Name: Honor Code Signature: Physics 102 Final Exam
6 May 2002 Prof L. Weinstein

There are 65 questions. Please give a short explanation for all of your non-numerical answers. Show your work for all numerical answers. A table of physical data and a periodic table are at the back of the test.

Most questions are 10 points.  Questions not needing explanation are only 5.  The question about radioactive decay is 20 points.  The total test had 615 points.  Of those, I deducted 60 points from the total for questions that were too hard or too misleading.  If you got those questions correct, they counted as extra credit.

Your percentage score is your score divided by 555.  I then added 10% to get your letter grade.

1. (No explanation needed) Light will always travel from one place to another along a path of least
1. distance
2. time
3. effort
4. expense
5. complication


This is why light bends when entering a medium with a different speed (like the lifeguard entering the water)
 

2. The shortest plane mirror in which you can see your entire image is (hint: draw a picture for your explanation)
1. half your height
2. about 1/3 your height
3. about 3/4 your height
4. equal to your height
5. dependent on the distance between you and the mirror


We did this in class.

 

3. If you walk toward a mirror with a speed of 3 m/s, at what speed are you and your image approaching each other?


You are walking at 3 m/s and your image is moving at 3 m/s so you approach at 6 m/s
 
 
 
 
 

4. Some surfaces that are considered rough for reflecting infrared waves may be considered polished for reflecting
1. radio waves
2. light waves
3. both
4. neither
5. need more information


A 'rough' surface is one where the surface irregularities are bigger than 1/8 of a wavelength.  Since the wavelength of radio waves (typically meters) is MUCH larger than the wavelength of infrared waves (typically about a millionth of a meter), you could have a surface that reflects infrared diffusely but reflects radio waves specularly.
 
 
 

5. (no explanation needed) Light refracts when traveling from air into glass because light
1. has a different intensity in glass than air
2. has a different frequency in glass than air
3. has a different velocity in glass than air
4. other
6. A beam of light emerges from water into air (see figure). Which light ray comes closest to the direction of the light ray in air?




1. A
2. B
3. C
4. D
5. none come close


When going from a slower medium to a faster one, light bends AWAY from the normal.
 

7. (no explanation needed) Rainbows are not usually seen as complete circles because
1. the ground is usually in the way
2. they are actually elliptical
3. they have no bottom part
4. raindrops are not perfectly round
5. rainbows are actually arch shaped

 
 
 
 
 
8. If you wish to spear a fish with a regular spear, you should compensate for refraction between the air and the water and throw your spear (draw a picture for your explanation)
1. directly at the sighted fish
2. above the sighted fish
3. below the sighted fish
4. need more information


The fish appears closer to the surface than it really is.

 
 
 

9. When a fish looks upward at angle of 45 degrees, does it see the sky or only a reflection of the bottom? Explain.


It sees the sky.  The critical angle for total internal reflection in water is 48.6 degrees.  If the fish looks up at an angle greater than this, it will only see the light from the bottom.  At angles less than this, it will see light from the sky and some light reflected from the bottom.
 
 
 
 
 

10. A planar wave of blue light passes through a very small hole. It then makes a bright spot on a screen a few meters away. If instead red light passes through the hole, the bright spot will be
1. larger
2. the same size
3. smaller
4. need more information


Assuming that 'a very small hole' means that it is small compared to the wavelength of blue light, then the size of the image is determined by the diffraction of light.  Red light has a longer wavelength so it diffracts more so the spot will become larger.
 
 
 
 

11. The colors seen when gasoline or oil forms a thin film on a puddle of water are a demonstration of
1. refraction
2. reflection
3. diffraction
4. polarization
5. interference

It is the interference between the light reflecting from the top surface of the film (the air-gas boundary) and the light reflecting from the bottom surface of the film (the gas-water boundary).
 
 
 

12. What fraction of sunlight passes through a) an ideal polarizing filter?


50%.  Sun light is unpolarized so only half of it can pass through a polarizing filter.  (No explanation was needed, just the number)

b) two ideal polarizing filters parallel to each other?

50%.  The light that passes through the first filter isnow perfectlyaligned to pass the second.

c) two ideal polarizing filters at right angles to each other?

None.  All the light that passes through the first filter is blocked by the second.
 

