PRUEBAS ILLIONOIS

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SPRING 2009 QUESTION 1* This and the following question should be considered together. Single-frequency sound waves emerging from two speakers are detected at the point shown in the figure below. The relative phase Φ of the two signals driving the speakers can be adjusted. The speakers are equidistant from the observer. The intensity at the observer from each wave alone is 2.0 W/m 2 . The net intensity of the sound received at the point shown is 3.5 W/m 2 . What is the relative phase Φ between the sources? (a) Φ = 43° (b) Φ = 60° (c) Φ = 97° QUESTION 2* The relative phase Φ is now changed to Φ = 0. The relative amplitudes of the waves are changed such that the intensity at the observer from the top speaker alone is 2.0 W/m 2 and the intensity at the observer from the bottom speaker alone is 1.0 W/m 2 . What is the net intensity I at the observer? (a) I = 2.0 W/m 2 (b) I = 2.5 W/m 2 (c) I = 3.0 W/m 2 (d) I = 4.3 W/m 2 (e) I = 5.8 W/m 2

Transcript of PRUEBAS ILLIONOIS

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SPRING 2009 QUESTION 1*

This and the following question should be considered together.

Single-frequency sound waves emerging from two speakers are detected at the point shown in the figure below. The relative phase Φ of the two signals driving the speakers can be adjusted. The speakers are equidistant from the observer.

The intensity at the observer from each wave alone is 2.0 W/m2. The net intensity of the sound received at the point shown is 3.5 W/m2. What is the relative phase Φ between the sources?

(a)   Φ = 43°

(b)   Φ = 60°

(c)   Φ = 97°

QUESTION 2*

The relative phase Φ is now changed to Φ = 0. The relative amplitudes of the waves are changed such that the intensity at the observer from the top speaker alone is 2.0 W/m2 and the intensity at the observer from the bottom speaker alone is 1.0 W/m2. What is the net intensity I at the observer?

(a)   I = 2.0 W/m2

(b)   I = 2.5 W/m2

(c)   I = 3.0 W/m2

(d)   I = 4.3 W/m2

(e)   I = 5.8 W/m2

QUESTION 3*

This and the following question should be considered together.

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A pure harmonic signal generator with adjustable frequency f is used to drive two speakers as shown in the figure below. Sound waves emerging from the speakers are detected at the point shown in the figure. The relative phase Φ of the two signals driving the speakers can be adjusted.

If the wave at the observer goes through a positive maximum every millisecond, what is the wavelength of the sound produced by these sources? (Assume the speed of sound is 330 m/sec.)

(a)   0.0010 m

(b)   0.053 m

(c)   0.33 m

QUESTION 4***

The frequency of the sound waves is now changed to f = 500 Hz. What is the value of Φ closest to 0° that produces an intensity at the observer of 0 W/m2 ?

(a)   -480°

(b)   -120°

(c)   0°

(d)   60°

(e)   180°

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QUESTION 5**

This and the following question should be considered together.

In a two-slit interference experiment, a viewing screen is placed 6 meters directly behind two slits separated by 0.4 mm. Coherent, monochromatic light emerges (in phase) from the slits.

If the distance y between the maximum of light intensity at the center of the screen and the third minimum away from the center is 3.0 cm, what is the wavelength of the light?

(a)   420 nm

(b)   680 nm

(c)   740 nm

(d)   800 nm

(e)   960 nm

QUESTION 6*

What happens to the separation between the intensity maxima on the screen as we decrease the slit spacing?

(a)   decreases

(b)   increases

(c)   no change

QUESTION 7*

Two speakers, S1 and S2, are adjusted so that the observer (at the location shown in the figure) hears an intensity of 10 W/m2 when either S1 or S2 is sounded alone. The speakers are coherent and in phase. The speed of sound is 330 m/s.

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What is the lowest non-zero frequency for which the observer will hear the maximum intensity?

(a)   165 Hz

(b)   330 Hz

(c)   780 Hz

(d)   920 Hz

(e)   1000 Hz

QUESTION 8*

This and the following question should be considered together.

We define the visible spectrum to span the wavelength range from 400 nm (violet) to 700 nm (red). Consider white light (that contains all visible wavelengths in this range) falling normally onto a plane grating with 600 slits per millimeter.

Find the angular width of the first-order visible spectrum produced by the grating. The angular width is the difference Δθ = | θ(700nm) - θ(400nm) | between the angles of the first interference maxima of the longest and the shortest wavelengths in the visible spectrum.

(a)   Δθ = 0°

(b)   Δθ = 2.3°

(c)   Δθ = 5.7°

(d)   Δθ = 10.9°

(e)   Δθ = 21.4°

QUESTION 9**

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Do the first- and second-order spectra of this wavelength range overlap?

