-18- Section 5: Special Relativity f. 1. The laws of nature are the same in all inertial reference frames. (No preferred frame of reference.
|
|
- Julie Whitehead
- 5 years ago
- Views:
Transcription
1 PHY 133 Einstein's postulates: -18- Section 5: Special Relativity f 1. The laws of nature are the same in all inertial reference frames. (No preferred frame of reference.) Inertial reference frame: one which isn't accelerating. 2. c (speed of light in a vacuum) is the same in all inertial reference frames. These are suggested by the Michelson - Morley experiment (see text) and also theoretical considerations. Notice #2 means Speed = (distance)/(time). So, for c to be the same, distance and time must be different in different reference frames. For example, the time interval between the bulb flashing and the light reaching the detector: They agree on d because there is no motion in the y direction. (c Δt) 2 = (v Δt) 2 + d 2 (c Δt) 2 = (v Δt) 2 + (c Δt p ) 2 (c Δt) 2 - (v Δt) 2 = (c Δt p ) 2 Δt 2 - (v/c Δt) 2 = Δt p 2 [1 - (v/c) 2 ](Δt) 2 = Δt p 2
2 -19- Δt = Δt p 1 ( v c )2 let γ = 1 1 ( v c )2 Time Dilation: Δt = γ Δt p (More time between the events in the frame where light has to catch up to the detector.) The Lorentz transformation: x'= γ(x - vt) y'= y z'= z t'= γ[t - (v/c 2 )x] Inverse transformation: Replace v with -v. Velocity transformation (Differentiate with respect to time.): Length in observer's rest frame: L = x 2 - x 1 Length in object's rest frame: L p = x 2 '-x 1 ' = γ(x 2 -vt) - γ(x 1 -vt) = γ(x 2 - x 1 ) Lorentz - FitzGerald Contraction: L p = γl Δt p = Measured in frame where clock is at rest. L p = Measured in frame where length is at rest. (Not necessarily the same frame, unless you re talking about the length of the clock.)
3 -20- Ex. 5-1: What is the speed of ship 2 relative to Earth? Ex. 5-2: How fast must something go for relativistic effects to make a 1% difference in time, length, etc? Ex. 5-3: The average lifetime of a stationary muon is 2.2 μs. If one is created 8.0 km above sea level (by a cosmic ray hitting an air molecule), and it travels at.998c, find a. its lifetime as seen by us, and b. the distance to sea level in its reference frame. Simultaneity: Events that are simultaneous to one observer are not to another. That is, events separated only by space to one observer are separated by space and time to another. So, space and time must all be part of the same thing. ( spacetime ) Momentum: In a collision between objects thrown from different frames of reference, p is conserved only if redefined as p = γmv where m = mass when object is at rest, V = its velocity
4 -21- Some people call γm "relativistic mass." Many others reserve the word mass for the rest mass. Terminology aside, as v c, objects gain extra inertia; they have more momentum than they should at that speed. (Gravitational effects depend on the rest mass.) Newton's 2nd law must then be rewritten as F = dp Energy: Work = F dx = (dp/dt)dx =... Put in p = γmv, make some clever substitutions, integrate. The result is that the work needed to get from rest to a speed V is: KE = γmc 2 mc 2 ( or KE = (γm m)c 2 ) The inertia gained from being in motion is proportional to the energy gained. So, energy has inertia. This suggests that the inertia of a body at rest is also proportional to some kind of energy, which we call mass. Total energy: E = γmc 2 Rest energy: E R = mc 2 = energy equivalent of the rest mass. Kinetic energy: KE = E - E R dt KE = γmc 2 mc 2 = mc 2 ( 1 + γ) = mc 2 { 1 + [1 ( v c )2 ] 1/2 } Binomial theorem: (1 x) n = 1 nx + n(n 1) 2! x 2 n(n 1)(n 2) 3! x 3 + x = ( v c )2 and n = ½ KE = mc 2 { 1 + [1 ( ½)( v c )2 + ( ½)( ½ 1) ( v c )4 ]} KE = mc 2 (½)( v c )2 + mc 2 ( ½)( ½ 1) 2 KE = 1/2 mv 2 is true only if v << c. Why no object can reach c: As v c, γm = ( v c )4 = 1 2 mv m(v4 c2) + 48 m(v6 c 4) + m 1 ( v c )2 approaches m 0 =. Increasing a body s energy, by adding KE, increases its inertia. Near c, the inertia becomes too great for further significant acceleration. Adding more energy makes the particle "heavier" not faster. Ex. 5-4: an electron is accelerated through a million volts, starting from rest. Find its final speed. Ex. 5-5: In atomic mass units (u), the mass of a proton = , mass of a neutron = , mass of a deuteron ( 2 1H nucleus) = What is the binding energy of the deuteron? 2
