Physics Particles and Waves

AP Learning Objectives ATOMIC AND NUCLEAR PHYSICS Atomic physics and quantum effects Photons, the photoelectric effect, Compton scattering, x-rays Students should know the properties of photons, so they can: Relate the energy of a photon in joules or electron-volts to its wavelength or frequency. Relate the linear momentum of a photon to its energy or wavelength, and apply linear momentum conservation to simple processes involving the emission, absorption, or reflection of photons. Calculate the number of photons per second emitted by a monochromatic source of specific wavelength and power.

AP Learning Objectives ATOMIC AND NUCLEAR PHYSICS Atomic physics and quantum effects Photons, the photoelectric effect, Compton scattering, x-rays Students should understand the photoelectric effect, so they can: Describe a typical photoelectric-effect experiment, and explain what experimental observations provide evidence for the photon nature of light. Describe qualitatively how the number of photoelectrons and their maximum kinetic energy depend on the wavelength and intensity of the light striking the surface, and account for this dependence in terms of a photon model of light. Determine the maximum kinetic energy of photoelectrons ejected by photons of one energy or wavelength, when given the maximum kinetic energy of photoelectrons for a different photon energy or wavelength. Sketch or identify a graph of stopping potential versus frequency for a photoelectric-effect experiment, determine from such a graph the threshold frequency and work function, and calculate an approximate value of h/e.

AP Learning Objectives ATOMIC AND NUCLEAR PHYSICS Atomic physics and quantum effects Photons, the photoelectric effect, Compton scattering, x-rays Students should understand Compton scattering, so they can: Describe Compton’s experiment, and state what results were observed and by what sort of analysis these results may be explained. Account qualitatively for the increase of photon wavelength that is observed, and explain the significance of the Compton wavelength. Students should understand the nature and production of x-rays, so they can calculate the shortest wavelength of x-rays that may be produced by electrons accelerated through a specified voltage.

AP Learning Objectives ATOMIC AND NUCLEAR PHYSICS Atomic physics and quantum effects Wave-particle duality Students should understand the concept of de Broglie wavelength, so they can: Calculate the wavelength of a particle as a function of its momentum. Describe the Davisson-Germer experiment, and explain how it provides evidence for the wave nature of electrons.

Table of Contents The Wave-Particle Duality Blackbody Radiation and Planck’s Constant Photons and the Photoelectric Effect The Momentum of a Photon and the Compton Effect The De Broglie Wavelength and the Wave Nature of Matter The Heisenberg Uncertainty Principle

Chapter 29: Particles and Waves Section 1: The Wave-Particle Duality

Wave-Particle Duality When a beam of electrons is used in a Young’s double slit experiment, a fringe pattern occurs, indicating interference effects. Waves can exhibit particle-like characteristics Particles can exhibit wave-like characteristics.

29.1.1. A beam of electrons is directed at two narrow slits and the resulting pattern is observed on a screen that produces a flash whenever an electron strikes it. What is the most surprising observation that is made in this experimental apparatus? a) The electrons do not all strike the screen at the same location. b) The electrons produce flashes on the screen. c) The pattern on the screen is an interference pattern. d) The shadow of the two slits is observed on the screen. e) The electrons produce the same pattern on the screen with or without the slits in place.

29.1.2. Which one of the following experiments demonstrates the wave nature of electrons? a) Small flashes of light can be observed when electrons strike a special screen. b) Electrons directed through a double slit can produce an interference pattern. c) The Michelson-Morley experiment confirmed the existence of electrons and their nature. d) In the photoelectric effect, electrons are observed to interfere with electrons in metals. e) Electrons are observed to interact with photons (light particles).

Chapter 29: Particles and Waves Section 2: Blackbody Radiation & Planck’s Constant

Blackbody Radiation All bodies, no matter how hot or cold, continuously radiate electromagnetic waves. Electromagnetic energy is quantized. frequency Planck’s constant

29.2.1. Which one of the following processes occurs when a charged atomic particle emits radiation? a) The particle’s charge is reduced. b) The particle turns into a light particle (photon). c) The particle shows no physical changes. d) The particle changes from a higher energy state to a lower energy state. e) The particle turns into a wave.

29.2.2. Upon which one of the following parameters does the energy of a photon depend? a) the mass of the photon b) the amplitude of the electric field c) the direction of the electric field d) the relative phase of the electromagnetic wave relative to the source that produced it e) the frequency of the photon

29. 2. 3. Two quantum oscillator energy levels are 7 29.2.3. Two quantum oscillator energy levels are 7.572 × 1019 J and 1.136 × 1018 J. Determine the frequency of the photon that is emitted from this atom when a transition is made between these two levels and determine n for the lower energy level. a) 2.571 × 1014 Hz b) 2.478 × 1014 Hz c) 3.381 × 1014 Hz d) 3.422 × 1014 Hz e) 4.369 × 1014 Hz

Chapter 29: Particles and Waves Section 3: Photons & the Photoelectric Effect

Photons Electromagnetic waves are composed of particle-like entities called photons.