(a)   Yes.

(b)   No.

(c)   The answer depends on the grating's spacing between the grating's slits.

QUESTION 10**

Monochromatic light of one wavelength and one frequency passes through a single slit of finite width. The diffraction pattern is observed on a screen at a certain distance from the slit. Which of the following changes would decrease the width of the central maximum?

(a)   decreasing the slit width

(b)   decreasing the frequency of the light

(c)   increasing the wavelength of the light

(d)   increasing the distance of the screen from the slit

(e)   none of the above

QUESTION 11**

While conducting a photoelectric effect experiment with light of a certain frequency, you find that a reverse potential difference of 1.25 V is required to reduce the current to zero. Find the maximum speed of the emitted photoelectrons.

(a)   0 m/s

(b)   1.2 m/s

(c)   3.7 × 103 m/s

(d)   6.6 × 105 m/s

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(e)   Not enough information given.

QUESTION 12*

The largest optical telescopes have apertures of about 10 m. Radio telescopes can be made that have apertures as large as the Earth (about 12.8 × 106 m). If the optical wavelengths are about 500 nm and radio wavelengths are about 1 cm, which kind of telescope can achieve better (i.e., smaller) angular resolution?

(a)   radio telescopes.

(b)   optical telescopes.

(c)   Both techniques achieve similar resolutions (within a factor of two).

QUESTION 13***

Suppose the two-slit experiment is performed with single photons of slightly different wavelengths: λ = 600 nm and λ + Δλ = 602 nm (i.e. Δλ = 2 nm). How does the interference pattern on the screen (created by a large number of photons) differ from the usual one with equal wavelengths?

(a)   The pattern is the same as the pattern that would be produced by monochromatic light with the average wavelength λ + Δλ/2 = 601 nm.

(b)   For Δλ = 2 nm there is an interference pattern. However, the pattern will disappear as Δλ → d, where d is the spacing between the two slits.

(c)   There is no interference pattern for Δλ = 2 nm.

QUESTION 14*

This and the following question should be considered together.

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If you shine light of frequency, f, on a metal, electrons may emerge and be collected. The maximum bias on the collector for which this occurs is the stopping voltage, Vstop. Here is a graph (without numbers) of Vstop versus f:

Suppose someone else makes the same measurement and obtains a larger slope (steeper line). How might he interpret the difference in the two results?

(a)   His measured value of Planck's constant is larger than yours.

(b)   His measured value of Planck's constant is smaller than yours.

(c)   His measured value of the metal's work function is smaller than yours.

QUESTION 15*

Suppose someone else makes the same measurement and obtains a smaller f0 (x-intercept). How might she interpret the difference in the two results?

(a)   Her measured value of Planck's constant is larger than yours.

(b)   Her measured value of Planck's constant is smaller than yours.

(c)   Her measured value of the metal's work function is smaller than yours.

QUESTION 16**

Suppose a lamp is emitting 100 W of orange light (λ = 600 nm). All the photons are emitted to move to the left. How large is the reaction force, F, on the lamp?

(a)   F = 4.135 × 10-13 N

(b)   F = 3.33 × 10-7 N

(c)   F = 0.0165 N

(d)   F = 100 N

(e)   F = 3.00 × 107 N

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QUESTION 17**

When passed through a thin crystal, what energy electrons will produce a diffraction pattern that is similar to (the same spot positions) the one produced by 10 keV x-rays?

(a)   Ee = 0.098 keV

(b)   Ee = 6.65 keV

(c)   Ee = 10 keV (i.e., the same energy)

(d)   Ee = 101 keV

(e)   Ee = 511 keV

QUESTION 18***

Light of various wavelengths is shined on a collection of "quantum wires" all of the same length. Each 'wire' consists of an electron trapped in a carbon nanotube, which we approximate as a 1-D infinite potential well of a width equal to the length of the wire.

It is observed that the longest wavelength that is absorbed by the collection of wires (corresponding to an electronic excitation in each wire), is 0.44 mm. What is the length of each wire?

(a)   4 nanometers

(b)   20 nanometers

(c)   0.22 millimeters

(d)   0.44 millimeters

(e)   0.88 millimeters

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QUESTION 19*

This and the following two questions should be considered together.

An electron in an infinite 1-D square potential well of width 8 nm, decays from the state with quantum number n (i.e., the n-1 excited state) to state m.

Compare the wavelengths of the emitted photon for the two transitions: 11→10, and 5→2 .

(a)   λ11→10 < λ5→2

(b)   λ11→10 > λ5→2

(c)   λ11→10 = λ5→2

QUESTION 20**

Now assume the electron is in the first excited state of the well, and that we shine on it photons that have an energy of 0.06 eV. Which of the following will happen and why?