13. An inventor proposes to equip an office with a polarized source of background music and let those who prefer not to hear it wear polarizing earplugs. His idea is
1. practical - it gives people a choice
2. too expensive
3. too much bother
4. nonsense - you can't polarize a sound wave


You cannot polarize a longitudinal wave, only a transverse wave.
 
 
 
 

14. Camera lenses coated with a layer of transparent material of the right thickness are almost completely non-reflective for light near the middle of the visible spectrum. They do, however, reflect a significant amount of
1. green
2. red
3. white
4. violet
5. red and violet

These are the colors farthest from the middle of the spectrum.
 
 
 

15. Red laser light passes through two thin parallel slits and forms a diffraction pattern (a pattern of alternating dark and light spots) on a screen a few meters away. The distance between adjacent light spots is$d$ . If the two slits are moved closer together, then the spacing between adjacent light spots will
1. increase
2. decrease
3. remain the same
4. need more information


The closer the slit spacing, the wider the diffraction pattern.  We did this in class.
 
 
 
 

16. You look at a thin yellow light source using diffraction glasses. You will see
1. thin lines that are the same color as the yellow light
2. thin lines of different colors
3. either one, it depends on the light source
4. need more information


You can make yellow light with either a) truly yellow light or b) with a mixture of red and green.  You do not know without using diffraction glasses which it is.

I gave half credit for answers a or b (with a suitable explanation)
 
 
 

17. (no explanation needed) To say that energy levels in an atoms are discrete, is to say that the energy levels are well defined and
1. separate from one another
2. separated from one another by the same energy increments
3. continuous
4. private
18. Light is emitted when an electron
1. is boosted to a higher energy level
2. makes a transition to a lower energy level
3. swings around the atom in the same orbit
4. other


When an electron makes a transition from a higher energy level to a lower energy level, the extra energy is radiated in the form of light.
 
 
 
 

19. (no explanation needed) A photon of which of the colors below has the longest wavelength?
1. red
2. orange
3. yellow
4. green
5. blue
20. The frequencies of light emitted by an incandescent lamp (eg: a typical 100 W bulb) depends on the
1. amount of electrical energy transformed
2. temperature of the filament
3. voltage applied to the lamp
4. electrical resistance of the lamp
5. energy differences between electron orbits in the gas inside the lightbulb


Incandescent lights work by thermal radiation.  The higher the temperature, the higher the average frequency of the light emitted.
 
 
 
 

21. A paint pigment that emits red light when it is illuminated with blue light
1. is fluorescent
2. is phosphorescent
3. is used in lasers
4. is polarized
5. doesn't exist


This is one of the questions that I did not count toward the exam total since we did not spend much time on this in class.
There are many pigments that glow when illuminated by black light (ie: ultraviolet).  These are fluorescent.  The same principle is at work here.
 
 
 
 

22. A star has a yellow spectral line at a frequency of $5.09 *10^{14}$ Hz. If the star is moving toward us, we will observe the same spectral line at
1. a slightly higher frequency
2. a slightly lower frequency
3. exactly the same frequency
4. need more information


The light will be doppler shifted to a slightly higher frequency
 
 
 
 
 

23. What is the energy of a red photon of frequency $4.6 * 10^{14}$ Hz? Give your answer in Joules and then convert it to electron-Volts.


E = hf = 6.6*10^(-34) J-s * 4.6*10^(14) 1/s = 3.0 * 10^(-19) J
3.0*10^(-19) J * [1 eV / 1.6 * 10^(-19) J ] = 1.9 eV
 
 
 

24. What is the frequency of a blue photon of wavelength 440 nm (nano-meters)?


f = c/lambda = 3 * 10^8 m/s / 440 * 10^(-9) m = 6.8 * 10^14 1/s
I only took off one point for not remembering what nano meant.
 
 
 

25. Light behaves as both a wave and a particle. Describe an experiment or a measurement that shows that light behaves as a particle.


possible answers: a) photoelectric effect (knocking out electrons with photons)
b) discrete lines in vapor lamps
c) slow buildup of photographic images as photons arrive
 
 
 

26. When a clean surface of potassium metal is exposed to blue light, electrons are emitted. If the intensity of the blue light is increased, which of the following will also increase (choose all that apply)?
1. the number of electrons ejected per second
2. the maximum kinetic energy of the ejected electrons
3. the threshold frequency of the ejected electrons
4. the time lag between the absorption of blue light and the start of emission of the electrons
5. none of these


Increasing the intensity increases the number of photons but does not change their energy.  Therefore the number of electrons emitted increases but nothing else changes.
 