Photoelectric Effect Experimental evidence that light consists of photons comes from a phenomenon called the photoelectric effect. The “Magic Brick Wall”

Photoelectric Effect When light shines on a metal, a photon can give up its energy to an electron in that metal. The minimum energy required to remove the least strongly held electrons is called the work function.

Graph of Kinetic Energy

Example 2 The Photoelectric Effect for a Silver Surface The work function for a silver surface is 4.73 eV. Find the minimum frequency that light must have to eject electrons from the surface.

Photoelectric Effect in Digital Cameras

Photoelectric Effect in Light Sensors

29.3.1. In the photoelectric effect experiment, what type of energy process is occurring? a) Kinetic energy is transformed into thermal energy. b) Thermal energy is transformed into electromagnetic energy. c) Radiant energy is transformed into kinetic energy. d) Electromagnetic energy is transformed into thermal energy. e) Radiant energy is transformed into potential energy.

29.3.2. Why can we not see individual photons, but rather light appears to us to be continuous? a) A light beam contains a multitude of photons, each with a very small amount of energy. b) The wave part of a photon superposes with the wave part of other photons in the beam, making the beam appear to be continuous. c) The wave part of the photon extends over a spatial region that is larger than our eyes can detect. d) The particle properties of photons do not interact with our eyes. e) Each photon carries information from the whole electromagnetic spectrum; and our eyes cannot interpret this information.

29.3.3. Consider the photoelectric effect experiment from the point of view of classical (or Newtonian) physics. Which one of the following is not one of the effects you would predict from a classical point of view? a) There should be a measurable time delay between the time that light first strikes the metal surface and the time when electrons are first emitted from the surface of the metal. b) The kinetic energy of the emitted electrons should vary linearly with the frequency of light shining on the metal. c) Light of any frequency shining on the metal surface should cause electrons to be emitted. d) The kinetic energy of the emitted electrons should increase proportionately to the intensity of the light.

29.3.4. A special camera has been designed that opens and closes its shutter for a very short time. A picture of an illuminated object is taken with this camera. When the film is developed, only tiny, bright dots appear randomly distributed on the picture. What does this experiment tell us about the nature of light? a) The dots are an interference pattern, which proves the wave nature of light. b) The small number of dots indicates that light waves were cut off by the shutter as it closed. c) The camera lens could not focus the light waves at a point on the film with such a short time. d) The random distribution of dots shows the particle nature of light.

29.3.5. When the photoelectric effect experiments were performed, one effect was inconsistent with classical physics. What was it? a) The kinetic energy of the ejected electrons did not vary with light intensity. b) The fact that electrons could form a current within a vacuum. c) The kinetic energy of the ejected electrons increased as the frequency of light increased. d) The fact that light could free electrons from the surface of a metal. e) The kinetic energy of the ejected electrons increased as the wavelength of light decreased.

29.3.6. What was a surprising result of the photoelectric effect experiments? a) The electrons behaved like matter waves. b) Below a certain frequency, no electrons could be ejected from the metal surface. c) Individual photons behaved like waves. d) Above a certain light frequency, the current became zero amperes. e) Light was proven to exhibit only a wave nature.

29.3.7. If light only had wave-like properties, you would not expect there to be a cutoff frequency. Why is this true? a) Only particles can eject electrons from a surface. b) The energy of a wave does not depend on its frequency. c) Light waves of lower frequency would still be able to eject electrons. d) An electromagnetic wave would be able to eject an electron from a surface. It would just take longer. e) None of the above answers are correct.

29.3.8. In an ideally dark room, a double-slit experiment is carried out using a source that releases one photon at a time at a slow rate. The observation screen in the experiment is replaced with photographic film which provides a recording of the photons striking it over time. After some time has passed, the film is removed and developed into a photograph. What is observed on the photograph? a) two bright bands that correspond to the two slits b) an interference pattern c) a single bright band d) It’s impossible to guess.

29.3.9. If a double-slit experiment is carried out using a source that releases one photon at a time at a slow rate, an interference pattern may be observed if the screen is replaced with photographic film. What produces the interference? a) Each photon interferes with the photons that have previously passed through a slit. b) Each photon interferes with the photons that pass through the slit after it. c) Each photon interferes with all of the photons that ever go through the slit. d) Each photon interferes with itself. e) Each photon interferes with the slit.

