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

Wait for oral instructions before starting the test.

INSTRUCTIONS

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 m0 = 1.0 x 10-28 kg and initially at rest breaks into two fragments of masses m1 and m2. The velocities of the two fragments are v1x = -0.6c and v2x = 0.8c with respect to the laboratory. a) Find the numerical values of the masses m1 and m2. [10 Points]

Answer: m1 = 4.57 x 10-29 kg and m2 = 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: T1 = 4.44 x 10-9 s and T2 = 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: Δt1 – Δt2 = 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

Vstop (V) 1.98 0.49

a) Using the above data, make a graph of KEmax 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 107 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 ni = 5 to nf = 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 ni = 1 to nf = 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, 210Bi, has a half-life of 5.00 days and an atomic mass of 209.9838 u. A sample of 210Bi initially contains 0.180 g.

a) Determine the initial number of bismuth nuclei. [4 Points] Answer: 5.16 x 1020 nuclei

b) What is the initial activity of the sample in curies? [4 Points]

Answer: 2.24 x 104 Ci c) How many bismuth nuclei remain after 15 days? [5 Points]

Answer: 0.645 x 1020 nuclei d) Find the activity after 15 days. [5 Points]

Answer: 0.280 x 104 Ci e) How many seconds elapse for 65% of the sample to decay? [4 Points]

Answer: 654435 s