Intermediate Physics PHYS102

Transcription

1 Intermediate Physics PHYS102

2 Dr Richard H. Cyburt Assistant Professor of Physics My office: 402c in the Science Building My phone: (304) My My webpage: In person or is the best way to get a hold of me. PHYS102

3 My Office Hours TWR 9:30-11:00am W 4:00-5:00pm Meetings may also be arranged at other times, by appointment PHYS102

4 Problem Solving Sections I would like to have hour-long sections for working through problems. This would be an extra component to the course and count towards extra credit TR 1-2 pm WF am S308 If you can t make these, you can still pick up the problem worksheet. PHYS102

5 Midterm 3 Bonus assignment is up Due Thursday, April 20 5:59pm PHYS102

6 Final Exam Pizza Party review??? Donations of $1, please. Review Monday, May 1 6pm-10pm in S300 Starting with the Pizza Final Exam Tuesday, May 2: 9:00-11:15am PHYS102

7 Joint Spring Meeting of the Appalachian and Chesapeake Sections of the AAPT Saturday, April 22 at Concord University ($15/students/guests, $25/AAPT) 8:00 8:45 Registration and Continental Breakfast 8:45 11:45 Contributed Talks and Demos I 11:45 12:45 Lunch 12:45 1:30 Poster Session 1:30 2:30 Invited lecture 2:30 3:15 Contributed Talks and Demos II 3:15 4:15 Invited workshop 4:15 5:00 CSAAPT Business Meeting (all are welcome) Invited lecture: Astrophysical Hoyle State Enhancement, Dr. Richard H. Cyburt, Concord University Invited Workshop: Women and Minorities in the History of Physics, Role Models for Today, Dr. Gregory Good, The Spencer Weart Director, Center for History of Physics American Institute of Physics PHYS102

8 Intermediate Physics PHYS102

9 Douglas Adams Hitchhiker s Guide to the Galaxy PHYS102

10 In class!! PHYS102

11 This lecture will help you understand: Relativistic Momentum Relativisitic Energy The Photoelectric Effect PHYS102

12 Section 27.9 Relativistic Momentum

13 Relativistic Momentum In Newtonian physics, the total momentum of a system is a conserved quantity. If we use Lorentz transformations, we see Newtonian momentum p = mu is not conserved in a frame moving relative to a frame in which momentum is conserved. Momentum conservation is a central and important feature of mechanics, so it seems likely it will hold in relativity as well.

14 Relativistic Momentum A relativistic analysis of particle collisions shows that momentum conservation does hold, provided we redefine the momentum of a particle as This reduces to the classical momentum p = mu when the particle s speed u << c. We define the quantity

15 Example 27.8 Momentum of a subatomic particle Electrons in a particle accelerator reach a speed of 0.999c relative to the laboratory. One collision of an electron with a target produces a muon that moves forward with a speed of 0.950c relative to the laboratory. The muon mass is kg. What is the muon s momentum in the laboratory frame and in the frame of the electron beam?

16 Example 27.8 Momentum of a subatomic particle (cont.) PREPARE Let the laboratory be reference frame S. The reference frame Sʹ of the electron beam (i.e., a reference frame in which the electrons are at rest) moves in the direction of the electrons at v = 0.999c. The muon velocity in frame S is u = 0.95c.

17 Example 27.8 Momentum of a subatomic particle (cont.) SOLVE g for the muon in the laboratory reference frame is

18 Example 27.8 Momentum of a subatomic particle (cont.) Thus the muon s momentum in the laboratory is

19 Example 27.8 Momentum of a subatomic particle (cont.) The momentum is a factor of 3.2 larger than the Newtonian momentum mu. To find the momentum in the electron-beam reference frame, we must first use the velocity transformation equation to find the muon s velocity in frame Sʹ:

20 Example 27.8 Momentum of a subatomic particle (cont.) In the laboratory frame, the faster electrons are overtaking the slower muon. Hence the muon s velocity in the electron-beam frame is negative. gʹ for the muon in frame Sʹ is

21 Example 27.8 Momentum of a subatomic particle (cont.) The muon s momentum in the electron-beam reference frame is

22 Example 27.8 Momentum of a subatomic particle (cont.) ASSESS From the laboratory perspective, the muon moves only slightly slower than the electron beam. But it turns out that the muon moves faster with respect to the electrons, although in the opposite direction, than it does with respect to the laboratory.

23 The Cosmic Speed Limit For a Newtonian particle with p = mu, the momentum is directly proportional to the velocity. The relativistic expression for momentum agrees with the Newtonian value if u << c, but p approaches as u approaches c.

24 The Cosmic Speed Limit From the impulse-momentum theorem we know Δp = mu = Ft. If Newtonian physics were correct, the velocity of a particle would increase without limit. We see from relativity that the particle s velocity approaches c as the momentum approaches.

25 The Cosmic Speed Limit The speed c is the cosmic speed limit for material particles. A force cannot accelerate a particle to a speed higher than c because the particle s momentum becomes infinitely large as the speed approaches c. The amount of effort required for each additional increment of velocity becomes larger and larger until no amount of effort can raise the velocity any higher.