 

27. A proton moving at 1700 m/s has a certain wavelength. If you double the speed, the wavelength will
1. quarter
2. halve
3. stay the same
4. double
5. quadruple
6. none of these


wavelength = h/momentum.  Double velocity -> double momentum -> half wavelength

You can't use f = c/lambda to find the wavelength since you do not know the frequency.
 

28. I want to use an electron beam to study the nucleus of the atom (diameter about $10^{-15}$ m). What electron momentum do I need?


You need an electron with a wavelength the size of the nucleus: lambda = 10^(-15) m.  Then
lambda = h/p -> p = h/lambda = 6.6*10^(-34) J-s / 10^(-15) m = 6.6 * 10^(-19) kg m/s

Nobody got this correct.  I didn't count the question.
 
 
 

29. Atoms can absorb energy from light or from heat. The absorbed energy lifts the electron wave from a low orbit near the nucleus to a higher orbit. When the atom radiates away the absorbed energy, the electron wave drops back down to the lower and smaller orbit. In the smallest orbit, the ground floor orbit, the electron cannot radiate any energy because
1. it has zero kinetic energy
2. the wave will not fit in a lower smaller orbit
3. both
4. neither


Electron orbits are fixed by the requirement that a even number of electron wavelengths must fit around the circumference of the orbit.  The lowest orbit is where only one wavelength fits around the circumference of the orbit.  You cannot have a lower orbit than that because the electron wave won't fit.

People have proposed infinite energy schemes claiming that hydrogen has an energy state lower than the ground floor orbit.  They are lying.  Do not give them your money.
 
 
 

30. (no explanation needed) The atomic number of an element is always the same as the number of its
1. electrons
2. protons
3. neutrons
4. nucleons
5. none of these
31. (no explanation needed) Different isotopes of an element have a different number of
1. electrons
2. protons
3. neutrons
4. none of these
32. The half-life of tritium, a radioactive isotope of hydrogen, depends on (circle all that apply)
1. the number of atoms in the substance
2. whether it is in the form of hydrogen molecules (H$_2$ ) or water molecules (H$_2$ O)
3. the temperature of the substance
4. the age of the substance
5. none of these


The half life is a property of the isotope.  You cannot change it.
 
 

33. What are the daughter nuclei of the following decays: a) Radioactive potassium, ${}^{40}_{19}$ K, decays by $\gamma$ emission.


No change.  40/19 K

b) Sodium, ${}^{22}_{11}$ Na, decays by positive $\beta$ emission.

22/11 Na -> 22/10 Ne + e+ + neutrino  (it is emitting a positive beta particle so the number of protons must decrease by 1)

c) Americium, ${}^{242}_{95}$ Am decays by $\alpha$ emission.

242/95 Am -> 238/93 Np + 4/2 He (the alpha particle is a helium nucleus)
 
 

34. (no explanation needed) Most of the radioactivity we personally encounter comes from
1. fallout from nuclear weapons tests
2. nuclear power plants
3. medical x-rays
4. other man-made sources
5. the natural environment
35. The half-life of Carbon 14 is 5730 years. If a 1-gram sample of old carbon is 1/8 as radioactive as 1 gram of a current sample, how old is the sample?


If the sample has only 1/8 the activity, then  3 half-lives have elapsed.  Age = 3 * 5730 years = 17190 years
 
 
 

36. In the fissioning of Uranium, a chain reaction is caused by
1. the enormous energy release
2. the kinetic energy of the decay products
3. ejected neutrons
4. the conversion of mass to energy
5. none of these


When a neutron hits (and is absorbed by) a uranium 235 nucleus, it makes the nucleus fission.  U235 -> two large fission fragments + neutrons.  It is the neutrons that make the other uranium nuclei fission and keep the chain reaction going.
 
 
 
 

37. Fissioning Helium would
1. release energy
2. require energy
3. neither
4. need more information


If you fission helium, you split it up into hydrogen nuclei.  This requires energy since hydrogen is less tightly bound than helium.  The sun gets its energy by fusing hydrogen  into helium.
 
 
 
 

38. Two glasses are filled with water to the same depth. One glass has straight vertical sides and the other is V shaped (see picture). Which glass has the higher pressure at the bottom?




1. straight sides
2. V shaped
3. both the same
4. need more information


pressure depends only on depth and the density of the fluid.
 