(a)   Nothing - each photon doesn't have enough energy to excite the electron to the next excited state.

(b)   Nothing - each photon has too much energy to excite the electron to the next excited state.

(c)   The electron can be excited to the second excited state.

QUESTION 21***

Now consider the following quantities, both for an electron in an infinite well of width 8 nm (the well extends from x = 0 to x = 8 nm), and for an electron in a finite well of the same width: P(middle) ≡ probability to find electron in the middle 10% of the well, i.e., in the interval from x = 3.6 nm to x = 4.4 nm

Eground ≡ kinetic energy of the electron in the ground state

λ2→3 ≡ wavelength of photons needed to excite the electron from the n = 2 to the n = 3 state.

Which one of the following statements is correct?

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(a)   P(middle)infinite < P(middle)finite

(b)   Eground,infinite < Eground,finite

(c)   λ2→3,infinite = λ2→3,finite

(d)   all of the above

(e)   none of the above

QUESTION 22*

This and the following three questions should be considered together.

The wavefunction shown below corresponds to an eigenstate (with quantum number n) of a particle in a potential well.

If we measure the location of the particle, where is it most likely to be found?

(a)   at position xA

(b)   at position xB

(c)   at position xC

QUESTION 23*

Where is the total energy of the particle the highest?

(a)   at position xA

(b)   at position xB

(c)   at position xC

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(d)   same at all positions

(e)   cannot be determined from the information given

QUESTION 24**

Which one of the following can we conclude about the potential?

(a)   It has infinite walls.

(b)   It is a symmetric potential, i.e., V(-x) = V(x).

(c)   It has at most three bound states, i.e., no more than three energy eigenstates.

(d)   all of the above

(e)   none of the above

QUESTION 25*

If we reduce the width of the potential well, what will happen to the energy of the eigenstate with quantum number n?

(a)   decrease

(b)   increase

(c)   Cannot determine from the information given.

FALL 2008 QUESTION 1*

This and the following question should be considered together.

Consider a propagating wave y(x,t) given by:

y(x,t) = (5.0 × 10-6) cos[(3.0 × 106 rad/m) x + (9.0 × 1014 rad/s) t ]

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Which one of the following describes the velocity v of the wave?

(a)   v = 0.0 m/s

(b)   v = 1.0 × 108 m/s traveling in the +x direction

(c)   v = 1.0 × 108 m/s traveling in the -x direction

(d)   v = 3.0 × 108 m/s traveling in the +x direction

(e)   v = 3.0 × 108 m/s traveling in the -x direction

QUESTION 2**

A second wave y'(x,t) propagates in the same space as y(x,t) but is given by: y'(x,t) = (3.0 × 10-6) sin[(3.0 × 106 rad/m) x + (9.0 × 1014 rad/sec) t ]

What is the intensity of the superposition of these two waves?

Note: the second wave is given by a sine, not a cosine function, and the waves have different amplitudes. Hint: draw the appropriate phasor diagram.

(a)   3.4 × 10-11

(b)   4.8 × 10-11

(c)   6.4 × 10-11

QUESTION 3*

This and the following question should be considered together.

Two 100 MHz radio antennas A and B emitting in phase are separated by 100 m along a north-south line.

A radio receiver placed 20.0 km east is equidistant from both transmitting antennas and picks up a strong signal. How far north (distance x) should that receiver C be moved if it is again to detect a signal nearly as strong?

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(a)   600 m

(b)   90 km

(c)   120 km

QUESTION 4***

The receiver C is moved to a point 832.58 m east of the antennas and equidistant to the antennas. The intensity that each antenna alone produces at the receiver is I0. A third antenna with adjustable amplitude A3 and phase Φ3 is added to the array along the north-south line and at the midpoint between the two original antennas. Which of the choices of amplitude and phase listed below for the third antenna lead to no net signal (i.e. Itot = 0) at the receiver?

(a)   A3 = 4sqrt(I0) and Φ3 = 0

(b)   A3 = 4sqrt(I0) and Φ3 = π

(c)   A3 = 2sqrt(I0) and Φ3 = 0

(d)   A3 = 2sqrt(I0) and Φ3 = π/2

(e)   A3 = 2sqrt(I0) and Φ3 = π

QUESTION 5**

This and the following question should be considered together.

Two identical slits are uniformly illuminated from the left with monochromatic light of wavelength 400 nm. The slits are separated by a distance d. A screen is 0.7 m behind the slits. An interference peak with intensity 4.0 W/m2 is observed at point O with both slits open.

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The intensity at x = 0.5 mm on the screen is 2.0 W/m2. What is the smallest possible slit spacing d?