5 -22- Section 6: Wave - Particle Duality: Blackbody Radiation: - Experimental graph of Intensity vs. λ. - Wein s displacement law. (λ of experimental curve s peak.) - Rayleigh-Jean s law, the prediction of classical physics, doesn t match experimental graph. ("Ultraviolet catastrophe") Planck's solution (1900): Assume molecules of cavity walls can only vibrate with certain energies. "Jumping" between energy states, they emit (or absorb) light in "quanta" of energy E = hf h = Planck's constant, f = frequency (Called "photons" today.) From this, he derived I(λ,T) = 2πhc 2 _ which matches the observed data. λ 5 (e hc/(λkt) - 1) Example 6-1: A simplified derivation of Wein s displacement law from the Planck radiation law. The Photoelectric Effect: Maximum KE of photoelectrons depends on light's frequency, not its intensity. Classical theory of electromagnetic waves predicts the opposite. KE max is measured by finding the stopping potential, V 0. (Voltage needed to turn back all electrons before they reach the opposite plate, stopping the current.) KE max = ev 0
6 -23- Einstein's solution (1905): Light is a stream of photons, each with energy hf. A photon is absorbed "all or nothing" by one electron on the plate they hit. - KE of e - depends on energy of photon that hit it, and thus on its frequency. - KE independent of intensity because each e - gets its energy from just one photon. KE max = hf - = work function = energy needed to tear an e - off of the surface. Example 6-2: What is the energy of a photon with a 500 nm wavelength? Example 6-3: Sodium has a work function of 2.46 ev. Find a. the maximum energy of photoelectrons when λ = 300 nm. b. the cutoff λ (above which there is no emission). de Broglie wavelength. Example 6-4: A beam of neutrons going 1000 m/s falls on a crystal with atomic planes 4.5 What will be the angle between incident and reflected beams for first order Bragg reflection? apart. If all objects have this dual wave/ particle nature, why don't we see wavelike behavior for baseballs, airplanes, etc? λ = h/(mv) λ is very small if m is very big. So, effects like diffraction are too small to measure for macroscopic objects. How can something be both a wave and a particle, when the behavior of waves and particles is as different as black and white? A blob of correction fluid on clear plastic looks white when front lit and black when back lit. It's black or white, depending on how you look at it. Similarly, light is a wave or a particle, depending on whether you look at it in a diffraction experiment, or a photoelectric experiment. (Either model is oversimplified.) Heisenberg's Uncertainty Principle: Example: What are x and p x of an electron as it goes through this slit? A convenient (but not really "true") picture of wave/ particle duality is to think of a pointlike particle "surfing" on some kind of wave.
7 -24- p x might be anywhere between these extremes. ("Particle" can be anywhere "wave" has a significant amplitude.) Narrower slit (reduced uncertainty in x) diffracts waves more. This could throw particle further to the side, increasing uncertainty in p x. From a more detailed, general analysis: Δx Δp x > ħ 2 where ħ = h/(2π) Similarly, ΔE Δt > ħ 2 The uncertainty principle is a useful "rule of thumb" for rough estimates: Example 6-5: The electron's momentum in hydrogen's ground state is 1.99 x kg m/s. If this is Δp x (p x could be anything between.), what is Δx? Example 6-6: (Quantum tunneling): With an order of magnitude estimate, I will explain how an alpha particle with ~10 MeV of energy can escape from a nucleus surrounded by a ~20 MeV energy barrier. (I also briefly mention some other applications of tunneling: tunnel diode, Josephson junction, scanning tunneling microscope.)
8 -25- Sec. 7: The Bohr model of the atom (1913), as later explained by de Broglie's ideas (1924): Hydrogen & H - like atoms (He +, Li ++, etc: 1 electron): I will explain, line by line on the board, how these follow from Coulomb's law and the electron's wave nature: - Bohr s quantization condition - Atom s radius when in the n th state - Energy levels Atomic spectra: An atom gives off light when an electron drops from a higher to a lower energy level. The energy it loses is given off as a photon (E = hf) ev 13.6 ev In hydrogen, E i = n2 E f = 2 i n f E photon = ΔE electron = (E f E i ) = + (13.6 ev)( 1 n f 2 1 n i 2) also, E photon = hf = h( c λ ) E hc = 1 λ 1 λ 13.6 ev = ( hc n f n2) i Rydberg constant: R = x 10 7 m -1 1 λ = R( 1 n f 2 1 n i 2) Allowed wavelengths in the spectrum of hydrogen. This model explains line spectra: Example, hydrogen:
9 -26- (Each element has its own pattern of wavelengths.) Example 7-1: Find wavelength, frequency and energy per photon for the first line in the Paschen series. Example 7-2: A hydrogen atom, initially in its ground state, absorbs a ev photon. How many times larger does the atom become? Spontaneous Emission: Electron falls on its own. Stimulated Emission: Electron is knocked down by an incoming photon identical to the one it emits. Both photons move off in phase. Used in lasers. Electrons are arranged in "shells": Multi-electron atoms: X-ray tube: Bremsstrahlung (braking radiation): Emitted as beam e - s suddenly decelerate. Beam knocks inner e - from target atom. Then, an outer e - drops to take its place, emitting an x-ray photon.
