Physics 237, Midterm Exam #1

Thursday February 18, 2010

12.30 pm – 1.45 pm

Do not turn the pages of the exam until you are instructed to do so.

Exam rules: You may use only a writing instrument while taking this test.  You may not consult any calculators, computers, books, or each other.

1.     Problems 1 and 2 must be answered in booklet # 1.

2.     Problems 3 and 4 must be answered in booklet # 2.

3.     The answers need to be well motivated and expressed in terms of the variables used in the problem.  You will receive partial credit where appropriate, but only when we can read your solution.  Answers that are not motivated will not receive any credit, even if correct.

At the end of the exam, you need to hand in your exam, your “cheat sheet”, and the two blue exam booklets.  All items must be clearly labeled with your name, your student ID number, and the day/time of your workshop.

Name:  __________________________________________________

ID number:  ______________________________________________

Workshop Day/Time:  ______________________________________

Problem 1 (35 points)                                                                       ANSWER IN BOOKLET 1

Consider a particle of mass m moving with a linear momentum p.  Assume the velocity of the particle is much less than the speed of light and relativistic effects do not need to be considered.  In order to describe the particle in terms of a matter wave, we first consider the following matter wave: a)     What is the propagation velocity of this matter wave?  Specify both the magnitude and the direction of the propagation velocity.  Express your answer in terms of k and n.

b)    How does the propagation velocity of the matter wave compare with the velocity of the particle?

Now consider that we describe the particle by the following matter wave: where dk << k and dn << n.

c)     This matter wave has a low- and a high-frequency component.  What are the propagation velocities associated with the low- and the high-frequency components?  Specify both the magnitude and the direction of these propagation velocities.  Express your answers in terms of k, n, dk, and dn.

d)    How do the propagation velocities of the matter wave obtained in c) compare with the velocity of the particle?

Your answers need to be well motivated.  A correct answer without any motivation will not receive any credit.

Problem 2 (30 points)                                                                       ANSWER IN BOOKLET 1

Consider a photon with an energy Eg travelling in a vacuum.  The energy of the photon is larger than 2 times the rest energy of the electron (Eg  > 2 mec2).

a)     Can the photon convert all of its energy by creating an electron-positron pair?  If you answer is yes, calculate the total kinetic energy of the electron and the positron.  If your answer is no, show why this process cannot happen in a vacuum.

Now consider a photon with an energy Eg producing an electron-positron pair in the vicinity of a nucleus of mass M.  The positron is at rest while the electron has a kinetic energy equal to 2 mec2 and moves in the same direction as the pair-producing photon was moving.

b)    What was the energy of the pair-producing photon?

c)     What fraction of the photon’s linear momentum is transferred to the nucleus?

Problem 3 (30 points)                                                                       ANSWER IN BOOKLET 2

The graph shows the voltage dependence of the current you measure in the Franck-Hertz experiment you carry out in the advanced laboratory. a)     Based on the information provided in the Figure, construct an energy-level diagram of the atoms used in the experiment.

b)    What are the energies of the photons that are emitted by the atoms used in the experiment when the experiment is operated with an accelerating potential of 7 V? Consider the two-slit experiment used to observe electron diffraction shown in the Figure.  The condition for constructive interference is .  The distance between adjacent maxima on the screen is .

c)     After observing the interference pattern we install a monitor system that determines the position of the electron just behind the slit screen with an accuracy so that we can tell through which slit each electron went.  Show that this measurement will wipe out the interference pattern.

Problem 4 (5 points)                                                                         ANSWER IN BOOKLET 2

How many times did the Yankees win the world series? 1.     4

2.     25

3.     27

4.     45