(a)   0.048 mm

(b)   0.092 mm

(c)   0.14 mm

(d)   0.18 mm

(e)   0.26 mm

QUESTION 6**

A third slit of equal size is created between the two slits, equidistant from each. By what factor does the total intensity at O increase by adding the third slit? The light source is exactly the same as in the preceding problem.

(a)   9/4

(b)   3/2

(c)   1

QUESTION 7*

This and the following two questions should be considered together.

A grating with a ruling density of 800 lines/mm is illuminated by a beam of light at normal incidence over an area of 1 cm × 1 cm.

Assume that the wavelength of the incident light is 500.0 nm. What is the angle of the second-order diffraction peak?

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(a)   5.37°

(b)   14.2°

(c)   28.6°

(d)   40.1°

(e)   53.1°

QUESTION 8*

Assume that the incident beam contains two wavelengths, one at λ1 = 500.00 nm, and the other at λ2 which is slightly greater than 500.00 nm. The two wavelengths can be barely resolved in the second order. What is λ2?

(a)   500.01 nm

(b)   500.03 nm

(c)   500.05 nm

QUESTION 9*

A screen is placed 50 cm from a single slit, which is illuminated with 690 nm light. If the distance between the first and third minima in the diffraction pattern is 3 mm, what is the width of the slit?

(a)   0.10 mm

(b)   0.23 mm

(c)   0.50 mm

QUESTION 10***

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What is the minimum slit width that still gives an interference minimum?

(a)   a = λ / 2

(b)   a = λ

(c)   There is no such minimum slit width; there is always a diffraction minimum.

QUESTION 11*

A HeNe laser emits light that has wavelength of 632.8 nm. The circular aperture through which the beam emerges has a diameter of 0.5 cm. Which of the following numbers is closest to the diameter of the beam 10 km from the laser?

(a)   0.07 m

(b)   3.09 m

(c)   21.3 m

QUESTION 12*

A certain painter created paintings with an enormous number of dots of pure pigment, each of which was approximately 2.00 mm in diameter. Outside which distance would one be unable to discern individual dots on the canvas (assume that λ = 500 nm and that the pupil diameter is 4 mm and that the dots are immediately next to each other.)

(a)   0.5 m

(b)   2.0 m

(c)   13.1 m

QUESTION 13*

This and the following question should be considered together.

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Molybdenum has a work function of 4.20 eV. Consider the photoelectric effect for this material.

What is the largest wavelength for which electrons are emitted through the photoelectric effect in this case?

(a)   0.61 nm

(b)   295 nm

(c)   500 nm

QUESTION 14*

What is the stopping potential if the incident light has a wavelength of 180 nm?

(a)   0 V

(b)   1.0 V

(c)   2.7 V

(d)   8.3 V

(e)   21 V

QUESTION 15*

The nucleus of an atom is of order 10-14 m in diameter. For an electron to be confined to a nucleus, its de Broglie wavelength would have to be on this order of magnitude or smaller.

What would be the kinetic energy of an electron confined to this region?

(a)   10 eV or less

(b)   10 keV

(c)   100 MeV or more

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QUESTION 16**

This and the following three questions should be considered together.

A collection of large molecules C60F48 (mass = 2.73 × 10-24 kg) are directed one at a time from a (small) source to a pair of nano-fabricated slits, 10 meters before a detection screen (figure below not to scale).

If the molecules are moving at 100 m/s, what slit spacing will lead to fringes separated by 24.3 μm?

(a)   10 nm

(b)   100 nm

(c)   1 μm

(d)   10 μm

(e)   There is no possibility to observe matter-wave interference with composite objects such as molecules -- only discrete point-like particles -- photons, electrons, neutrons -- can display such wave-like phenomena.

QUESTION 17*

What is the ratio of the momentum of a 400-nm photon to the momentum of one of these C60F48 molecules?

(a)   pphoton / pmolecule  =  6.1 × 10-6

(b)   pphoton / pmolecule  =  4.3 × 10-6

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(c)   pphoton / pmolecule  =  1

(d)   pphoton / pmolecule  =  12

(e)   pphoton / pmolecule  =  7.2 × 103

QUESTION 18**

Next we focus a beam of blue laser light (400 nm) just after the top slit, so that any molecule passing through the top slit will scatter at least one photon, but any molecule passing through the bottom slit will not scatter any photons.

Which one of the following best describes what happens to the interference pattern on the detection screen?

(a)   There is no change -- the momentum transferred to the molecule by the photon is too small to affect the pattern.

(b)   The interference pattern will disappear, but only if we measure the scattered photons, which then yield information on which slit a molecule passed through.

(c)   The interference pattern will disappear even if we donÕt measure the scattered photons, because the interfering processes are not indistinguishable, due to the availability of information on which slit a molecule passed through.