Chapter 29: Particles and Waves Section 4: The Momentum of a Photon & the Compton Effect

Momentum of Light? Arthur Compton directed Xrays at a sample of graphite, and found that the frequency of the scattered light was a different frequency The scattered photon and the recoil electron depart the collision in different directions. Due to conservation of energy, the scattered photon must have a smaller frequency. This is called the Compton effect.

Derivation of Compton Wavelength Energy is conserved in the collision. Solve for (pec)2

Derivation of Compton Wavelength Momentum is conserved in the collision.

Derivation of Compton Wavelength Divide both sides by 2hfofmec

Conceptual Example 4 Solar Sails and the Propulsion of Spaceships One propulsion method that is currently being studied for interstellar travel uses a large sail. The intent is that sunlight striking the sail creates a force that pushes the ship away from the sun, much as wind propels a sailboat. Does such a design have any hope of working and, if so, should the surface facing the sun be shiny like a mirror or black, in order to produce the greatest force?

29.4.1. A photon of wavelength Δ and frequency f strikes an electron that is initially at rest. Which one of the following processes occurs as a result of this collision? a) The photon gains energy, so the final photon has a frequency greater than f. b) The photon loses energy, so the final photon has a frequency less than f. c) The photon loses energy, so the final photon has a wavelength less than l. d) The photon gains energy, so the final photon has a wavelength greater than l. e) The photon is completely absorbed by the electron.

29.4.2. An x-ray photon with an initial wavelength  strikes an electron that is initially at rest. Which one of the following statements best describes the wavelength of the photon after the collision? a) No photon remains after the collision. b) The scattered photon’s wavelength will still be , but its frequency will decrease. c) The scattered photon’s wavelength will be longer than . d) The scattered photon’s wavelength will be /2. e) The scattered photon’s wavelength will be between /2 and .

29. 4. 3. X-rays with a wavelength of 0 29.4.3. X-rays with a wavelength of 0.10 nm are scattered from an argon atom. The scattered x-rays are detected at an angle of 85 relative to the incident beam. What is the Compton shift for the scattered x-rays? a) 0.0022 nm b) 0.011 nm c) 0.022 nm d) 0.041 nm e) 0.12 nm

Chapter 29: Particles and Waves Section 5: The De Broglie Wavelength & the Wave Nature of Matter

Wave Nature of Matter? http://www.youtube.com/watch?v=DfPeprQ7oGc

The de Broglie Wavelength The wavelength of a particle is given by the same relation that applies to a photon:

Example 5 The de Broglie Wavelength of an Electron and a Baseball Determine the de Broglie wavelength of (a) an electron moving at a speed of 6.0x106 m/s and (b) a baseball (mass = 0.15 kg) moving at a speed of 13 m/s.

29.5.1. Estimate the de Broglie wavelength of a honey bee flying at its maximum speed. a) A honey bee cannot have a wavelength. b) 2  1018 m c) 5  1032 m d) 4  1036 m e) 1  1040 m

29.5.2. What is the de Broglie wavelength of a particle, such as an electron, at rest? a) The wavelength would be zero meters. b) The wavelength would be infinitely small and not measureable. c) This has no meaning. The de Broglie wavelength only applies to moving particles. d) Davisson and Germer measured this wavelength in their apparatus and found it to be around 1010 m.

Chapter 29: Particles and Waves Section 6: The Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle Momentum and position Uncertainty in particle’s position along the y direction Uncertainty in y component of the particle’s momentum

The Heisenberg Uncertainty Principle Energy and time time interval during which the particle is in that state Uncertainty in the energy of a particle when the particle is in a certain state

Conceptual Example 7 What if Planck’s Constant Were Large? A bullet leaving the barrel of a gun is analogous to an electron passing through the single slit. With this analogy in mind, what would hunting be like if Planck’s constant has a relatively large value?

29.6.1. Which one of the following statements provides the best description of the Heisenberg Uncertainty Principle? a) If a particle is confined to a region x, then its momentum is within some range p. b) If the error in measuring the position is x, then we can determine the error in measuring the momentum p. c) If one measures the position of a particle, then the value of the momentum will change. d) It is not possible to be certain of any measurement. e) Depending on the degree of certainty in measuring the position of a particle, the degree of certainty in measuring the momentum is affected.

29.6.2. The position along the x axis of an electron is known to be between 0.31 nm and + 0.31 nm. How would the uncertainty in the momentum of the electron change if the electron were allowed to be between 0.62 nm and +0.62 nm? a) The uncertainty in the momentum would be twice its previous value. b) The uncertainty in the momentum would be half of its previous value. c) The uncertainty in the momentum would not be affected by this change. d) The uncertainty in the momentum would be four times its previous value. e) The uncertainty in the momentum would be one fourth its previous value.

END