10 -27- K series: electron falls into K shell. L series: electron falls into L shell. α: from the level just above. β: from the second level above. And so on. To estimate the wavelengths: If only one electron in atom: E n = (13.6 ev)z 2 /n 2 With more: Use the net charge within the electron's orbit as an effective value for Z. (Other electrons "shield" the nucleus.) For K and L electrons, Z eff = Z 1 works pretty well. M electrons: Z eff = Z 9 Example 7-3: Electrons are accelerated through 35 kv, and strike a Mo target (atomic number = 42). Find: a. The wavelength of the K α line, b. The shortest wavelength emitted.
11 -28- Section 8: Introduction to Quantum Mechanics The Bohr model was successful as far as it went, but left some things unexplained. Quantum mechanics is what replaced it. Wave function. Just as surfers prefer the ocean over Lake Ontario, electrons tend to go where the waves are bigger. In a particle beam, the number per unit volume is proportional to ψ 2. However, if you turn down the intensity to one electron at a time (in an electron diffraction experiment, for example), where that electron will go is fundamentally unpredictable. The wave function only gives a probability of what it will do. (Like flipping coins: You can predict the overall behavior of many - half heads and half tails. But what one individual coin will do is unknowable.) This is a fundamental difference from classical physics. Ex. 8-1: If there is a 50% chance of finding the particle between x = 0 and x = a, what is a? Normalization. Ex. 8-2: If ψ = Ae x2 2, what is A? The Schrödinger equation. (In the special case of a one dimensional problem, with ψ not a function of time.) One dimensional square well. ("Particle in a box") (I will show how the wave functions and energy levels follow from Schrödinger's equation.) The particle can exist only in certain quantum states. (Each different ψ the particle could have is called a state.) Notice there is no E 0 : The particle can not come to rest. Zero-point energy = the least energy the particle can have. Ex.8-3: In a well 2.5 Å across, an electron drops from n = 2 to n = 1. What is the wavelength of the photon given off?
12 -29- Other quantum behaviors: Superposition. A particle can be in more than one state at the same time. Example: Hydrogen transitioning from n = 2 to n = 1. Electron s wave function before = ψ 2, after = ψ 1. During the transition, e is in both at once: ψ = aψ 1 + bψ 2 (a & b are constants.) Example: Double slit experiment. Each electron is in a superposition of (went through one slit) and (went through the other). Record where each hits the screen and an interference pattern builds up. Then put a wire loop connected to a voltage sensor around each slit. Detecting which slit each e went through means it no longer has two possible paths. e s are no longer in a superposition of interfering states, so now they act like particles. - Schrödinger s cat. Entanglement. Measurement of one entangled particle determines what will be measured for the other. Example: The pair of particles is in a superposition of ψ 1 = (A spin up, B spin down) and ψ 2 = (A spin down, B spin up). If A measures along z axis, B gets. Or along x axis, if A gets, B gets. Why? Either one was and the other all along and not really in a superposition ( hidden variables interpretation ) or they are linked so that when one becomes the other instantaneously knows and becomes. (Copenhagen interpretation.) Bell s inequality (John Bell, 1964) compares the probabilities of seeing spin up on various axes in the xz plane based on the assumption of hidden variables. Experiments violate Bell s inequality and agree with quantum mechanics. (But this does not allow A and B instantaneous communication, violating causality.)
13 -30- Review for Exam 2: 1. Some measurements from a photoelectric effect experiment similar to lab 6A are shown. V 0 is the stopping potential, λ is the wavelength of the incident light. Use this data to find a value for Planck's constant. (It will be a little off of the accepted value.) ans: 3.87 x ev s 2. An observer on the spaceship sees Earth coming at him at.7c, and the electrons in the beam going toward Earth at.9c. What is the speed of the electrons relative to Earth? ans:.982 c 3. For an electron circling a proton: a. Think of the electron as a wave. From the fact that a standing wave along a circular path must have a whole number of wavelengths around its circumference (circumference = nλ) derive Bohr's quantization condition, mvr = n. b. Now, thinking of the electron as a classical particle, it can be shown that mv 2 = (1/4πε 0 )(e 2 /r). From this and Bohr's quantization condition, derive the expression for the radius of the n th orbit. (Leave it in terms of n and fundamental constants: no need to fill in numbers.) 4. Show that if U = 0 everywhere (a free particle) then ψ = Ae i(kx ωt), where i = 1 and A is a constant, is a solution of the Schrödinger equation. (Take each side of the equation separately, and show that they are in fact equal if this is ψ.) Remember that k = 2π/λ, λ = h/p and E = p 2 /(2m). (½mv 2 = (mv) 2 /(2m).) Treat t like a constant when you differentiate. 5. Short answer, 5 points each: a. A hydrogen atom in its ground state (n = 1) absorbs a photon. What is the smallest possible energy this photon could have? (Refer to the energy level diagram for hydrogen at right.) b. The Heisenberg uncertainty principle limits the precision with which you can measure a particle's position when its momentum is measured at the same time. Is there any limit on the precision of a position measurement when momentum is not measured? c. Make a rough sketch of the intensity versus wavelength curve given by the Planck radiation law. (I goes on the vertical axis.) d. What is meant by an "inertial reference frame?" e. Just to the left of the origin, a particle's wave function is given by ψ =.3 x 2. Just to the right of the origin, ψ = k, where k is a constant. What value must k have?