39. At sea level, even a perfect vacuum can raise water only 10 meters up a straw. How high can you raise water up a straw in Bozeman, Montana (elevation 5000 feet)?
1. less than 10 m
2. 10 m
3. more than 10 m
4. need more information


At higher altitude, air pressure is less, so it cannot raise the water as high.
 
 
 
 

40. Salt water is slightly denser than fresh water. Will a 1 cubic meter, 3.5 ton rock feel a greater buoyant force at a depth of 100 m in the ocean or in a freshwater lake (assuming the water is the same temperature)?
1. the ocean
2. the lake
3. both the same
4. need more information


A submerged object displaces its volume of water.  The buoyant force is the weight of the displaced water.  Since salt water is denser than fresh water, the displaced ocean water weighs more than the displaced lake water.
 
 

41. Salt water is slightly denser than fresh water. Will a 3.5 ton boat feel a greater buoyant force floating in the ocean or in a freshwater lakee (assuming the water is the same temperature)?
1. the ocean
2. the lake
3. both the same
4. need more information


A floating object displaces its weight of water.  Therefore it will be 3.5 tons in both cases.  The ship will float higher in the ocean because it is denser, but that wasn't the question.
 
 

42. A submarine in the arctic ocean (where the water is $4^o$ C from surface to bottom) experiences a buoyant force of 23,000 tons when it is at a depth of 1000 m. What is the buoyant force on the submarine when it is at a depth of 100 m?
1. less than 23,000 tons
2. approximately 23,000 tons
3. more than 23,000 tons
4. need more information


The buoyant force doesn't depend on depth.  Since the water has the same density at 100 m and and 1000 m, the buoyancy force will be the same.
 
 

43. Blood flows through arteries to all parts of our body. An aneurysm is a widening of an artery (see figure, the arrow shows the direction of blood flow). How does the blood pressure in the aneurysm compare to the blood pressure in the rest of the artery?




1. the aneurysm blood pressure is higher $\rightarrow$ the aneurysm will get bigger (uh-oh!)
2. the aneurysm blood pressure is lower $\rightarrow$ the aneurysm will get smaller (whew!)
3. the pressures are the same
4. need more information


Blood flow will be slower in the aneurysm because it is wider there.  Slower flow -> more pressure (Bernoulli!).
 
 

44. A bag is filled with 2 cubic meters of an ideal gas at a pressure of 1 atmosphere and a temperature of $20^o$ C (about 68$^o$ F). If the temperature is doubled to $40^o$ C without changing the pressure, then the volume of the gas becomes
1. less than 2 m$^3$
2. more than 2 m$^3$ but less than 4 m$^3$
3. 4 m$^3$
4. more than 4 m$^3$
5. need more information


The temperature did not really double.  It only increased from 293 K to 313 K.  Therefore the volume will increase, but by less than double (PV = nRT).
 
 

45. How and why would placing a large aluminum nail through a potato before baking it affect the cooking time?


Aluminum has a much higher thermal conductivity than the potato.  Therefore it will conduct heat into the middle of the potato and cook it faster.  Many restaurants do this.
 
 
 
 
 

46. You add 100 J of heat each to 100 g of water and to 100 g of iron. Which material has the greatest increase in internal energy?
1. the water
2. the iron
3. both the same
4. need more information


heat added = change in internal energy plus work done.  Assuming that neither sample does work, both will have the same increase in internal energy.
 
 

47. You add 100 J of heat each to 100 g of water and to 100 g of iron. Which material has the greatest increase in temperature?
1. the water
2. the iron
3. both the same
4. need more information


Water has a much greater heat capacity than iron.  Therefore, for the same change in internal energy, its temperature will increase less.
 
 
 

48. Which gets hotter in sunlight, a black car or a white car?
1. black
2. white
3. both the same
4. need more information


black absorbs better
 
 

49. Which gets colder on a clear night, a black car or a white car?
1. black
2. white
3. both the same
4. need more information

a good absorber is a good emitter.  Black emits better.
 
 
 

50. A mechanic is testing an air conditioner by running it on a workbench in an isolated room. What happens to the temperature of the room?
1. it increases
2. it decreases
3. it stays the same
4. need more information


An air conditioner is a heat pump.  It uses electrical energy to pump heat from inside the room to outside the room.  If it is sitting on a bench in the middle of the room, then the heat will not go anywhere.  The electrical energy used by the air conditioner will turn to heat and heat up the room.
 
