D 1 6 B 1 2 C 1 Paper Mark scheme Question C C 3 D 4 A 5 C 6 B 7 A 8 C 9 C 0 D (Total for Multiple Choice Questions 0 marks) 8 (a) The energy equivalent to the mass deficit () When nucleons bind together to form an atomic

More information

AS PHYSICS TERMS, DEFINITIONS & UNITS

AS PHYSICS TERMS, DEFINITIONS & UNITS AS PHYSICS TERMS, DEFINITIONS & UNITS May 2015 This document is issued by WJEC Eduqas to assist teachers with the preparation of candidates for the GCE examination in PHYSICS. It consists of the definitions

More information

Rb, which had been compressed to a density of 1013

Rb, which had been compressed to a density of 1013 Modern Physics Study Questions for the Spring 2018 Departmental Exam December 3, 2017 1. An electron is initially at rest in a uniform electric field E in the negative y direction and a uniform magnetic

More information

Bohr s Correspondence Principle

Bohr s Correspondence Principle Bohr s Correspondence Principle In limit that n, quantum mechanics must agree with classical physics E photon = 13.6 ev 1 n f n 1 i = hf photon In this limit, n i n f, and then f photon electron s frequency

More information

Chapter 2 Problem Solutions

Chapter 2 Problem Solutions Chapter Problem Solutions 1. If Planck's constant were smaller than it is, would quantum phenomena be more or less conspicuous than they are now? Planck s constant gives a measure of the energy at which

More information

Introduction to Quantum Physics. Early Atomic Physics

Introduction to Quantum Physics. Early Atomic Physics Introduction to Quantum Physics Early Atomic Physics What is Quantum Physics Quantum Physics is a collection of laws which explain observations of the tiny building blocks of all matter. The world of the

More information

Interaction X-rays - Matter

Interaction X-rays - Matter Interaction X-rays - Matter Pair production hν > M ev Photoelectric absorption hν MATTER hν Transmission X-rays hν' < hν Scattering hν Decay processes hν f Compton Thomson Fluorescence Auger electrons

More information

Chapter 6: The Electronic Structure of the Atom Electromagnetic Spectrum. All EM radiation travels at the speed of light, c = 3 x 10 8 m/s

Chapter 6: The Electronic Structure of the Atom Electromagnetic Spectrum. All EM radiation travels at the speed of light, c = 3 x 10 8 m/s Chapter 6: The Electronic Structure of the Atom Electromagnetic Spectrum V I B G Y O R All EM radiation travels at the speed of light, c = 3 x 10 8 m/s Electromagnetic radiation is a wave with a wavelength

More information

THE UNIVERSITY OF PRETORIA

THE UNIVERSITY OF PRETORIA PHY 255 THE UNIVERSITY OF PRETORIA FIRST SEMESTER, 2011 Campus: Hatfield PHYSICS 255 Modern Physics Exam Total: 70 (Time allowed: THREE hours Internal Examiner: M. van den Worm External Examiner: Q. Odendaal

More information

2. The figure shows the path of a portion of a ray of light as it passes through three different materials. Note: The figure is drawn to scale.

2. The figure shows the path of a portion of a ray of light as it passes through three different materials. Note: The figure is drawn to scale. 1. The bending of light as it moves from one medium to another with differing indices of refraction is due to a change in what property of the light? A) amplitude B) period C) frequency D) speed E) color

More information

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 1-1B: THE INTERACTION OF MATTER WITH RADIATION Introductory Video Quantum Mechanics Essential Idea: The microscopic quantum world offers

More information

Problem Set 4: Whither, thou turbid wave SOLUTIONS

Problem Set 4: Whither, thou turbid wave SOLUTIONS PH 253 / LeClair Spring 2013 Problem Set 4: Witer, tou turbid wave SOLUTIONS Question zero is probably were te name of te problem set came from: Witer, tou turbid wave? It is from a Longfellow poem, Te

More information

Physics 222, Modern Physics, Exam 1 NAME

Physics 222, Modern Physics, Exam 1 NAME Physics 222, Modern Physics, Exam 1 NAME You are graded on your work, with partial credit where it is deserved. Please be clear and well-organized in all your steps. 1. Gold has a work function of 4.83

