Physics 237, Final Exam
Wednesday
May 6, 2009
7.15 pm
– 10.15 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
and your equation sheet 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. Problems 5, 6, and 7 must be answered in booklet # 3.
4. 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 equation sheet, and the three 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: ______________________________________
INTENTIONALLY LEFT BLANK
Problem 1 (35 points) ANSWER
IN BOOKLET 1
Consider the following eigenfunction
of the electron in a one-electron atom with atomic number Z:
.
a)
What is the magnetic
quantum number 
of this
eigenfunction? Note: you will not receive any credit
for a correct answer if it not properly justified.
b)
What is the azimuthal
quantum number 
of this eigenfunctions?
Note: you will not receive any
credit for a correct answer if it not properly justified.
c)
How would you
calculate the energy of the electron?
Note: you do not have to do the actual calculation, but you should
provide sufficient details on how you would carry out this calculation.
Problem 2 (35 points) ANSWER
IN BOOKLET 1
Consider the three lowest energy
levels in Na, shown in the Figure below.
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E2 |
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2P3/2 |
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E1 |
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2P1/2 |
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E0 |
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2S1/2 |
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a)
What are the
Land g factors for these levels?
b)
When the atom is
placed in a weak magnetic field, the energy levels split. Draw an energy level diagram showing
the energy levels and determine the corresponding energies.
c)
Which
transitions between the 2P and the 2S energy levels are
possible? Explain why you selected
these transitions?
d)
How many
different photon energies will be observed if all 2P states are
initially populated with equal probability?
Problem 3 (35 points) ANSWER
IN BOOKLET 2
Consider a system of N distinguishable atoms, maintained at a
temperature T, which are distributed
over two energy levels e1 = 0
and e2 = e.
a)
What is the
energy of this system?
b)
What is cV for this system?
Problem 4 (30 points) ANSWER
IN BOOKLET 2
The
energy of a linear harmonic oscillator is equal to 
. The angular
frequency of this oscillator is 
.
a)
Show, using the
uncertainty relations, that the energy of the linear harmonic oscillator can be
written as
b)
Show that the
minimum energy of the oscillator is hv/2
where
Problem 5 (30 points) ANSWER
IN BOOKLET 3
a)
Figure 5.1 shows
the ratio of the cross section for e+ + e– ¨ hadrons to e+ + e– ¨ ΅+ + ΅– plotted as function of the
center-of-mass energy of the e+ + e– system. At energies above 12.5 GeV the ration
is around 11/3. Explain the
significance of this observation.
Figure 5.1.
b)
Figure 5.2 shows
the differential cross section ds/dW for scattering of 90-MeV neutrons by protons as
function of the center-of-mass scattering angle of the neutron. What reaction mechanism dominates at
small scattering angles?
Figure 5.2.
c)
What reaction
mechanism dominated at large scattering angles?
d)
What important
conclusion about the nuclear potential can be obtained on the basis of the
measurement shown in Figure 5.2?
Problem 6 (30 points) ANSWER
IN BOOKLET 3
A particle of mass m and energy 
is approaching x = 0 from the left. The potential seen by the particle can
be described by the following function of x:
a)
What is the wave
function in the region x < 0? Note: you do no yet have to determine
the value of the constants that appear in the wavefunction.
b)
What is the wave
function in the region x ³ 0? Note: you do no yet have to determine
the value of the constants that appear in the wavefunction.
c)
Calculate the
reflection coefficient.
Problem 7 (5 points) ANSWER
IN BOOKLET 3
a) What do the Yankees and the Dodgers have in common?
- Manny Ramirez
- Play in the American League.
- Joe Torre
- Play in the National League.