 
 

51. What input energy is required if an engine performs 200 J of work and exhausts 400 J of heat to the cold reservoir?


600 J.
 
 
 
 
 

52. What is the efficiency of an ideal heat engine with a boiler at 200$^o$ C that exhausts its heat at room temperature (27$^o$ C)?


e = (T_hot - T_cold) / T_hot = (473 K - 300 K) / 473 K = 37%
 
 
 
 

53. We can treat people's legs as pendulums to analyze how they walk. Which legs take longer to swing back and forth, those of tall people or short people?
1. tall
2. short
3. both the same
4. need more information


longer pendulums have a longer period.  Tall people still walk faster than short people (in general) because their stride is longer.

This effect is very obvious when you see people walking their dogs (especially dachshunds).
 
 

54. You stand just to the side of the low point of a child's swing and always push the child in the same direction. The period of the swing is 3 s. You push the swing at even intervals. Which intervals will make the swing go very high (resonance)? Circle all that apply.
1. pushing once every 1 s
2. pushing once every 2 s
3. pushing once every 3 s
4. pushing once every 4 s
5. pushing once every 5 s
6. pushing once every 6 s
7. none of the above


You want to push at the same point in the swing each time.  This means waiting an even number of periods between pushes.  If you push every 3 s, then you are pushing once for each swing.  If you push every 6 s, then you are pushing once for every two swings.
 
 
 
 

55. If you double the speed of a wave while keeping the wavelength fixed, what happens to the period?
1. it gets 4 times smaller
2. it gets 2 times smaller
3. it stays the same
4. it gets 2 times bigger
5. it gets 4 times bigger
6. need more information


speed = wavelength / period.  Double speed -> halve period.
 
 

56. When you yell at a friend, are the air molecules that strike his ear the same ones that left your lungs?
1. Yes
2. No


No.  The disturbance in the air (the pressure wave) reaches his ears.  The air molecules are not shifted by the sound wave.
 
 
 
 

57. (no explanation needed) When you see your friend, are the photons that reach your eyes the same ones that bounced off her?
1. Yes
2. No
58. Draw diagrams to show the standing wave pattern for the first three harmonics of a rope fixed at both ends.



 
 

59. A pipe organ has pipes of many different lengths. Which ones make the highest notes?
1. the shortest ones
2. the middle ones
3. the longest ones
4. need more information


The shortest ones have the shortest wavelengths and thus the highest frequencies.
 
 

60. Your real estate agent assures you that extra traffic from the new shopping mall will only increase noise from cars by about 15%, from 60 dB to 70 dB. What does this imply about the number of cars using the street?
1. It will increase by less than 15%
2. It will increase by about 15%
3. It will increase by more than 15%
4. need more information


An increase in noise from 60 dB to 70 dB means that the sound intensity has increase by a factor of 10.  This implies that the number of cars has increased by A LOT!
 
 
 
 

61. A green cloth is illuminated by magenta light. What color does it appear?


The only color that green reflects is green.  It absorbs red and blue light.  This means that it absorbs all the light that hits it so tht it appears BLACK.
 
 
 

62. If you mix cyan and magenta paint, what color paint will result? (ie: if you shine white light on the mixture, what color will it appear?)


Cyan paint absorbs red light and reflects green and blue light.  Magenta paint absorbs green light and reflects red and blue light.  The combinationwill absorb both red and green, reflecting only blue.
 
 
 

63. Light travels through the air at $3\cdot 10^8$ m/s and hits a piece of glass. The light in the glass travels more slowly than the light in the air (at about $2\cdot 10^8$ m/s). When the light re-emerges into the air its speed is
1. less than $2\cdot 10^8$ m/s
2. $2\cdot 10^8$ m/s
3. between 2 and $3\cdot 10^8$ m/s
4. $3\cdot 10^8$ m/s
5. more than $3\cdot 10^8$ m/s
6. need more information


The speed is 3 * 10^8 m/s.  Light slows down in materials because it spends so much time being absorbed and reemitted by atoms.  In between atoms light always travels at 3 * 10^8 m/s.
 
 
 

64. Why don't we see colors at night when there is a half-moon?


Because there is not enough light for our cone cells to function.
 
 
 
 

65. Rank the following photons from least to most energetic: radio, ultraviolet, blue, infrared, gamma ray, green


radio (least), infrared, green, blue, ultraviolet, gamma ray (most)