Sample Final Exam

PHYSICS 213 – PRACTICE FINAL EXAM*
*The actual final exam will contain 16 multiple choice quiz-type questions (32 points,
8 covering concepts from the current lecture material and 8 from the previous three
exams), 2 essay-type questions (8 points, one covering an important fundamental
principle from the current lecture material and one from the previous three exams),
and 6 problems (132 points, 3 from the previous exams / sample exams and 3
similar to the problems that follow).
NAME (printed)
SIGNATURE
Student Number
SECTION
INSTRUCTIONS
Wait for oral instructions before starting the test.
Remember to show (in English) your problem solving steps for FULL
CREDIT.
A calculator and 2 one-sided 8½X11 student reference sheets are
permitted. Your 2 reference sheets may contain equations, graphs,
and notes; however, quiz questions and worked out problems CANNOT
be included. Cell phones/communication devices must be put away.
For the graders:
Q1-18
P1
P2
P3
P4
P5
P6
TOTAL

Special Relativity [22 Points]
An astronomer on Earth observes a meteoroid in the southern sky
approaching Earth at a speed of 0.800C. At the time of its discovery, the
meteoroid is 20 light years from Earth.
a) Calculate the time required for the meteoroid to reach Earth, as measured
by the Earthbound astronomer. [5½ Points]
Answer: 25 yr
b) Determine this required time as measured by an observer on the
meteoroid. [5½ Points]
Answer: 15 yr
c) Calculate the distance to Earth as measured by the observer on the
meteoroid. [5½ Points]
Answer: 12 light-years
d) If the meteoroid has a 200 m diameter as measured by the observer on
the meteoroid, what diameter does the Earthbound astronomer measure?
[5½ Points]
Answer: 120 m

Relativity and Conservation Laws [22 Points]
A physicist is working with unstable particles in a laboratory. One particle of
rest mass m 0 = 1.0 x 10 -28 kg and initially at rest breaks into two fragments
of masses m 1 and m 2 . The velocities of the two fragments are v 1x = -0.6c
and v 2x = 0.8c with respect to the laboratory.
a) Find the numerical values of the masses m 1 and m 2 . [10 Points]
Answer: m 1 = 4.57 x 10 -29 kg and m 2 = 2.57 x 10 -29 kg
b) The first fragment travels 80.0 cm to the left before being stopped in a
laboratory target and the second fragment travels 80.0 cm to the right
before being stopped in another laboratory target. How long does it take
each fragment to impact its respective target as measured by the
physicist in the laboratory? [6 Points]
Answer: T 1 = 4.44 x 10 -9 s and T 2 = 3.33 x 10 -9 s
c) The age of a fragment is measured from the time of its formation as
measured in a frame at rest with respect to the fragment. How much
older is the first fragment than the second fragment at the time when the
first fragment finally impacts its target? [6 Points]
Answer: Δt 1 – Δt 2 = 0.45 x 10 -9 s

Photoelectric Effect [22 Points]
When a photoelectric experiment is performed using calcium as the emitter,
the following data are observed.
λ (nm) 254 366
f (PHz) 1.18 0.82
V stop (V) 1.98 0.49
a) Using the above data, make a graph of KE max vs f. From the graph find
Planck’s constant h and the work function for calcium. [12 Points]
Answer: 6.62 x 10 -34 J∙s, 2.90 eV
b) Determine the cutoff wavelength and frequency for calcium. [6 Points]
Answer: 429 nm, 0.70 PHz
c) Find the maximum kinetic energy of the photoelectrons for λ = 200 nm.
[4 Points]
Answer: 3.30 eV

Compton Effect [22 Points]
X-rays with initial energy 250 keV undergo Compton scattering from a target.
The scattered rays are deflected at 17.0° relative to the direction of the
incident rays.
a) Calculate the wavelength of an incident x-ray? [4 Points]
Answer: 0.004973 nm
b) Find the Compton shift in wavelength. [4 Points]
Answer: 0.000106 nm
c) Determine the energy of a scattered x-ray. [5 Points]
Answer: 245 keV
d) What is the kinetic energy and speed of a recoiling electron? [5 Points]
Answer: 5 keV, 4.19 x 10 7 m/s
e) Find the de Broglie wavelength of a recoiling electron. [4 Points]
Answer: 0.0174 nm

Atomic Physics [22 Points]
Consider the Bohr theory for the hydrogen atom.
a) Calculate the orbital radius, angular momentum, and energy for the n = 3
and n = 5 states. [6 Points]
Answer: For n = 3: 0.476 nm, 3.17 x 10 -34 J∙s, -1.51 eV
Answer: For n = 5: 1.32 nm, 5.28 x 10 -34 J∙s, -0.54 eV
b) Is energy lost or gained when a n i = 5 to n f = 3 transition occurs? Calculate
the energy change. Is a photon absorbed or emitted during this transition?
Calculate the wavelength of the photon. What region of the electromagnetic
spectrum corresponds to the photon’s wavelength? [5 Points]
Answer: lost, 0.97 eV, emitted, 1282 nm, infrared
c) Calculate the orbital radius, angular momentum, and energy for the n = 1
and n = 4 states? [6 Points]
Answer: For n = 1: 0.0529 nm, 1.06 x 10 -34 J∙s, -13.6 eV
Answer: For n = 4: 0.846 nm, 4.22 x 10 -34 J∙s, -0.85 eV
d) Is energy lost or gained when a n i = 1 to n f = 4 transition occurs? Calculate
the energy change. Is a photon absorbed or emitted during this transition?
Calculate the wavelength of the photon. What region of the electromagnetic
spectrum corresponds to the photon’s wavelength? [5 Points]
Answer: gained, 12.8 eV, absorbed, 97 nm, ultraviolet

Nuclear Physics [22 Points]
An isotope of Bismuth, 210 Bi, has a half-life of 5.00 days and an atomic mass
of 209.9838 u. A sample of 210 Bi initially contains 0.180 g.
a) Determine the initial number of bismuth nuclei. [4 Points]
Answer: 5.16 x 10 20 nuclei
b) What is the initial activity of the sample in curies? [4 Points]
Answer: 2.24 x 10 4 Ci
c) How many bismuth nuclei remain after 15 days? [5 Points]
Answer: 0.645 x 10 20 nuclei
d) Find the activity after 15 days. [5 Points]
Answer: 0.280 x 10 4 Ci
e) How many seconds elapse for 65% of the sample to decay? [4 Points]
Answer: 654435 s