Name _________________
Final Exam
December 9, 2013
This test consists of five parts. Please note that in parts II through V, you can skip one
question of those offered.
Part I: Multiple Choice (mixed new and review questions) [50 points]
For each question, choose the best answer (2 points each)
1. The force that binds quarks together is carried by particles called
A) Stickons B) Gluons
C) Forceons D) Mesons E) Baryons
2. Which of the following is not a quark?
A) Up
B) Charm C) Muon D) Bottom E) Top
3. Suppose a particle impacts on a step potential (infinite in extent) with an energy too
low to make it over the potential, E < V0. What does the wave function   x  look
like in the classically forbidden region, where it has insufficient energy to go?
A) It doesn’t go into the classically forbidden region at all
B) It continues, still an oscillating wave but much smaller
C) It continues, still an oscillating wave, with a magnitude equal to before
D) I continues, and increases exponentially with distance
E) It continues, but falls off exponentially with distance
4. Which of the following is not a prediction of general relativity?
A) Masses orbiting each other should generate gravitational waves
B) Objects orbiting a point mass should not be exact ellipses; instead, these
approximate ellipses should gradually rotate, or precess
C) Time speeds up when you are near a gravitational source
D) A rotating mass will cause a twisting of space and time near it
E) If you squeeze a massive object small enough, it will form a black hole
5. Which combination of quarks or anti-quarks never occurs?
A) Two quarks
B) Three quarks
C) Three anti-quarks
D) One quark and one anti-quark
E) Actually, all of these do occur
6. The expectation value of the Hamiltonian, H , tells you the average value of the
A) Momentum
B) Position
C) Energy
D) Mass
E) Time
7. A spaceship going at v  34 c emits a light ray that, in its view, is traveling sideways at
c. What is the speed of the light ray as viewed in a frame not moving with the
spaceship?
A) 14 c
B) 47 c
C) c
D) 54 c
E) 74 c
8. Momentum is a three-dimensional vector, but in four dimensional spacetime, all
vectors should have four components. What is the corresponding fourth component
or momentum?
A) Time
B) Distance C) Space D) Mass
E) Energy
9. Which of the following roughly sums up general relativity?
A) Matter causes gravity, gravity causes matter
B) Matter tells space how to curve; space tells matter how to move
C) Energy causes motion through time; momentum causes motion through space
D) Spacetime can be curved because of a change in coordinates, even when there is
no gravity
E) The distance formula should generally be calculated using infinitesimal distances,
not long distances
10. Our text lists the following as the masses (in u) of some isotopes of Mg. Which one
is obviously wrong?
A) 24.985838 B) 25.982594 C) 26.984341 D) 27.983876 E) 28.375346
11. If a man travels at half the speed of light to the star Sirius and back, he would be
A) The same age as when he left
B) Older than when he left, but younger than if he had stayed on Earth
C) Older than when he left, and older than if he had stayed on Earth
D) Older than when he left, and the same age as if he had stayed on Earth
E) Older or younger than if he had stayed on Earth, depending on exactly what path
he follows
12. Which types of interactions conserve strangeness?
A) Weak (only)
B) Electromagnetic (only)
C) Strong (only)
D) Strong and electromagnetic, but not weak
E) All interactions conserve strangeness
13. Which of the following is an impossible amount of energy to have in photons of
frequency f (zero photons is a possibility)?
A) 0
B) 12 hf
C) hf
D) 7hf
E) All of these are possible
14. If you have a perfectly thermal distribution of light, which of the following is false
A) The total amount of power is finite
B) There is a wavelength where the light is strongest, inversely proportional to the
temperature
C) The power at any given wavelength is finite
D) The contribution from extremely short wavelengths is always much more than all
other wavelengths (the ultraviolet catastrophe)
E) The total amount of power grows as the temperature increases
15. Which of the following is a pretty good statement of the equivalence principle in
general relativity?
A) The effects of gravity are equivalent to the effects of being in an accelerated
reference frame
B) Mass and energy are equivalent in terms of their gravitational effects
C) Calculating motion in a curved coordinate system is equivalent to calculating it in
standard Cartesian coordinates
D) All coordinate systems are equivalent in general relativity
E) A geodesic in curved coordinates is equivalent to a straight line in flat coordinates
16. For which of the following types of radioactive decay will there not necessarily be
any even slightly dangerous radiation at all from a radioactive atom?
A)  decay B) + decay C) - decay D)  decay
E) electron capture
17. Which of the following assumptions of the Bohr model actually hold up when you
have a full quantum theory of the atom?
A) The angular momentum of an electron about the z-axis is an integer multiple of 