QUESTION 19*

If the laser has a power of 10 mW, how many 400-nm photons are emitted from he laser each second?

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(a)   2 × 1012

(b)   2 × 1013

(c)   2 × 1016

QUESTION 20**

This and the following three questions should be considered together.

An electron is in the second excited state of an infinite 1-D square potential well of width 3.5 nm.

What is the longest wavelength photon that could be emitted by this electron? (Hint: Draw an energy level diagram, and label it carefully.)

(a)   3.14 nm

(b)   9.84 nm

(c)   8.07 μm

(d)   12.1 μm

(e)   33.4 μm

QUESTION 21**

Which of the following could decrease the answer to the previous question, i.e., lead to a shorter wavelength photon?

(a)   Use a finite well (of the same width) instead.

(b)   Use a wider infinite well

(c)   Replace the electron with a more massive particle (with the same charge).

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(d)   Both (a) and (c) work.

(e)   None of these modifications have that effect.

QUESTION 22***

Now assume the electron is in the ground state of the well (E1 = 0.0307 eV), and that we shine on photons that have an energy of 0.12 eV. Which of the following will happen and why?

(a)   Nothing -- each photon doesn't have enough energy to excite the electron to the first excited state.

(b)   Nothing -- each photon has too much energy to excite the electron to the first excited state.

(c)   The electron can be excited to the first excited state.

QUESTION 23**

Compare the deBroglie wavelength λe of an electron in the ground state of the well with the wavelength λp of a proton in the ground state of a well of the same width.

(a)   λe < λp

(b)   λe > λp

(c)   λe = λp

QUESTION 24*

This and the following two questions should be considered together.

Consider the wavefunction shown below of a particle in a potential well.

Rank the probabilities of finding the particle within a small interval Δx of the location specified:

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(a)   P(xB) > P(xD) > P(xA) > P(xC)

(b)   P(xB) > P(xC) > P(xD) > P(xA)

(c)   P(xA) > P(xB) = P(xD) > P(xC)

QUESTION 25*

What energy state is the particle in (call the ground state n = 1)

(a)   2

(b)   3

(c)   4

QUESTION 26**

Where is the total energy of the particle the highest?

(a)   at position xA

(b)   at position xB

(c)   at position xC

(d)   same at all positions

(e)   cannot be determined from the information given

QUESTION 1*

This and the following question should be considered together.

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The figure shows the displacement of a sinusoidal wave as a function of time. The wave travels with a speed of 300 m/s.

What is the amplitude?

(a)   0 cm

(b)   0.6 cm

(c)   1.2 cm

(d)   2.5 cm

(e)   5.0 cm

QUESTION 2*

What is the wavelength?

(a)   0 m

(b)   1.2 m

(c)   2.5 m

(d)   120 m

(e)   750 m

QUESTION 3*

Which one of these functions describes a wave traveling toward the +x direction?

(a)   

(b)   

(c)   

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(d)   

(e)   

QUESTION 4*

The Keck telescope in Hawaii has a 10 m diameter mirror that functions as the aperture. Assuming diffraction-limited performance, what minimum separation Δx can this telescope in principle resolve two objects on a satellite that is a distance of 3400 km away? Assume the wavelength of light is λ = 550 nm.

(a)   Δx = 0.23 m

(b)   Δx = 0.87 m

(c)   Δx = 1.4 m

(d)   Δx = 5.9 m

(e)   Δx = 11.8 m

QUESTION 5*

This and the following question should be considered together.

Two loudspeakers 2 m apart each emit sound at a wavelength of 0.04 m, which is detected by a dense array of microphones located on a ring 100 m from the speakers. The intensity measured by each microphone is 5 mW/m2 from speaker #1 alone and 10 mW/m2 from speaker #2 alone.

What is the maximum intensity that is measured at any microphone when both speakers are on?

(a)   11 mW/m2

(b)   15 mW/m2

(c)   29 mW/m2

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(d)   125 mW/m2

(e)   not determined by information given

QUESTION 6*

What is the average intensity measured by the microphones when both speakers are on?

(a)   11 mW/m2

(b)   15 mW/m2

(c)   29 mW/m2

(d)   125 mW/m2

(e)   not determined by information given

QUESTION 7*

This and the following two questions should be considered together.

Three narrow slits with equal spacing d are at a distance L = 1.4 m away from a screen. L is much greater than d. The slits are illuminated at normal incidence with light of wavelength λ = 570 nm. The first principal maximum on the screen is at y = 2.0 mm.

What is the slit spacing d?

(a)   0.2 mm

(b)   0.4 mm

(c)   1.0 mm

(d)   2.0 mm

(e)   4.0 mm

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QUESTION 8***

What is the position y of the first interference minimum on the screen?