Semiconductor Physics and Devices
Introduction to Quantum Mechanics In order to understand the current-voltage characteristics, we need some knowledge of electron behavior in semiconductor when the electron is subjected to various potential
More informationClass 21. Early Quantum Mechanics and the Wave Nature of Matter. Physics 106. Winter Press CTRL-L to view as a slide show. Class 21.
Early and the Wave Nature of Matter Winter 2018 Press CTRL-L to view as a slide show. Last Time Last time we discussed: Optical systems Midterm 2 Today we will discuss: Quick of X-ray diffraction Compton
More informationPlanck s Quantum Hypothesis Blackbody Radiation
Planck s Quantum Hypothesis Blackbody Radiation The spectrum of blackbody radiation has been measured(next slide); it is found that the frequency of peak intensity increases linearly with temperature.
More informationCHAPTER 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 informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 27 Modern Physics Quantum Physics Blackbody radiation Plank s hypothesis http://www.physics.wayne.edu/~apetrov/phy2140/ Chapter 27 1 Quantum Physics 2 Introduction: Need
More informationChapter 27. Quantum Physics
Chapter 27 Quantum Physics Need for Quantum Physics Problems remained from classical mechanics that relativity didn t explain Blackbody Radiation The electromagnetic radiation emitted by a heated object
More informationGeneral Physics (PHY 2140) Lecture 14
General Physics (PHY 2140) Lecture 14 Modern Physics 1. Relativity Einstein s General Relativity 2. Quantum Physics Blackbody Radiation Photoelectric Effect X-Rays Diffraction by Crystals The Compton Effect
More informationNotes for Special Relativity, Quantum Mechanics, and Nuclear Physics
Notes for Special Relativity, Quantum Mechanics, and Nuclear Physics 1. More on special relativity Normally, when two objects are moving with velocity v and u with respect to the stationary observer, the
More informationProblems with Classical Physics. Blackbody Radiation Photoelectric Effect Compton Effect Bohr Model of Atom
The Quantum Gang Problems with Classical Physics Blackbody Radiation Photoelectric Effect Compton Effect Bohr Model of Atom Why this shape? Why the drop? Blackbody Radiation A black body is an ideal system
More informationChapter 27 Early Quantum Theory and Models of the Atom Discovery and Properties of the electron
Chapter 27 Early Quantum Theory and Models of the Atom 27-1 Discovery and Properties of the electron Measure charge to mass ratio e/m (J. J. Thomson, 1897) When apply magnetic field only, the rays are
More informationModern Physics Part 2: Special Relativity
Modern Physics Part 2: Special Relativity Last modified: 23/08/2018 Links Relative Velocity Fluffy and the Tennis Ball Fluffy and the Car Headlights Special Relativity Relative Velocity Example 1 Example
More informationLecture 16 Quantum Physics Chapter 28
Lecture 16 Quantum Physics Chapter 28 Particles vs. Waves Physics of particles p = mv K = ½ mv2 Particles collide and do not pass through each other Conservation of: Momentum Energy Electric Charge Physics
More informationExplain how Planck resolved the ultraviolet catastrophe in blackbody radiation. Calculate energy of quanta using Planck s equation.
Objectives Explain how Planck resolved the ultraviolet catastrophe in blackbody radiation. Calculate energy of quanta using Planck s equation. Solve problems involving maximum kinetic energy, work function,
More informationChapter 37 Early Quantum Theory and Models of the Atom. Copyright 2009 Pearson Education, Inc.
Chapter 37 Early Quantum Theory and Models of the Atom Planck s Quantum Hypothesis; Blackbody Radiation Photon Theory of Light and the Photoelectric Effect Energy, Mass, and Momentum of a Photon Compton
More informationDavid J. Starling Penn State Hazleton PHYS 214
All the fifty years of conscious brooding have brought me no closer to answer the question, What are light quanta? Of course today every rascal thinks he knows the answer, but he is deluding himself. -Albert
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS LSN 12-1A: INTERACTIONS OF MATTER WITH RADIATION Questions From Reading Activity? Essential Idea: The microscopic quantum world offers a range of phenomena,
More informationTitle / paragraph example Topic: Quantum Computers. Course essay. Photoelectric effect summary. From Last Time. Photon interference?
Course essay Friday, Nov 3: Due in class essay topic(review article, operating experiment, noble prize) short description - one paragraph http://www.hep.wisc.edu/~herndon/107-0609/essay.htm Friday, Nov
More informationChapter 27 Lecture Notes
Chapter 27 Lecture Notes Physics 2424 - Strauss Formulas: λ P T = 2.80 10-3 m K E = nhf = nhc/λ fλ = c hf = K max + W 0 λ = h/p λ - λ = (h/mc)(1 - cosθ) 1/λ = R(1/n 2 f - 1/n 2 i ) Lyman Series n f = 1,
More informationThe Photoelectric Effect
Stellar Astrophysics: The Interaction of Light and Matter The Photoelectric Effect Methods of electron emission Thermionic emission: Application of heat allows electrons to gain enough energy to escape
More informationElectron in a Box. A wave packet in a square well (an electron in a box) changing with time.
