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Physics 152 Roster No.: Score: 23 pts. possible
FALL 2004 Final Exam, Part A
Exam time limit: 2 hours. You may use a calculator and both sides of 2 sheets of notes, handwritten only****. Closed book; no collaboration. For multiple choice questions, circle the letter of the one best answer (unless more than one answer is asked for). Ignore friction, air resistance, and gravity in all problems unless told otherwise, and ignore relativistic effects in non-relativistic problems. Physical constants: k e = 8.988 × 109 N·m^2 /C^2 e = 1.602 × 10 –^19 C h = 6.626 × 10 –^34 J·s ε 0 = 1/(4π k e) = 8.854 × 10 –^12 C^2 /(N·m^2 ) c = 2.998 × 108 m/s = 4.136 × 10 –^15 eV·s μ 0 = 4π × 10 –^7 T·m/A σB = 5.671 × 10 –^8 W/(m^2 ·K^4 ) Wien constant (λ)=2.898× 10 –^3 m·K Useful rest masses: Wien constant ( f )=1.034× 1011 Hz/K m p = 1.6726231 × 10 –^27 kg m n = 1.6749286 × 10 –^27 kg m e = 9.1093897 × 10 –^31 kg = 1.007 276 470 u = 1.008 664 904 u = 0.000 548 579 903 u 1 u = 1.6605 × 10 –^27 kg = 931.49432 MeV/ c^2 (1 pt. each, unless otherwise specified)
1. (2 pts.) You take measurements of E - field strength and V at distance r from a large point charge Q. As you reduce your distance to r /2 , you find that… A. E field strength is multiplied by 2, and V is multiplied by √2. B. E field strength is multiplied by √2, and V is multiplied by 2. C. E field strength is multiplied by 2, and V is multiplied by 2. D. E field strength is multiplied by 4, and V is multiplied by 2. E. E field strength is multiplied by 2, and V is multiplied by 4. F. E field strength is multiplied by 4, and V is multiplied by 4. 2. (2 pts.) You and your friend are standing 1.0 m apart, each holding an equal amount of charge. If the electrostatic force between the two charges equals 750 N (approx. the weight of one person), how much charge is each of you holding? A. 4.4 nC D. 58 μC B. 380 nC E. 290 μC C. 9.1 μC F. 1.7 mC 3. (2 pts.) Which one of the following is TRUE for the circuit at right? A. The units of L are webers. B. The L creates an emf which acts to oppose any change in I. C. The cycles of I are exactly in phase with the cycles of V AC. D. The reactance of L does not depend on the frequency of the voltage source. 4. a. (2 pts.) The wire loop shown at right is located in a uniform B field that extends infinitely in all directions. Any one of the following would induce an emf in the wire, EXCEPT : A. Moving the loop in the x - direction. B. Making the loop larger. C. Spinning the loop about its y - axis. D. Shutting off the B - field. b. If the B field as shown were quickly doubled in strength , in which direction would a current be induced in the wire? A. clockwise B. counter-clockwise C. no current is induced
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5. (2 pts.) Your cell phone recharger contains a transformer whose input uses 40. mA at 120 V. If its output voltage is 4.4 V, what is its output current? (Assume that the transformer is 100% efficient.) A. 9.2 mA D. 250 mA B. 33 mA E. 1.1 A C. 40. mA F. 3.0 A 6. (2 pts.) You look through a peephole’s lens at a visitor (the “object”) standing d o = 1.0 m away from the peephole. You see an upright image which you estimate has a magnification of +0.010 (i.e., one-hundredth of the visitor’s actual size). The focal length of the lens must be: A. – 0.10 cm D. – 9.0 cm B. – 0.9 cm E. – 1.0 m C. – 1.0 cm F. – 9.0 m 7. (2 pts.) Which one of the following is always TRUE for the image created by a concave mirror? A. The image is always upright. B. The image is always taller than the object. C. The image is always located farther from the mirror than f. D. The image is always virtual. E. All of the above. F. None of the above. 8. (2 pts.) Monochromatic light from a helium-neon laser (λ = 632.8 nm) passes through a single slit 0.30 mm wide. The resulting pattern is observed on a screen 2.0 m away. How wide is the broad central maximum on the screen? A. 8.4 mm D. 54 mm B. 19 mm E. 13 cm C. 38 mm F. 30. cm 9. (2 pts.) What is the angle between two crossed polarizers if only 10.% of the intensity of light that passes through the first also makes it through the second? A. 72˚ D. 81˚ B. 75˚ E. 84˚ C. 77˚ F. 89˚ 10. (2 pts.) How fast must an electron be traveling so that an observer at rest measuring its mass would find it to have increased by exactly 10% due to relativity? A. 0.1 c D. 0.9 c B. 0.42 c E. 0.98 c C. 0.87 c F. 0.993 c 11. (2 pts.) Which one of the following statements about special relativity is TRUE? A. An observer at rest measures clocks in a moving frame to run faster than his own. B. Length contraction occurs only along the direction of relative motion, not in all 3 dimensions. C. Every observer measures c to have a different value, depending on the speed of his reference frame. D. A baseball thrown at 0.75 c inside a spaceship moving (in the same direction) at 0.75 c will appear to an observer at rest to be moving at 1.5 c.