26 The Cosmic Speed Limit At a fundamental level, c is the speed limit for any kind of causal influence. A causal influence can be any kind of particle, wave, or information that travels from A to B and allows A to be the cause of B. For two unrelated events, the relativity of simultaneity tells us that in one reference frame, A could happen before B, but in another reference frame, B could happen before A.

27 The Cosmic Speed Limit For two causally related events A causes B it would be nonsense for an experimenter in any reference frame to find that B occurs before A. According to relativity, a causal influence traveling faster than the speed of light could result in B causing A, a logical absurdity. Thus, no causal events of any kind a particle, wave, or other influence can travel faster than c.

28 Section Relativistic Energy

29 Relativistic Energy Space, time, velocity, and momentum are changed by relativity, so it seems inevitable that we ll need a new view of energy. One of the most profound results of relativity is the fundamental relationship between energy and mass. Einstein found that the total energy of an object of m mass moving at speed u is

30 Relativistic Energy Let s examine the behavior of objects traveling at speeds much less than the speed of light. We use the binomial approximation to find For low speeds, u, the object s total energy is then The second term is the Newtonian kinetic energy. The additional term is the rest energy given by

31 Example 27.9 The rest energy of an apple What is the rest energy of a 200 g apple? SOLVE From Equation we have E 0 = mc 2 = (0.20 kg)( m/s) 2 = J ASSESS This is an enormous energy, enough to power a medium-sized city for about a year.

32 Relativistic Energy For high speeds, we must use the full expression for energy. We can find the relativistic expression for kinetic energy K by subtracting the rest energy E 0 from the total energy: Thus we can write the total energy of an object of mass m as

33 Example Comparing energies of a ball and an electron Calculate the rest energy and the kinetic energy of (a) a 100 g ball moving with a speed of 100 m/s and (b) an electron with a speed of 0.999c. PREPARE The ball, with u << c, is a classical particle. We don t need to use the relativistic expression for its kinetic energy. The electron is highly relativistic.

34 Example Comparing energies of a ball and an electron (cont.) SOLVE a. For the ball, with m = kg,

35 Example Comparing energies of a ball and an electron (cont.) b. For the electron, we start by calculating Then, using m e = kg,

36 Example Comparing energies of a ball and an electron (cont.) ASSESS The ball s kinetic energy is a typical kinetic energy. Its rest energy, by contrast, is a staggeringly large number. For a relativistic electron, on the other hand, the kinetic energy is more important than the rest energy.

37 The Equivalence of Mass and Energy Now we are ready to explore the significance of Einstein s famous equation E = mc 2. When a high-energy electron collides with an atom in the target material, it can knock one electron out of the atom. Thus we would expect to see two electrons: the incident electron and the ejected electron.

38 The Equivalence of Mass and Energy Instead of two electrons, four particles emerge from the target: three electrons and a positron. A positron is the antimatter of an electron. It is identical to the electron in all respects other than having a charge q = +e. The positron has the same mass m e as an electron.

39 The Equivalence of Mass and Energy In chemical-reaction notation, the collision is The electron and positron appear to have been created out of nothing. Although the mass increased, it was not out of nothing : The new particles were created out of energy.

40 The Equivalence of Mass and Energy Not only can particles be created out of energy, particles can return to energy. When a particle and an antiparticle meet, they annihilate each other. The mass disappears, and the energy equivalent of the mass is transformed into two high-energy photons.

41 Conservation of Energy Neither mass nor the Newtonian definition of energy is conserved, however the total energy the kinetic energy and the energy equivalent of mass remains a conserved quantity.

42 Conservation of Energy The most well-known application of the conservation of total energy is nuclear fission. The Uranium isotope 236 U, containing 236 protons and neutrons, does not exist in nature. It can be created when a 235 U nucleus absorbs a neutron, increasing its atomic mass. The 236 U nucleus quickly fragments into two smaller nuclei and several extra neutrons in a process called nuclear fission. One way it fissions is

43 Conservation of Energy The mass after the 236 U fission is u less than the mass before the fission. The mass has been lost, but the equivalent energy of the mass has not. It has been converted to kinetic energy: ΔK = m lost c 2 The energy released from one fission is small, but the energy from all the nuclei fission is enormous.

44 Conservation of Energy

45 QuickCheck An electron has rest energy 0.5 MeV. An electron traveling at 0.968c has g p = 4. The electron s kinetic energy is 1.0 MeV 1.5 MeV 2.0 MeV 4.0 MeV I would need my calculator and several minutes to figure it out.

46 QuickCheck An electron has rest energy 0.5 MeV. An electron traveling at 0.968c has g p = 4. The electron s kinetic energy is 1.0 MeV K = (g p 1)E MeV 2.0 MeV 4.0 MeV I would need my calculator and several minutes to figure it out.

47 QuickCheck A proton has rest energy 938 MeV. A proton and an antiproton are each traveling at the same slow (g p << 1) speed in opposite directions. They collide and annihilate. What is the outcome? Each is a photon. A. D.A or C B. C. E.All are possible outcomes

48 QuickCheck A proton has rest energy 938 MeV. A proton and an antiproton are each traveling at the same slow (g p << 1) speed in opposite directions. They collide and annihilate. What is the outcome? Each is a photon. D.A or C E.All are possible outcomes A. B. C. The outcome must conserve both energy (1876 MeV) and momentum (0).