More information

MODERN PHYSICS. Kenneth S. Krane. Third edition DEPARTMENT OF PHYSICS OREGON STATE UNIVERSITY JOHN WILEY & SONS, INC

MODERN PHYSICS. Kenneth S. Krane. Third edition DEPARTMENT OF PHYSICS OREGON STATE UNIVERSITY JOHN WILEY & SONS, INC MODERN PHYSICS Third edition Kenneth S. Krane DEPARTMENT OF PHYSICS OREGON STATE UNIVERSITY JOHN WILEY & SONS, INC Chapter 4 THE WAVELIKE PROPERTIES OF PARTICLES Just as we produce images from light waves

More information

Theoretical Biophysics. Quantum Theory and Molecular Dynamics. Pawel Romanczuk WS 2017/18

Theoretical Biophysics. Quantum Theory and Molecular Dynamics. Pawel Romanczuk WS 2017/18 Theoretical Biophysics Quantum Theory and Molecular Dynamics Pawel Romanczuk WS 2017/18 http://lab.romanczuk.de/teaching/ 1 Introduction Two pillars of classical theoretical physics at the begin of 20th

More information

KEELE UNIVERSITY PHYSICS/ASTROPHYSICS MODULE PHY OSCILLATIONS AND WAVES PRACTICE EXAM

KEELE UNIVERSITY PHYSICS/ASTROPHYSICS MODULE PHY OSCILLATIONS AND WAVES PRACTICE EXAM KEELE UNIVERSITY PHYSICS/ASTROPHYSICS MODULE PHY-10012 OSCILLATIONS AND WAVES PRACTICE EXAM Candidates should attempt ALL of PARTS A and B, and TWO questions from PART C. PARTS A and B should be answered

More information

PHYS 5012 Radiation Physics and Dosimetry

PHYS 5012 Radiation Physics and Dosimetry PHYS 5012 Radiation Physics and Dosimetry Tuesday 12 March 2013 What are the dominant photon interactions? (cont.) Compton scattering, photoelectric absorption and pair production are the three main energy

More information

Solution Derivations for Capa #12

Solution Derivations for Capa #12 Solution Derivations for Capa #12 1) A hoop of radius 0.200 m and mass 0.460 kg, is suspended by a point on it s perimeter as shown in the figure. If the hoop is allowed to oscillate side to side as a

More information

Pilot Waves and the wave function

Pilot Waves and the wave function Announcements: Pilot Waves and the wave function No class next Friday, Oct. 18! Important Lecture in how wave packets work. Material is not in the book. Today we will define the wave function and see how

More information

12.2 Photons and the Quantum Theory of Light

12.2 Photons and the Quantum Theory of Light 12.2 Photons and the Quantum Theory of Light Lasers are used everywhere, from concert light shows to grocery store checkout lines to cutting-edge research labs (Figure 1). Although classical physics says

More information

OPTI 511R: OPTICAL PHYSICS & LASERS

OPTI 511R: OPTICAL PHYSICS & LASERS OPTI 511R: OPTICAL PHYSICS & LASERS Instructor: R. Jason Jones Office Hours: TBD Teaching Assistant: Robert Rockmore Office Hours: Wed. (TBD) h"p://wp.op)cs.arizona.edu/op)511r/ h"p://wp.op)cs.arizona.edu/op)511r/

More information

1 Basics of Quantum Mechanics

1 Basics of Quantum Mechanics 1 Basics of Quantum Mechanics 1.1 Admin The course is based on the book Quantum Mechanics (2nd edition or new international edition NOT 1st edition) by Griffiths as its just genius for this level. There

More information

PHYSICS 4750 Physics of Modern Materials Chapter 5: The Band Theory of Solids

PHYSICS 4750 Physics of Modern Materials Chapter 5: The Band Theory of Solids PHYSICS 4750 Physics of Modern Materials Chapter 5: The Band Theory of Solids 1. Introduction We have seen that when the electrons in two hydrogen atoms interact, their energy levels will split, i.e.,

More information

Einstein. Quantum Physics at a glance. Planck s Hypothesis (blackbody radiation) (ultraviolet catastrophe) Quantized Energy