17. (2 pts.) What percentage of an initially pure radioactive sample has decayed after 6 half-lives have passed? A. 92.0% D. 98.4% B. 96.0% E. 99.5% C. 97.5% F. 99.8% 18. Two different isotopes of the same element have: A. different numbers of protons, but the same number of neutrons B. the same number of protons, but different numbers of neutrons C. the same number of protons and the same number of neutrons, but different atomic masses D. different numbers of both protons and neutrons, but the same atomic mass 19. Potassium has two stable isotopes: 3919 K and 4119 K. One unstable isotope, 4019 K, has such a long half-life (1.28 × 109 years), that it is easily found as “naturally occurring” on Earth. a. (2 pts.) If potassium-40 undergoes β–^ decay, which nucleus is produced? A. 3918 Ar D. 3920 Ca B. 4018 Ar E. 4020 Ca C. 3919 K F. 4120 Ca b. (2 pts.) Suppose that a geologist finds that only 8.1% of the original potassium-40 remains in a very old meteorite, while 91.9% of it has decayed into the daughter nucleus you determined in part (a). How long ago did the meteorite form? A. 4.2 × 109 years D. 4.8 × 109 years B. 4.4 × 109 years E. 5.0 × 109 years C. 4.6 × 109 years F. 5.2 × 109 years 20. (2 pts.) You are told that a nucleus of element number 98 undergoes a spontaneous decay, which might be alpha, beta, or gamma, but you don’t know which one. Which one of the following CANNOT be the atomic number of the nucleus produced by the decay? A. 96 D. 99 B. 97 E. 100 C. 98 21. Neutrons and neutrinos both are… A. the same mass D. leptons B. the same charge E. baryons C. found in the nucleus F. anti-particles of each other 22. (2 pts.) Which one of the following is TRUE about nuclear fission and nuclear fusion? A. Fission is the primary energy source of stars. B. Fusion can be used as an energy source for human society, while fission cannot. C. Fusion of any two nuclei always results in the net release of energy, no matter how large the nuclei involved. D. Fission results in the net release of energy only if the parent nucleus is very large. 23. (2 pts.) The nucleons in the nucleus of an atom… A. are bound together by the electrostatic force B. can be either positively or negatively charged C. are each made up of 3 quarks D. can be leptons or baryons
Physics 152 Roster No.: Score: 27 pts. possible
FALL 2004 Final Exam, Part C
Show your work on all free-response questions. Be sure to use proper units and significant figures in your final answers. Ignore friction, air resistance, and gravity in all problems unless told otherwise, and ignore relativistic effects in non-relativistic problems.