Electron in a Box A wave packet in a square well (an electron in a box) changing with time. Last Time: Light Wave model: Interference pattern is in terms of wave intensity Photon model: Interference in
More informationRevision Guide. Chapter 7 Quantum Behaviour
Revision Guide Chapter 7 Quantum Behaviour Contents CONTENTS... 2 REVISION CHECKLIST... 3 REVISION NOTES... 4 QUANTUM BEHAVIOUR... 4 Random arrival of photons... 4 Photoelectric effect... 5 PHASE AN PHASORS...
More informationModern 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 informationLecture 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 informationQuantum 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 informationRED. BLUE Light. Light-Matter
1 Light-Matter This experiment demonstrated that light behaves as a wave. Essentially Thomas Young passed a light of a single frequency ( colour) through a pair of closely spaced narrow slits and on the
More informationChapter 38. Photons Light Waves Behaving as Particles
Chapter 38 Photons Light Waves Behaving as Particles 38.1 The Photoelectric Effect The photoelectric effect was first discovered by Hertz in 1887, and was explained by Einstein in 1905. The photoelectric
More informationDEVIL 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 informationTitle / paragraph example Topic: Quantum Computers. Course Essay. Photoelectric effect summary. From Last Time. Compton scattering
Course Essay 500-750 word typed essay due Wed. Apr. 26 First deadline: Fri. this week (Mar. 24) turn in Topic and Paragraph Description Topic ideas: Nobel prize winner: work & importance Big science project:
More informationPhysics 102: Lecture 23
Physics 102: Lecture 23 De Broglie Waves & Compton Scattering Physics 102: Lecture 23, Slide 1 Early Indications of Problems with Classical Physics Blackbody radiation Photoelectric effect Wave-particle
More informationPhysics. Light Quanta
Physics Light Quanta Quantum Theory Is light a WAVE or a PARTICLE? Particle tiny object like a bullet, has mass and travels in straight lines unless a force acts upon it Waves phenomena that extend in
More informationElectromagnetic Radiation
Chapter 6: The Periodic Table and Atomic Structure Electromagnetic Radiation Atomic Spectra The Bohr Atom Quantum Mechanical Model of the Atom Wave Mechanics Quantum Numbers and Electron Orbitals Interpreting
More informationPreview. Atomic Physics Section 1. Section 1 Quantization of Energy. Section 2 Models of the Atom. Section 3 Quantum Mechanics
Atomic Physics Section 1 Preview Section 1 Quantization of Energy Section 2 Models of the Atom Section 3 Quantum Mechanics Atomic Physics Section 1 TEKS The student is expected to: 8A describe the photoelectric
More informationIt s a wave. It s a particle It s an electron It s a photon. It s light!
It s a wave It s a particle It s an electron It s a photon It s light! What they expected Young s famous experiment using a beam of electrons instead of a light beam. And, what they saw Wave-Particle Duality
More informationChapter 37 Early Quantum Theory and Models of the Atom
Chapter 37 Early Quantum Theory and Models of the Atom Units of Chapter 37 37-7 Wave Nature of Matter 37-8 Electron Microscopes 37-9 Early Models of the Atom 37-10 Atomic Spectra: Key to the Structure
More informationPHYS 3313 Section 001 Lecture #16
PHYS 3313 Section 001 Lecture #16 Monday, Mar. 24, 2014 De Broglie Waves Bohr s Quantization Conditions Electron Scattering Wave Packets and Packet Envelops Superposition of Waves Electron Double Slit
More informationChapter 1. From Classical to Quantum Mechanics
Chapter 1. From Classical to Quantum Mechanics Classical Mechanics (Newton): It describes the motion of a classical particle (discrete object). dp F ma, p = m = dt dx m dt F: force (N) a: acceleration
More informationSCH4U: History of the Quantum Theory
SCH4U: History of the Quantum Theory Black Body Radiation When an object is heated, it initially glows red hot and at higher temperatures becomes white hot. This white light must consist of all of the
More informationPhysics 102: Lecture 23
Physics 102: Lecture 23 De Broglie Waves & Compton Scattering Place exam revisions in box at front of room either now or at end of lecture Physics 102: Lecture 23, Slide 1 Exam 3 Monday April 21! Material
More informationEarly Quantum Theory and Models of the Atom
Early Quantum Theory and Models of the Atom Electron Discharge tube (circa 1900 s) There is something ( cathode rays ) which is emitted by the cathode and causes glowing Unlike light, these rays are deflected
More informationWe 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 informationPhysics Lecture 6
Physics 3313 - Lecture 6 Monday February 8, 2010 Dr. Andrew Brandt 1. HW1 Due today HW2 weds 2/10 2. Electron+X-rays 3. Black body radiation 4. Compton Effect 5. Pair Production 2/8/10 3313 Andrew Brandt
More informationGeneral Physics (PHY 2140) Lecture 15
General Physics (PHY 2140) Lecture 15 Modern Physics Chapter 27 1. Quantum Physics The Compton Effect Photons and EM Waves Wave Properties of Particles Wave Functions The Uncertainty Principle http://www.physics.wayne.edu/~alan/2140website/main.htm
More informationFinal Exam Sample Problems
UNIVERSITY OF ALABAMA Department of Physics and Astronomy PH 253 / LeClair Spring 2010 Final Exam Sample Problems 1. The orbital speed of the Earth around the Sun is 30 km/s. In one year, how many seconds
More informationAtomic Spectra. if you pass white light through a gas dark narrow lines on a bright continuum "Absorption spectrum"
By the end of the 1800 s, classical physics had many successes. One prominent physicist even had suggested that all that remained was to further increase the significant digits for measurements. However,
More informationLecture Outline Chapter 30. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.