(a)   0.25 mm

(b)   0.333 mm

(c)   0.50 mm

(d)   0.667 mm

(e)   1.0 mm

QUESTION 9*

If the wave length of the light is changed from 570 nm to 650 nm, what happens to the width of the central maximum?

(a)   It becomes wider.

(b)   It becomes narrower.

(c)   It remains the same.

QUESTION 10*

This and the following question should be considered together.

Normal-incidence green light with λ = 515 nm is diffracted by a 2 cm wide grating with N = 3000 lines (assume that the entire grating is illuminated).

Through what angle θ is the 515 nm light diffracted in the 3rd order spectrum?

(a)   θ = 3.8°

(b)   θ = 8.2°

(c)   θ = 13.4°

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(d)   θ = 24.1°

(e)   θ = 38.6°

QUESTION 11*

What is the minimum wavelength difference Δλ from λ = 515 nm that can be resolved by this grating in the 3rd order spectrum?

(a)   Δλ = 0.0082 nm

(b)   Δλ = 0.056 nm

(c)   Δλ = 0.24 nm

(d)   Δλ = 0.84 nm

(e)   Δλ = 1.8 nm

QUESTION 12**

Compare a blue LED (light emitting diode) and a red LED. Which one of the following statements is false?

(a)   The frequency of the light from the blue LED is higher than that of the red LED.

(b)   The color of each LED does not change as the current through the LED increases.

(c)   The intensity of the emitted light depends on the current through the LED.

(d)   The turn-on voltage of each LED is within the range of 1 to 3 volts.

(e)   The blue LED has a lower turn-on voltage.

QUESTION 13*

A helium-neon laser emits red light of wavelength λ = 633 nm. Its output power is 1.00 mW. How many photons per second are produced by the laser?

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(a)   2.70 × 107 photons/s

(b)   1.17 × 109 photons/s

(c)   3.19 × 1015 photons/s

(d)   8.10 × 1017 photons/s

(e)   3.52 × 1019 photons/s

QUESTION 14*

This and the following question should be considered together.

Consider the photoelectric effect for platinum which is a metal with work function 5.50 eV.

What is the maximum wavelength of light λ max that can be used to eject electrons from the metal?

(a)   176 nm

(b)   225 nm

(c)   487 nm

(d)   589 nm

(e)   680 nm

QUESTION 15*

If one uses photons with energy 5.82 eV, the stopping voltage, Vstop, that must be applied to stop the photoemitted electrons is

(a)   2.00 × 1018 V

(b)   11.3 V

(c)   0.320 V

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QUESTION 16*

This and the following question should be considered together.

The interference pattern of a diffraction grating is observed on a screen at a distance of 2 m as shown in the figure (not too scale). The grating is 2.54 cm wide and has 5,000 lines and the light source is a red laser with wavelength λ = 650 nm.

What is the position s of the first order interference maximum?

(a)   s = 4.10 cm

(b)   s = 8.40 cm

(c)   s = 17.1 cm

(d)   s = 25.8 cm

(e)   s = 48.2 cm

QUESTION 17*

What is the highest order interference maximum mmax that can be observed?

(a)   mmax = 7

(b)   mmax = 9

(c)   There is no limit. The intensity decreases for higher orders but very high orders can be observed with sensitive instruments.

QUESTION 18*

Quantum interference effects are shown by

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(a)   electrons and photons only.

(b)   any type of small particle.

(c)   only particles traveling at or near the speed of light.

QUESTION 19*

Which one of the following is true for any particle? If you double the wavelength you always get:

(a)   double the energy

(b)   half the energy

(c)   double the momentum

(d)   half the momentum

(e)   None of the above.

QUESTION 20*

The Heisenberg uncertainty principle says that

(a)   no variable can have a precise value.

(b)   momentum and position cannot both have precise values.

(c)   no experimental results are predictable.

QUESTION 21**

A beam of atoms with speed 1000 m/sec and masses of 10-25 kg passes in the x direction through a hole with a radius of 10-7 m. What is the minimum possible spread in the y-velocity of the atoms right after they pass through the hole? Pick the answer below that is closest to your calculated result.

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(a)   0 m/s

(b)   10-12 m/s

(c)   10-7 m/s

(d)   10-2 m/s

(e)   103 m/s

QUESTION 22**

A particle is in the ground state of a finite well, with potential energy zero inside the well and U outside. If U is made larger, while keeping everything else fixed, the ground state energy

(a)   increases.

(b)   decreases.

(c)   stays the same.