1. Three light bulbs ( A , B , and C ) of identical 3.00-Ω resistance are connected to a battery ( V 0 = 12.0 V) as shown at right. Assume that the resistance of each bulb is constant (independent of temperature, current, etc.) a. (10 pts.) Determine the following values while switch S is closed (as shown). You do NOT need to show your work, but your answers must have proper units and 3 significant figures to receive full credit. Current through Bulb A: __________ Current through Bulb B: __________ Current through Bulb C: __________ Voltage drop across Bulb A: __________ Voltage drop across Bulb B: __________ Voltage drop across Bulb C: __________ Power dissipated by Bulb A: __________ Power dissipated by Bulb B: __________ Power dissipated by Bulb C: __________ Which bulb is the brightest? __________ b. (3 pts.) Switch S is opened. How does the brightness of each bulb change? i. The brightness of bulb A … A. increases B. decreases C. is unchanged ii. The brightness of bulb B … A. increases B. decreases C. is unchanged iii. The brightness of bulb C … A. increases B. decreases C. is unchanged + – Bulb C V 0 Bulb B Switch S Bulb A
Physics 152 Roster No.: Score: 24 pts. possible
FALL 2004 Final Exam, Part D
3. After taking a spectrum of sunlight, you find that the most common photons emitted by the Sun have a wavelength of 510 nm. a. (3 pts.) Assuming that the Sun is a blackbody, calculate the temperature , in kelvins, of the Sun’s “surface.” For the sake of simplicity in the following parts, assume that the Sun is a monochromatic 510 - nm light source. b. (5 pts.) You go outside to measure the power of sunlight at the Earth’s distance from the Sun. You find that your light meter measures a maximum power of 0.14 W when its detecting area is oriented exactly perpendicular to the incident sunlight. How many 510-nm photons are striking the light meter each second? (Your answer should be between 10^17 and 10^18 photons/s.) c. (3 pts.) Determine the momentum of a single 510-nm photon. Use simplified MKS units on your answer. d. (2 pts.) A proposed “Solar Sail” spacecraft would spread out a huge sheet of metal foil to act as a sail: as it is struck by photons from the Sun, the photons’ momentum would propel the sail (and spacecraft) away from the Sun. If the spacecraft is at the same distance from the Sun as the Earth is, and if the sail has an area of 3500 m^2 (approx. one football field), calculate the total force acting on the sail by the sunlight. Your light detector in part (b) had an area of 1.0 cm^2. Assume that incident photons are absorbed by the sail, not reflected. ( Reminder: Force = Δ p /Δ t [momentum absorbed per second]. You do NOT need to show your work.) A. 0.016 N C. 920 N E. 9.3 × 106 N B. 2.3 N D. 42,000 N F. 4.5 × 108 N
4. Here is an energy-level diagram for four electron orbitals of a sodium atom. (Many other orbitals exist, but are not shown here.) Suppose that the only permitted de-excitations for excited electrons are the three transitions shown at right ( A , B , and C ); all other possible transitions between the 3 s , 3 p , 4 s , and 3 d orbitals are forbidden. For convenience, the 3 s energy level is set at 0 eV, and all other energies are given relative to the 3 s level. a. (1 pt.) All of the permitted transitions obey which one of the following rules? A. the electron’s value of n must not change B. the electron’s value of n must change by ± C. the electron’s value of n may change by 0 or ±2, but NOT by ± D. the electron’s value of l must not change E. the electron’s value of l must change by ± F. the electron’s value of l may change by 0 or ±2, but NOT by ± b. (1 pt.) How many electrons are allowed to occupy a sodium atom’s 3 s orbital at the same time? A. 1 C. 4 E. 8 B. 2 D. 6 F. 10 c. (1 pt.) An electron residing in the 3 p orbital of sodium may have which of the following values for its m s (electron spin) quantum number? A. 0 C. – 1, 0, or +1 E. – 1/2 or +1/ B. – 1 or +1 D. 1/2 F. – 1/2, 0, or +1/ d. (1 pt.) You take a spectrum of the light emitted by some excited sodium gas (just like the arc lamps used in PHYS 152L lab), and you find that the spectrum is: A. discrete B. continuous e. (7 pts.) Assume that transitions A , B , and C are the only transitions occurring in the sodium gas. Determine the wavelengths of the photons emitted by all three. How many emission lines do you see in the visible region of the spectrum? (Show your work for at least one of the three calculations. Explain your reasoning: if not all three transitions are visible, state why.) 0.000 eV
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2.105 eV 3.192 eV 3.617 eV 3 s 3 p 4 s 3 d C