Lecture Outline Chapter 30 Physics, 4 th Edition James S. Walker Chapter 30 Quantum Physics Units of Chapter 30 Blackbody Radiation and Planck s Hypothesis of Quantized Energy Photons and the Photoelectric
More informationWave nature of particles
Wave nature of particles We have thus far developed a model of atomic structure based on the particle nature of matter: Atoms have a dense nucleus of positive charge with electrons orbiting the nucleus
More informationThe Atom. Result for Hydrogen. For example: the emission spectrum of Hydrogen: Screen. light. Hydrogen gas. Diffraction grating (or prism)
The Atom What was know about the atom in 1900? First, the existence of atoms was not universally accepted at this time, but for those who did think atoms existed, they knew: 1. Atoms are small, but they
More informationChemistry (
Question 2.1: (i) Calculate the number of electrons which will together weigh one gram. (ii) Calculate the mass and charge of one mole of electrons. Answer 2.1: (i) Mass of one electron = 9.10939 10 31
More informationThe Bohr Model of Hydrogen, a Summary, Review
The Bohr Model of Hydrogen, a Summary, Review Allowed electron orbital radii and speeds: Allowed electron energy levels: Problems with the Bohr Model Bohr s model for the atom was a huge success in that
More informationUNIT : QUANTUM THEORY AND THE ATOM
Name St.No. Date(YY/MM/DD) / / Section UNIT 102-10: QUANTUM THEORY AND THE ATOM OBJECTIVES Atomic Spectra for Hydrogen, Mercury and Neon. 1. To observe various atomic spectra with a diffraction grating
More informationQuantum Chemistry I : CHEM 565
Quantum Chemistry I : CHEM 565 Lasse Jensen October 26, 2008 1 1 Introduction This set of lecture note is for the course Quantum Chemistry I (CHEM 565) taught Fall 2008. The notes are at this stage rather
More information1) Introduction 2) Photo electric effect 3) Dual nature of matter 4) Bohr s atom model 5) LASERS
1) Introduction 2) Photo electric effect 3) Dual nature of matter 4) Bohr s atom model 5) LASERS 1. Introduction Types of electron emission, Dunnington s method, different types of spectra, Fraunhoffer
More informationQuantum Mechanics & Atomic Structure (Chapter 11)
Quantum Mechanics & Atomic Structure (Chapter 11) Quantum mechanics: Microscopic theory of light & matter at molecular scale and smaller. Atoms and radiation (light) have both wave-like and particlelike
More informationQuantum Theory of Light
King Saud University College of Applied Studies and Community Service Department of Natural Sciences Quantum Theory of Light General Physics II PHYS 111 Nouf Alkathran nalkathran@ksu.edu.sa Outline Definition
More informationThe Photoelectric Effect
The Photoelectric Effect Light can strike the surface of some metals causing an electron to be ejected No matter how brightly the light shines, electrons are ejected only if the light has sufficient energy
More informationThe 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 informationSharif University of Technology Physics Department. Modern Physics Spring 2016 Prof. Akhavan
Sharif University of Technology Physics Department Modern Physics Spring 2016 Prof. Akhavan Problems Set #5. Due on: 03 th of April / 15 th of Farvardin. 1 Blackbody Radiation. (Required text book is Modern
More information27-1 Planck Solves the Ultraviolet Catastrophe
27-1 Planck Solves the Ultraviolet Catastrophe By the end of the 19 th century, most physicists were confident that the world was well understood. Aside from a few nagging questions, everything seemed
More informationExplain how line spectra are produced. In your answer you should describe:
The diagram below shows the line spectrum of a gas. Explain how line spectra are produced. In your answer you should describe: how the collisions of charged particles with gas atoms can cause the atoms
More informationDownloaded from
7. DUAL NATURE OF MATTER & RADIATION GIST ELECTRON EMISSION 1. There are three types of electron emission, namely, Thermionic Emission, Photoelectric Emission and Field Emission. 2. The minimum energy
More informationPhysics 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 informationChapter 39. Particles Behaving as Waves
Chapter 39 Particles Behaving as Waves 39.1 Electron Waves Light has a dual nature. Light exhibits both wave and particle characteristics. Louis de Broglie postulated in 1924 that if nature is symmetric,
More informationDUAL NATURE OF RADIATION AND MATTER
Chapter Eleven DUAL NATURE OF RADIATION AND MATTER MCQ I 111 A particle is dropped from a height H The de Broglie wavelength of the particle as a function of height is proportional to (a) H (b) H 1/2 (c)
More informationChapter 28 Quantum Theory Lecture 24
Chapter 28 Quantum Theory Lecture 24 28.1 Particles, Waves, and Particles-Waves 28.2 Photons 28.3 Wavelike Properties Classical Particles 28.4 Electron Spin 28.5 Meaning of the Wave Function 28.6 Tunneling
More informationSECTION A Quantum Physics and Atom Models
AP Physics Multiple Choice Practice Modern Physics SECTION A Quantum Physics and Atom Models 1. Light of a single frequency falls on a photoelectric material but no electrons are emitted. Electrons may
More informationElectronic structure of atoms
Chapter 1 Electronic structure of atoms light photons spectra Heisenberg s uncertainty principle atomic orbitals electron configurations the periodic table 1.1 The wave nature of light Much of our understanding
More information5.111 Principles of Chemical Science
MIT OpenCourseWare http://ocw.mit.edu 5.111 Principles of Chemical Science Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.111 Lecture Summary
More informationChapter 30 Quantum Physics 30.1 Blackbody Radiation and Planck s Hypothesis of Quantum Energy 30.2 Photons and the Photoelectric Effect 30.