QUESTION 23*

The kinetic energy of an electron in the ground state of an infinite one-dimensional square well 4 nm wide is:

(a)   0.00102 eV

(b)   0.00135 eV

(c)   0.0235 eV

(d)   not a definite value because of the uncertainly principle.

(e)   not determined by information given. 

QUESTION 24*

A particle is confined in an infinite one-dimensional square well. If you double the particle's mass without changing the size of the well, what happens to the particle's ground-state kinetic energy?

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(a)   It does not change.

(b)   It doubles.

(c)   It quadruples.

(d)   It halves.

(e)   It becomes uncertain and cannot be determined.

QUESTION 25*

The figure shows the wave function describing a particle in one dimension. Near which of the three positions is the particle most likely to be found?

(a)   

(b)   

(c)   

QUESTION 26*

An electron drops from the n = 3 to the n = 2 level of an infinite square well, emitting a photon with wavelength λA. Then it drops from the n = 2 level to the n = 1 level, emitting a photon with wavelength λB. What is the ratio λB / λA ?

(a)   3/4

(b)   1

(c)   4/3

(d)   5/3

(e)   9/4

SPRING 2007 QUESTION 1*

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To the right is a list of some equations describing how some field y(x,t) that depends on position x and time t changes. Which one of them does NOT obey the superposition principle?

(a)   

(b)   

(c)   

(d)   

(e)   

QUESTION 2*

Two sound waves with a frequency of 600 Hz and intensities 1.0 W/m2 and 3.0 W/m2 arrive at a microphone. What is the minimum possible intensity at the microphone?

(a)   0.536 W/m2

(b)   0.821 W/m2

(c)   1.000 W/m2

(d)   1.414 W/m2

(e)   4.000 W/m2

QUESTION 3***

Two speakers separated by 2 m emit sound of equal intensity in phase with a wavelength of 1 m. A listener walks around the speakers in a circle of radius 10 m. How many minima does the listener observe as he/she walks around the full circle?

(a)   0

(b)   2

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(c)   4

(d)   8

(e)   16

QUESTION 4**

If three waves of equal amplitude A1 are superimposed so that the total is A1cos(kx - ωt) + A1cos(kx - ωt + π/4) + A1cos(kx - ωt + π/2) what is the amplitude Atot of the resulting wave?

(a)   Atot = 1.000 A1

(b)   Atot = 1.732 A1

(c)   Atot = 1.848 A1

(d)   Atot = 2.414 A1

(e)   Atot = 3.000 A1

QUESTION 5*

This and the following two questions should be considered together.

The figure below (not to scale) shows a light wave from a monochromatic source of wavelength λ = 6.0 × 10-7 m, which goes through two small openings separated by a distance d = 3.3 mm, and forms a pattern on the screen which is at a distance L = 3 m.

What is the frequency of the light?

(a)   f = 6.0 × 1012 Hz

(b)   f = 5.0 × 1014 Hz

(c)   f = 4.0 × 1015 Hz

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QUESTION 6*

What is the separation between bright spots Δy in the resulting interference pattern?

(a)   Δy = 4.3 × 10-1 m

(b)   Δy = 8.4 × 10-2 m

(c)   Δy = 6.2 × 10-3 m

(d)   Δy = 5.4 × 10-4 m

(e)   Δy = 2.1 × 10-5 m

QUESTION 7*

If the spacing d between the openings is increased slightly, does the separation between bright spots Δy increase, decrease, or stay the same?

(a)   increase

(b)   decrease

(c)   stay the same

QUESTION 8*

This and the following two questions should be considered together.

Three loudspeakers, A, B, and C, are driven in phase with sound wavelength 0.75 m. They are arranged along a line as shown. The separation between adjacent speakers is d = 3.00 m. The sound intensity received from the speakers along a line far from the speakers is measured as a function of angle θ. When speaker A is alone, 2.00 μW/m2 is received. When speaker B or C are alone, 1.00 μW/m2 is received. Assume that the loudspeakers can be treated as point sources of sound.

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What sound intensity is received at θ = 0° when all three are driven?

(a)   2.00 μW/m2

(b)   3.41 μW/m2

(c)   4.00 μW/m2

(d)   7.41 μW/m2

(e)   11.7 μW/m2

QUESTION 9***

What sound intensity is received at sin(θ) = 1/32 when all three speakers are driven?

(a)   2.00 μW/m2

(b)   3.41 μW/m2

(c)   4.00 μW/m2

(d)   7.41 μW/m2

(e)   11.7 μW/m2

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QUESTION 10**

Suppose that the intensity of the speakers is changed so that when speakers A or C are alone, 1 μW/m2 is received, and when speaker B is alone, 2 μW/m2 is received. If we were to compare the intensity pattern in this situation to the original intensity pattern, what would we find? Choose the best answer from the choices below.