B) The electron has a specific location at all times as it orbits the atom
C) The electron follows a circular orbit around the atom
D) The electron is at one of several well-defined distances from the atom
E) In fact, all of these are invalid in the quantum theory
18. The only type of radioactive decay that changes neither Z nor A is
E) electron capture
A)  decay B) + decay C) - decay D)  decay
19. Under what circumstances can light falling on a metal dislodge electrons from the
metal?
A) Only if the frequency of the light is high enough
B) Only if the frequency of the light is low enough
C) Only if the intensity of the light is high enough
D) Only if the intensity of the light is low enough
E) Only if the metal is heated to a certain critical temperature
20. How many different colors does any given quark come in?
A) One
B) Two
C) Three D) Four
E) Five or more
21. A geodesic in four-dimensional spacetime is
A) A straight line, just possibly expressed in curved coordinates
B)
C)
D)
E)
The path followed by a particle feeling external forces on it
A line following a constant coordinate value, in any set of coordinates
The path that takes the longest proper time between two points in spacetime
The path of an object moving in a circle, as written in arbitrary coordinates
22. How many neutrons are there in 235U (Uranium is element 92)?
A) 92
B) 143
C) 235
D) 327
E) None of the preceding
23. Another name for an -particle would be
A) 4He nucleus B) electron C) proton
D) neutron
E) photon
24. Which of the following is the correct formula for the momentum of a particle with
mass m and speed v in special relativity?
mv
mv
A) mv
B) mv 1  v 2 c 2  C) mv 1  v 2 c 2 D)
E)
2
2
1 v c
1  v2 c2
25. Which sorts of particles are believed to have wave-like properties in quantum
mechanics?
A) Electrons
B) Electrons and any other fundamental particles
C) Fundamental particles and very small objects like atoms, but not molecules
D) All particles
E) No particles
Part II: Short answer (review material) [20 points]
Choose two of the following three questions and give a short answer (1-3
sentences) (10 points each).
26. Suppose I have two equal masses M connected by a string that are orbiting each other
at high velocity. Explain why one cannot simply add their masses, so that the
composite object can be thought of as a single object of mass 2M.
27. Classically, the electron in a hydrogen atom would tend to fall directly into the
nucleus, ending up at r = 0. Explain using the uncertainty principle why this doesn’t
happen.
28. Give at least three restrictions on the wave function   r, t  that it must satisfy.
Equations are allowed but not necessary.
Part III: Short answer (new material) [30 points]
Choose three of the following four questions and give a short answer (1-3
sentences) (10 points each).
29. Explain qualitatively why very heavy nuclei (anything heavier than lead) are
unstable.
30. For a stable light nucleus (A < 50), approximately what fraction of the nucleons tends
to be protons? For a stable heavy nucleus (A > 150), approximately what fraction of
the nucleons tends to be protons?
31. What are the three most common/lightest types of quarks, and give their spins and
charges. A neutron is a baryon that has no strangeness. Which quarks (or antiquarks) is it made of?
32. Explain qualitatively the difference between curved coordinates and actual curvature.
Part IV: Calculation (review material) [40 points]
Choose two of the following three questions and perform the indicated
calculations (20 points each)
A
33. An alien triangle ship is in the shape of a 30-60-90
triangle, with angle A being 60. This triangle ship is
then accelerated to high speed, such that it still looks
like a 30-60-90 triangle, but now angle A looks like
30.
C
(a) How fast must the triangle be moving? In which
B
direction? Give your answer as a fraction of c.
(b) The moving ship is discovered to have a total energy of E  5.40  1019 J . What
is the rest mass of the ship in kg?
34. Joe Atom is driving his molecular car, which has a mass of 1.0010-19 kg. He wants
to park it in a space that is 6.4010-8 m long.
(a) Estimate the minimum uncertainty in the car’s position, if the owner wants to
make sure it is within the parking space.
(b) Estimate the corresponding uncertainty in its momentum. Assuming the owner
TRIED to put it in park (v = 0), estimate the ACTUAL velocity caused by this
uncertainty in momentum.
(c) Estimate how long Joe can safely leave his car parked before the quantum
velocity found in (b) will cause his car to drift out of its parking space.
35. A particle in the first excited state of the harmonic oscillator has wave function
  x   Nxe  Ax
2
2
,
where A is real and positive, and N is a normalization factor. Some useful integrals
can be found below.
(a) What is the correct normalization factor N for this wave function?
(b) If the position of the particle is measured, what is the average value x that
would be obtained? If we measure the average value of the position squared,
what is the average value x 2 ?
(c) What is the uncertainty in its position x ?
Possibly helpful integrals:



x 2 e  x dx 
2



x n e  x dx  0 if n is odd ,
1 
,
2 3
2



x 4 e  x dx 
2
3 
,
4 5

e  x dx 

,

x 6 e  x dx 
15 
.
8 7

2




2
Part V: Calculation (new material): [60 points]
Choose three of the following four questions and perform the indicated
calculations (20 points each)
36. Most modern smoke detectors contain Americium, typically, about 0.28 g of 241Am,
which has a half-life of 432.2 years
(a) What is the approximate weight, in u, of 241Am? How many atoms of 241Am
would be in 0.28g?
(b) What is the decay rate  in y-1 and in s-1 for 241Am (1 y = 3.156107 s)?
(c) How many radioactive decays per second would occur for 0.28g of 241Am?
(d) How long would we have to wait for the decay rate to drop to 1000. s-1?
baryons mesons
37. Photocopied with the equations on the next page is a portion of Appendix A from the
text. 146Pm is an unstable nucleus with half-life of
Daughte
mode
Q (MeV)
5.5 yr. You may use the table at right if you wish.
r
(a) What would be the resulting isotope if this

isotope underwent – decay, + decay, electron
capture, and -decay?
–
(b) What is the Q-value for each of these processes?
+
(c) Which of these modes is allowed or excluded?
e.c.
38. The 0 baryon decays almost always to one of the
All masses in MeV/c2
particle pairs listed below:
Name Mass Spin Strange
+ 0
+ –
– +
+
+ –
0
1193
½
-1
e  pK Ke p p
+

1189
½
-1
A table of particles is listed at right. The charges are
0

1116
½
-1
implied by their names (the photon  is neutral).
p+
938
½
0
(a) Four of these are impossible. Give a reason in
K
494
0
-1
each case why they cannot occur
–

135
0
0
(b) For the remaining two, determine which type of

0.5
½
0
e
interaction (strong, electromagnetic, weak) is

0
1
0
likely to be responsible.
39. A white dwarf star of one solar mass (M = 1.9891030 kg) is estimated to have a
radius of about R = 5730 km. The Hydrogen-alpha line normally has a wavelength of
0 = 656.28 nm.
(a) What would be the wavelength  of H- light coming from the surface of this
white dwarf?
(b) The star is now increased to two solar masses, and becomes a neutron star. The H line is now observed at  = 1038.00 nm. What is the radius of the neutron star?
(c) The star’s mass is increased to three solar masses and becomes a black hole.
What is the Schwarzschild radius of this black hole?
?
Equations
Constants:
h  6.626  1034 J  s  4.136 1015 eV  s
u  931.494 MeV / c 2
  1.055 1034 J  s  6.582 1016 eV  s
u  1.661 1027 kg
G  6.673 1011 m3 / kg / s 2
2me c 2  1.022 MeV
M He  4.002602 u
N A  6.022 1023
Gravitational time dilation:
2GM
  t 1 2
cr
Red Shift:
2GM
  0  1  2 
cr 

1/ 2
Schwarzschild radius: RS  2GM c 2
Compton Effect:
Expectation values:
   
h
1  cos   ,
mc

h
 2.426 pm
mc
    *  x    x  dx

Uncertainty:
Isotope Masses
  
2
 2  
2