Chapter 30 Quantum Physics 30.1 Blackbody Radiation and Planck s Hypothesis of Quantum Energy 30.2 Photons and the Photoelectric Effect 30.3 The Mass and Momentum of a Photon 30.4 Photon Scattering and
More informationGen. Phys. II Exam 4 - Chs. 27,28,29 - Wave Optics, Relativity, Quantum Physics Apr. 16, 2018
Gen. Phys. II Exam 4 - Chs. 27,28,29 - Wave Optics, Relativity, Quantum Physics Apr. 16, 2018 Rec. Time Name For full credit, make your work clear. Show formulas used, essential steps, and results with
More informationChapter 38. Photons and Matter Waves
Chapter 38 Photons and Matter Waves The sub-atomic world behaves very differently from the world of our ordinary experiences. Quantum physics deals with this strange world and has successfully answered
More informationRb, 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 informationAn object capable of emitting/absorbing all frequencies of radiation uniformly
1 IIT Delhi - CML 100:1 The shortfalls of classical mechanics Classical Physics 1) precise trajectories for particles simultaneous specification of position and momentum 2) any amount of energy can be
More information( ) # velocity. Wavelengths of massive objects. From Last Time. Wavelength of electron. Wavelength of 1 ev electron. A little complicated ( ) " = h mv
From Last Time Wavelengths of massive objects Light shows both particle and wavelike properties Matter shows both particle and wavelike properties. How can we make sense of this? debroglie wavelength =
More informationChapter 28. Atomic Physics
Chapter 28 Atomic Physics Quantum Numbers and Atomic Structure The characteristic wavelengths emitted by a hot gas can be understood using quantum numbers. No two electrons can have the same set of quantum
More informationOutline Chapter 9 The Atom Photons Photons The Photoelectron Effect Photons Photons
Outline Chapter 9 The Atom 9-1. Photoelectric Effect 9-3. What Is Light? 9-4. X-rays 9-5. De Broglie Waves 9-6. Waves of What? 9-7. Uncertainty Principle 9-8. Atomic Spectra 9-9. The Bohr Model 9-10. Electron
More informationA) 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 informationEarlier we learned that hot, opaque objects produce continuous spectra of radiation of different wavelengths.
Section7: The Bohr Atom Earlier we learned that hot, opaque objects produce continuous spectra of radiation of different wavelengths. Continuous Spectrum Everyone has seen the spectrum produced when white
More informationIntroduction. Classical vs Modern Physics. Classical Physics: High speeds Small (or very large) distances
Introduction Classical vs Modern Physics High speeds Small (or very large) distances Classical Physics: Conservation laws: energy, momentum (linear & angular), charge Mechanics Newton s laws Electromagnetism
More informationPhysical Electronics. First class (1)
Physical Electronics First class (1) Bohr s Model Why don t the electrons fall into the nucleus? Move like planets around the sun. In circular orbits at different levels. Amounts of energy separate one
More informationSometimes light acts like a wave Reminder: Schedule changes (see web page)
Announcements Sometimes light acts like a wave Reminder: Schedule changes (see web page) No class on Thursday 3/18 Exam 2 pushed back to Tues. 3/30 Today: Quantum Mechanics (Ch.13/14) Bright: Constructive
More information2.1- CLASSICAL CONCEPTS; Dr. A. DAYALAN, Former Prof & Head 1
2.1- CLASSICAL CONCEPTS; Dr. A. DAYALAN, Former Prof & Head 1 QC-2 QUANTUM CHEMISTRY (Classical Concept) Dr. A. DAYALAN,Former Professor & Head, Dept. of Chemistry, LOYOLA COLLEGE (Autonomous), Chennai
More informationLECTURE 6 QUANTUM PHYSICS II. Instructor: Shih-Chieh Hsu
LECTURE 6 QUANTUM PHYSICS II Instructor: Shih-Chieh Hsu Development of Quantum Mechanics 2 In 1862, Kirchhoff coined black body radiation or known as cavity radiation The experiments raised the question
More informationPhysics 1C Lecture 28C. "For those who are not shocked when they first come across quantum theory cannot possibly have understood it.
