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Instructor(s): D. Reitze
Physics 3101, Introduction to Modern Physics
PHYSICS DEPARTMENT
Springl 2006, EXAM #1
Name (print, last first):
Friday, February 10, 2006
Signature:
On my honor, I have neither given nor received unauthorized aid on this examination.
YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP OF EACH PAGE.
(1) Code your test number on your answer sheet (use lines 76–80 on the answer sheet for the 5-digit
number). Code your name on your answer sheet. DARKEN CIRCLES COMPLETELY. Code your UFID
number on your answer sheet.
(2) Print your name on this sheet and sign it also.
(3) Do all scratch work anywhere on this exam that you like. Circle your answers on the test form. At the end of
the test, this exam printout is to be turned in. No credit will be given without both answer sheet and printout with
scratch work most questions demand.
(4) Blacken the circle of your intended answer completely, using a #2 pencil or blue or black ink. Do not
make any stray marks or some answers may be counted as incorrect.
(5) The answers are rounded off. Choose the closest to exact. There is no penalty for guessing.
(6) Hand in the answer sheet separately.
Instructions
Read each problem carefully before starting. There are 6 multiple choice problems each worth 10 points and 1 partial credit
problem worth 40 points. Show all of your work on the partial credit problem!!
Constants:
c = 3 × 108 m/s
h̄ = h/2π
h = 6.63 × 10−34 J s = 4.14 × 10−15 eV s
1
hc = 1240 eV nm
Area of a sphere = 4πr2
k = 4π²
= 8.99 × 109 N 2 /C2
0
k = Boltzmann’s constant = 1.38 × 10−23 J/K = 8.61 × 10−5 eV/K
−31
me = 9.11 × 10
kg
me c2 = 0.511 MeV
1 MeV/c2 = 1.783 × 10−30 kg
1 eV = 1.6022 × 10−19 J
σ = Stefan’s constant = 5.607 × 10−8 W/(m2 K4 )
Wien’s constant = 2.898 × 10−3 m K
1 u (unified atomic mass unit) = 1.66054 × 10−27 kg
Multiple Choice (each worth 10 points)
1. A muon with a proper lifetime of 2.2µs travels a distance of 95 m before decaying into an electron and two neutrinos.
What is the speed of the muon (with respect to c) in the lab?
(1) 0.14c
(2) 0.27c
(3) 0.99c
(4) 0.91c
(5) 0.54c
2. An exotic jaon particle is traveling with a velocity of 0.993c and total energy of 2.340 GeV with respect to a laboratory.
What is the mass (in GeV/c2 ) of the jaon?
(1) 2.762
(2) 1.343
(3) 5.839 × 10−2
(4) 1.343 × 10−2
(5) 2.010
3. A star with a radius of 2.27 × 108 m radiates 1.0 × 1026 W. What color is the star?
(1) violet (λm = 400 nm) (2) green (λm = 530 nm) (3) red (λm = 700 nm) (4) infrared (λm = 1500 nm) (5) deep
ultraviolet (λm = 100 nm)
4. What is the average energy E per mode of oscillation if λ = hc/2kT for that mode?
(1) 0.313 kT
(2) 1.482 kT
(3) 1.00 kT
(4) 0.096 kT
(5) 5.461 kT
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5. Look at the plots which show the photocurrent i vs. anode voltage V for different light
intensities (graph (a)) and light frequencies
(graph (b)). Which of the following statements is not true?
I1
f1
I2
f2
f3
(1)
(2)
(3)
(4)
(5)
f3 > f2 , f1
f3 is the threshold frequency for photoemission.
I1 > I2
Both I1 and I2 have the same threshold frequency for photoemission
The maximum kinetic energy of the photo-emitted electrons in graph (a) is independent of intensities I1 and I2 .
6. Which of the following statements are true?
I. The experiments of Fizeau and Michelson-Morley proved the existence of a preferred inertial frame.
II. It is in principle possible for a massive high energy cosmic particle to cover the distance from the earth to the sun
(approximately 1.46 × 1011 m) in less than 1 second (as measured by a clock co-moving with the particle).
III. The work function of a material is a measure of the minimum energy needed for an electron to be ejected from it
surface.
(1) II, III
(2) I, II
(3) I, III
(4) III
(5) II
Partial Credit Problem (worth 40 points)
The typical fission reaction in nuclear reactors that generate elecctricity is:
235
The atomic masses of 235 U, 92 Kr, and
1.00866 in unified atomic mass units.
U + n →142 Ba +92 Kr + 2n + 179.4MeV
142
Ba are 235.04393, 141.91645, 91.92616 and the atomic mass of the neutron is
(a) How much mass (in unified atomic mass units) is converted into energy in one reaction? (14 points)
(b) The United States consumed approximately 1.23 × 1020 J of energy in 2005.
(i) If all of this power were produced by nuclear power, how much mass (in kg) would be converted into energy to
produce the energy needs of the US in 2005? (7 points)
(ii) How much initial mass (in kg) of
(c) If the neutrons ejected from the
235
235
U is needed? (7 points)
U nucleus travel at a velocity of 0.9c:
(i) what is the total energy of each neutron (in MeV)? (6 points)
(ii) what is the total momentum of each neutron (in MeV/c)? (6 points)