49 Example Problem Through what potential difference must an electron be accelerated to reach a speed 99% of the speed of light? The mass of an electron is kg.

50 Section 28.2 The Photoelectric Effect

51 The Photoelectric Effect The first hints about the photon nature of light came with discovery that a negatively charged electroscope could be discharged by shining UV light on it. The emission of electrons from a substance due to light striking its surface is called the photoelectric effect.

52 Characteristics of the Photoelectric Effect An experimental device to study the photoelectric effect.

53 Characteristics of the Photoelectric Effect When UV light shines on the cathode, a steady counterclockwise current passes through the ammeter. The incident light causes electrons to be ejected from the cathode at a steady rate. There is no current if the electrodes are in the dark, so electrons don t spontaneously leap off the cathode.

54 Characteristics of the Photoelectric Effect The battery in this device establishes an adjustable potential difference ΔV between the two electrodes. With it, we can study how the current I varies as the potential difference and the light s wavelength and intensity are changed.

55 Characteristics of the Photoelectric Effect The photoelectric effect has the following characteristics: 1. The current I is directly proportional to the light intensity. If the light intensity is doubled, the current also doubles. 2. The current appears without delay when the light is applied. 3. Electrons are emitted only if the light frequency f exceeds a threshold frequency f The value of the threshold frequency depends on the type of metal from which the cathode is made.

56 Characteristics of the Photoelectric Effect 5. If the potential difference ΔV is more than about 1 V positive (anode positive with respect to the cathode), the current changes very little as ΔV is increased. If ΔV is made negative (anode negative with respect to cathode), by reversing the battery, the current decreases until at some voltage ΔV = V stop the current reaches zero. The value of V stop is called the stopping potential. 6. The value of V stop is the same for both weak light and intense light. A more intense light causes a larger current, but in both cases the current ceases when ΔV = V stop.

57 Characteristics of the Photoelectric Effect The photoelectric current dependence on the light frequency f and the battery potential difference ΔV.

58 Characteristics of the Photoelectric Effect

59 QuickCheck 28.1 In this experiment, a current is detected when ultraviolet light shines on the metal cathode. What is the source or cause of the current? The battery The light The cathode

60 QuickCheck 28.1 In this experiment, a current is detected when ultraviolet light shines on the metal cathode. What is the source or cause of the current? The battery The light The cathode

61 Understanding the Photoelectric Effect A minimum energy is needed to free an electron from a metal. To extract an electron, you need to increase its energy until its speed is fast enough to escape. The minimum energy E 0 needed to free an electron is called the work function of the metal. Some electrons will require an energy greater than E 0 to escape, but all will require at least E 0.

62 Understanding the Photoelectric Effect

63 Understanding the Photoelectric Effect An electron with energy E elec inside a metal loses energy ΔE as it escapes, so it emerges as an electron with kinetic energy K = E elec ΔE. The work function energy E 0 is the minimum energy needed to remove an electron, so the maximum possible kinetic energy of an ejected electron is K max = E elec E 0

64 Understanding the Photoelectric Effect In the experimental device we used to study the photoelectric effect, the electrons, after leaving the cathode, move out in all directions. If the potential difference between the cathode and anode is ΔV = 0, there will be no electric field between the plates. Some electrons will reach the anode, creating a measurable current, but many do not.

65 Understanding the Photoelectric Effect In the photoelectric effect measuring device, if the anode is positive, it attracts all of the electrons to the anode. A further increase in ΔV does not cause any more electrons to reach the anode and thus does not cause a further increase in the current I.

66 Understanding the Photoelectric Effect In the photoelectric effect measuring device, if the anode is negative, it repels the electrons. However, an electron leaving the cathode with sufficient kinetic energy can still reach the anode. A slightly negative anode voltage turns back only the slowest electrons. The current steadily decreases as the anode voltage becomes increasingly negative until, at the stopping potential, all electrons are turned back and the current ceases.

67 Understanding the Photoelectric Effect We can use the conservation of energy to relate the maximum kinetic energy to the stopping potential. Electrons convert kinetic energy to potential energy as they slow down. ΔU = eδv = ΔK When ΔV = ΔV stop, the current ceases and the fastest electrons with K max are being turned back just as they reach the anode. 100% of their kinetic energy is converted to potential energy, so ev stop = K max or Measuring the stopping potential tells us the maximum kinetic energy of the electrons.

68 QuickCheck 28.2 In this experiment, a current is detected when ultraviolet light shines on the metal cathode. What happens to the current if the battery voltage is reduced to zero? The current is unchanged. The current decreases slightly. The current becomes zero. The current goes the other direction.

69 QuickCheck 28.2 In this experiment, a current is detected when ultraviolet light shines on the metal cathode. What happens to the current if the battery voltage is reduced to zero? The current is unchanged. The current decreases slightly. The current becomes zero. The current goes the other direction.