Physics 1C Lecture 28C "For those who are not shocked when they first come across quantum theory cannot possibly have understood it." --Neils Bohr Outline CAPE and extra credit problems Wave-particle duality
More informationFrom Last Time. Summary of Photoelectric effect. Photon properties of light
Exam 3 is Tuesday Nov. 25 5:30-7 pm, 203 Ch (here) Students w / scheduled academic conflict please stay after class Tues. Nov. 8 (TODAY) to arrange alternate time. From Last Time Photoelectric effect and
More informationQuantum and Atomic Physics - Multiple Choice
PSI AP Physics 2 Name 1. The Cathode Ray Tube experiment is associated with: (A) J. J. Thomson (B) J. S. Townsend (C) M. Plank (D) A. H. Compton 2. The electron charge was measured the first time in: (A)
More informationChapter 9: Quantization of Light
Chapter 9: Quantization of Light Max Planck started the revolution of quantum theory by challenging the classical physics and the classical wave theory of light. He proposed the concept of quantization
More informationAlan Mortimer PhD. Ideas of Modern Physics
Alan Mortimer PhD Ideas of Modern Physics Electromagnetic Waves Last Week Special Relativity General Relativity The Quantum World Index Planck s Law Atomic Structure and emission lines Matter waves Uncertainty
More informationFundamental of Spectroscopy for Optical Remote Sensing Xinzhao Chu I 10 3.4. Principle of Uncertainty Indeterminacy 0. Expression of Heisenberg s Principle of Uncertainty It is worth to point out that
More informationChapter 31 Atomic Physics
100 92 86 100 92 84 100 92 84 98 92 83 97 92 82 96 91 80 96 91 76 95 91 74 95 90 68 95 89 67 95 89 66 94 87 93 86 No. of Students in Range Exam 3 Score Distribution 25 22 20 15 10 10 5 3 2 0 0 0 0 0 0
More informationPhysics 116. Nov 21, Session 31 De Broglie, duality, and uncertainty. R. J. Wilkes
Physics 116 Session 31 De Broglie, duality, and uncertainty Nov 21, 2011 R. J. Wilkes Email: ph116@u.washington.edu Announcements HW 6 due today Clicker scores have been updated on Webassign gradebook
More informationCHEMISTRY Matter and Change
CHEMISTRY Matter and Change Chapter 5: Electrons in Atoms 5 Section 5.1 Section Section 5.3 Table Of Contents Light and Quantized Energy Electron Configuration Compare the wave and particle natures of
More informationPhysics 280 Quantum Mechanics Lecture
Spring 2015 1 1 Department of Physics Drexel University August 3, 2016 Objectives Review Early Quantum Mechanics Objectives Review Early Quantum Mechanics Schrödinger s Wave Equation Objectives Review
More informationChapter 5. The Electromagnetic Spectrum. What is visible light? What is visible light? Which of the following would you consider dangerous?
Which of the following would you consider dangerous? X-rays Radio waves Gamma rays UV radiation Visible light Microwaves Infrared radiation Chapter 5 Periodicity and Atomic Structure 2 The Electromagnetic
More informationCHAPTER 28 Quantum Mechanics of Atoms Units
CHAPTER 28 Quantum Mechanics of Atoms Units Quantum Mechanics A New Theory The Wave Function and Its Interpretation; the Double-Slit Experiment The Heisenberg Uncertainty Principle Philosophic Implications;
More informationParticle nature of light & Quantization
Particle nature of light & Quantization A quantity is quantized if its possible values are limited to a discrete set. An example from classical physics is the allowed frequencies of standing waves on a
More informationModern Physics. Overview
Modern Physics Overview History ~1850s Classical (Newtonian) mechanics could not explain the new area of investigation atomic physics Macro vs Micro New field of Quantum Mechanics, focused on explaining
More informationPHYS 280 Practice Final Exam Summer Choose the better choice of all choices given.
PHYS 280 Practice Final Exam Summer 2016 Name: Multiple Choice Choose the better choice of all choices given. 1. Which of the following isn t a truth about quantum mechanics? A. Physicists are at a consensus
More information4/14/2015. Models of the Atom. Quantum Physics versus Classical Physics The Thirty-Year War ( ) Classical Model of Atom
Quantum Physics versus Classical Physics The Thirty-Year War (1900-1930) Models of the Atom Interactions between Matter and Radiation Models of the Atom Bohr s Model of the Atom Planck s Blackbody Radiation
More informationLecture 8: Wave-Particle Duality. Lecture 8, p 2
We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery.
More informationEnergy levels and atomic structures lectures chapter one
Structure of Atom An atom is the smallest constituent unit of ordinary matter that has the properties of a element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are
More information