Physics 141, Midterm Exam #2

Thursday November 1, 2007

8.00 am – 9.30 am

 

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

 

You are responsible for reading the following rules carefully before beginning.

Exam rules: You may use only a writing instrument while taking this test.  You may not consult any calculators, computers, books, nor each other.

Answer the multiple-choice questions (problems 1 – 10) by marking your answer on the scantron form.  For each multiple-choice question (problems 1 – 10), select only one answer.  Questions with more than one answer selected will be considered incorrect.  Problems 11, 12, and 13 must be answered in the blue exam booklets (answer questions 11 and 12 in booklet 1 and question 13 in booklet 2.)  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, the blue exam booklets, and the scantron form.  All items must be clearly labeled with your name and student ID number.  If any of these items are missing, we will not grade your exam, and you will receive a score of 0 points.

NOTE: If your student ID is not listed properly on the Scantron form, the form will not be processed and you loose points for all multiple-choice questions.

 

Name:  __________________________________________________

 

ID number:  ______________________________________________

 

Recitation Day/Time:  ______________________________________


Useful Relations:

 

 

 

 

 

 

 

Problem 1 (2.5. points)

The typical energy level spacing of a set of states is 10-2 eV.  What type of states are we dealing with?

1.     Hadronic states.

2.     Nuclear states.

3.     Electronic states in atoms.

4.     Vibrational states in molecules.

5.     Rotational states in molecules.

 

Problem 2 (2.5 points)

 

 

The Figure shows a set of photographic images, taken at equal time intervals, of an object falling in the vertical direction under the influence of gravity.  Based on the images, what can you say about the drag force acting on the object?

1.     The drag force depends on the velocity of the object.

2.     The drag force does not depend on the velocity of the object.

3.     I need to have more information in order to be able to answer this question.

 

Problem 3 (2.5 points)

A cart on an air track is moving with a speed of 0.5 m/s when the air is suddenly turned off.  The cart comes to rest after traveling a distance of 1 m.  The experiment is repeated, but now the same cart is moving with a speed of 1 m/s when the air is turned off.  How far does the cart now travel before coming to rest?

1.     1 m.

2.     2 m.

3.     3 m.

4.     4 m.

5.     5 m.

6.     Impossible to determine.

 

Problem 4 (2.5 points)

A 3000-kg boat is being moved from a position <2 m, 0 m, 3 m> to a position <4 m, 0 m, 2 m>.  One of the two people moving the boat applies a force < -400 N, 0 N, 200 N>.  What is the work done by this person while the boat is being moved?

1.     -1200 J.

2.     -1000 J.

3.     -200 J.

4.     1000 J.

 

 

Problem 5 (2.5 points)

Some of the properties of the diatomic molecule NO can be described in terms of a simple model in which the two atoms are connected by a spring.  Experiments show that the spacing between allowed vibrational energy levels in NO is 0.23 eV.  Suppose you have a gas of 4 NO molecules.  One molecule's vibrational energy is in the ground state (n = 0), the second molecule is in the first excited state (n = 1), the third molecule is in the second excited state (n = 2), and the fourth molecule is in the third excited state (n = 3).  If we assume that all transitions from one excited states to lower-lying excited states occur with equal probability, what is the ratio of the intensities of 0.69 eV, 0.46 eV, and 0.23 eV photons?

1.     1:3:9.

2.     1:3:6.

3.     1:2:3.

4.     1:1:1.

 

Problem 6 (2.5 points)

Some of the properties of diatomic molecules NO and HCl can be described in terms of a simple model in which the two atoms are connected by a spring.  Experiments show that the spacing between allowed vibrational energy levels in NO is 0.23 eV and the spacing between levels in HCl is 0.35 eV.  The NO and HCl molecules have nearly the same mass.  Which molecule has the greater bond stiffness (spring constant)?

1.     NO.

2.     HCl.

3.     They have approximately the same bond stiffness.

 

Problem 7 (2.5 points)

 

A

B

C

D

E

 

Match the pictures of the ball parks shown above to the team names listed below.

1.     Yankees

2.     White Sox

3.     Mets

4.     Cubs

5.     Red Sox

ABCDE =

1.     12345

2.     21453

3.     21534

4.     31542

5.     31254

6.     42351

Problem 8 (2.5 points)

Consider the following potential energy distributions.  The horizontal axis shows the distance between the components of the system and the vertical axis shows the potential energy of the system.

Which of these distributions can represent the potential energy distribution of a two-electron system?

 

Problem 9 (2.5 points)

Consider the following potential energy distributions.  The horizontal axis shows the distance between the components of the system and the vertical axis shows the potential energy of the system.

Which of these distributions can represent the potential energy distribution between the two atoms of a diatomic system?

 

Problem 10 (2.5 points)

In positron-emission tomography (PET), used in medical research and diagnosis, compounds containing unstable nuclei that emit positrons are introduced into the brain, destined for a site of interest in the brain.  When a positron is emitted, it travels only a short distance before nearly coming to rest.  The positron forms a bound state with an electron, called positronium, which is rather similar to a hydrogen atom.  The binding energy of positronium is very small compared to the rest energy of an electron.  After a short time the positron and the electron annihilate.  In the annihilation, the positron and the electron disappear, and all their rest energy goes into two massless photons.  What is the energy of the photons that are emitted when positronium decays?  The mass of the electron or the positron is 511.0 keV/c2.

1.     1022.0 keV.

2.     766.5 keV.

3.     511.0 keV.

4.     255.5 keV.

 

 

Problem 11 (25 points)

A package of mass m sits at the equator of an airless asteroid of mass M and radius R.  The asteroid rotates around its rotation axis with a constant angular speed w.

 

 

We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with a speed v.  The package can be launched from the surface of the asteroid using a powerful spring with spring constant k.

a.     What is the total energy of the package when it is located on the surface of the asteroid?

b.     By how much do we have to compress the spring in order to ensure that the package travels with speed v when it is far away from the asteroid?

Assume that the speeds are well below the speed of light, and ignore the rest mass of the package.  Express all your answers in terms of the variables provided.  Your answers must be well motivated.

Problem 12 (25 points)

A material consisting of a collection of microscopic systems is kept at a high temperature.  A photon detector, capable of detecting photon energies from infrared through ultraviolet, observes photons emitted with energies of 0.3 eV, 0.5 eV, 0.8 eV, 2.0 eV, 2.5 eV, and 2.8 eV.  These are the only photon energies observed.

a.     Draw and label a possible energy-level diagram of a microscopic system that is consistent with the observed emission pattern.  On the diagram, indicate the transitions corresponding to the emitted photons.

b.     Would a spring-mass model be a good model for these microscopic systems?  Why or why not?

c.     The material is now cooled down to a very low temperature, and the photon detector stops detecting photon emission.  Next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material.  What photon energies in this beam are observed to be significantly reduced in intensity?  Explain.

 

Problem 13 (25 points)

The Stanford Linear Accelerator Center (SLAC), located at Stanford University in Palo Alto, California, accelerates electrons through a vacuum tube of length L.

 

 

Electrons of mass m, which are initially at rest, are subjected to a continuous force F along the entire length of the tube and reach speeds very close to the speed of light.

a.     Calculate the final energy of the electrons.

b.     Calculate the final momentum of the electrons.

c.     Calculate the final speed of the electrons.

d.     Calculate the time required to travel the distance L.

Express all your answers in terms of the variables provided.