Einstein. Quantum Physics at a glance. Planck s Hypothesis (blackbody radiation) (ultraviolet catastrophe) Quantized Energy Quantum Physics at a glance Quantum Physics deals with the study of light and particles at atomic and smaller levels. Planck s Hypothesis (blackbody radiation) (ultraviolet catastrophe) Quantized Energy

More information

dt r r r V(x,t) = F(x,t)dx

dt r r r V(x,t) = F(x,t)dx Quantum Mechanics and Atomic Physics Lecture 3: Schroedinger s Equation: Part I http://www.physics.rutgers.edu/ugrad/361 Prof. Sean Oh Announcement First homework due on Wednesday Sept 14 at the beginning

More information

Outline. Chapter 6 The Basic Interactions between Photons and Charged Particles with Matter. Photon interactions. Photoelectric effect

Outline. Chapter 6 The Basic Interactions between Photons and Charged Particles with Matter. Photon interactions. Photoelectric effect Chapter 6 The Basic Interactions between Photons and Charged Particles with Matter Radiation Dosimetry I Text: H.E Johns and J.R. Cunningham, The physics of radiology, 4 th ed. http://www.utoledo.edu/med/depts/radther

More information

THE NATURE OF THE ATOM. alpha particle source

THE NATURE OF THE ATOM. alpha particle source chapter THE NATURE OF THE ATOM www.tutor-homework.com (for tutoring, homework help, or help with online classes) Section 30.1 Rutherford Scattering and the Nuclear Atom 1. Which model of atomic structure

More information

A Much Closer Look at Atomic Structure

A Much Closer Look at Atomic Structure Ideas We Will Clear Up Before You Graduate: WRONG IDEAS 1. The electron always behaves as a particle. BETTER SUPPORTED BY EXPERIMENTS 1. There s a wavelength associated with very small particles like the

More information

2 u 1-D: 3-D: x + 2 u

2 u 1-D: 3-D: x + 2 u c 2013 C.S. Casari - Politecnico di Milano - Introduction to Nanoscience 2013-14 Onde 1 1 Waves 1.1 wave propagation 1.1.1 field Field: a physical quantity (measurable, at least in principle) function

More information

LECTURE 4 PRINCIPLE OF IMAGE FORMATION KAMARUL AMIN BIN ABDULLAH

LECTURE 4 PRINCIPLE OF IMAGE FORMATION KAMARUL AMIN BIN ABDULLAH LECTURE 4 PRINCIPLE OF IMAGE FORMATION KAMARUL AMIN BIN ABDULLAH Lesson Objectives At the end of the lesson, student should able to: Define attenuation Explain interactions between x-rays and matter in

More information

8 Wavefunctions - Schrödinger s Equation

8 Wavefunctions - Schrödinger s Equation 8 Wavefunctions - Schrödinger s Equation So far we have considered only free particles - i.e. particles whose energy consists entirely of its kinetic energy. In general, however, a particle moves under

More information

M14/4/PHYSI/HPM/ENG/TZ1/XX. Physics Higher level Paper 1. Wednesday 7 May 2014 (morning) 1 hour INSTRUCTIONS TO CANDIDATES

M14/4/PHYSI/HPM/ENG/TZ1/XX. Physics Higher level Paper 1. Wednesday 7 May 2014 (morning) 1 hour INSTRUCTIONS TO CANDIDATES M14/4/PHYSI/HPM/ENG/TZ1/XX 14657 Physics Higher level Paper 1 Wednesday 7 May 14 (morning) 1 hour INSTRUCTIONS TO CANDIDATES Do not open this examination paper until instructed to do so. Answer all the

More information

Lecture 30. Chapter 21 Examine two wave superposition (-ωt and +ωt) Examine two wave superposition (-ω 1 t and -ω 2 t)

Lecture 30. Chapter 21 Examine two wave superposition (-ωt and +ωt) Examine two wave superposition (-ω 1 t and -ω 2 t) To do : Lecture 30 Chapter 21 Examine two wave superposition (-ωt and +ωt) Examine two wave superposition (-ω 1 t and -ω 2 t) Review for final (Location: CHEM 1351, 7:45 am ) Tomorrow: Review session,

More information