(a)   The positions of the principal maxima do not change, but they become more intense.

(b)   The positions of the principal maxima change, but their intensities do not change.

(c)   The positions and intensities of the principal maxima do not change.

QUESTION 11*

This and the following question should be considered together.

Music is played by a loudspeaker that is far from a number of equally spaced slits. The spacing between the slits is 2.50 m. The width of the slits is 0.10 m. The distance L between the loud speaker and the slits is large so that the relative phase of the sound reaching adjacent slits is zero. Use 330 m/s for the speed of sound. Sound is measured along a line far from the slits as shown in the figure.

At what angle, θ, is the first order principal interference maximum for sound with frequency f = 256 Hz (middle C)?

(a)   25.6°

(b)   31.0°

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(c)   37.9°

(d)   43.2°

(e)   48.6°

QUESTION 12*

Compare the angle, θ', at which the first interference maximum f = 271 Hz (C-sharp) occurs to the angle, θ, at which the first interference maximum for C occurs.

(a)   θ' > θ

(b)   θ' = θ

(c)   θ' < θ

QUESTION 13*

This and the following two questions should be considered together.

Blue-green light with wavelength 495 nm strikes a single hole and is transmitted onto a screen 5 meters away, as shown. The pattern on the screen is sketched below. The diameter of the smallest ring of intensity minima is 4 mm. i.e. that ring is 2 mm from the central peak.

What is the hole diameter?

(a)   102 μm

(b)   200 μm

(c)   411 μm

(d)   806 μm

(e)   1500 μm

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QUESTION 14***

If the hole diameter is doubled, about how much will the intensity at the very center of the central peak change?

(a)   stay roughly the same

(b)   about double

(c)   increase about sixteen-fold

QUESTION 15*

In order to take a fairly clear picture of the hole, using a camera 5 m away, about what is the minimum lens diameter you could use?

(a)   83 μm

(b)   4 mm

(c)   2.5 m

QUESTION 16***

Say that a beam of atoms with speed 1000 m/sec and masses of 10-25 kg passes in the x direction through a hole with a radius of 10-7 m. About what's the minimum possible spread in the y-velocity of the atoms right after they pass through the hole?

(a)   0 m/s

(b)   10-12 m/s

(c)   10-7 m/s

(d)   10-2 m/s

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(e)   103 m/s

QUESTION 17*

Light of wavelength 500 nm hits a metal with work-function 1.5 eV. What's the maximum kinetic energy of the emitted electrons?

(a)   0.98 eV

(b)   2.48 eV

(c)   3.98 eV

(d)   76.0 eV

(e)   None are emitted.

QUESTION 18*

Say you are offered a chance to buy a device which extracts energy forever from quantum fluctuations. According to current quantum theory,

(a)   you cannot test whether the device works because measurement always perturbs the system.

(b)   it might work, because Heisenberg proved that everything is uncertain.

(c)   it can't work because energy is still conserved.

QUESTION 19*

The wavelength of a virus whose mass is 10-21 kg traveling at 10 m/s is about

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(a)   6.6 × 10-14 m

(b)   1.5 × 10-10 m

(c)   2.0 × 10-8 m

QUESTION 20**

Say someone proposed doing a two-slit experiment with large molecules, like C60. Which of these is true?

(a)   It will be tricky because the relation between momentum and wavelength is complicated for big molecules.

(b)   It can't work if the wavelengths are smaller than the molecular size.

(c)   It's been done.

QUESTION 21*

A photon and an electron with the same wavelength have the same

(a)   speed.

(b)   energy.

(c)   mass.

(d)   momentum.

(e)   none of the above

QUESTION 22*

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We study the time-independent Schrödinger equation because

(a)   every particle must be in a state of definite energy.

(b)   in practice, states with superpositions of different energies aren't found.

(c)   any state can be expressed as a superposition of states with different definite energies.

QUESTION 23*

Consider the following wavefunction describing a particle in one dimension.

Near which of the three positions is the particle most likely to be found?

(a)   

(b)   

(c)   

QUESTION 24**

Say you are completely color blind, but you want to know what color a photodiode emits. So, you set up the photodiode in the configuration shown, and measure the current voltage curve across the diode, as shown below.

Approximately what wavelength is the light emitted by the diode?

(a)   310 nm

(b)   450 nm

(c)   620 nm

(d)   3200 nm

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(e)   not enough information, even approximately

QUESTION 25**

This and the following question should be considered together.

To measure the diameter of a hair, you shine a laser beam of 500 nm light onto a vertically stretched hair, and the diffracted light shines onto a screen 1 meter from the hair.

The horizontal diffraction pattern you see is

(a)   many equally spaced peaks with about the same intensity, separated by zeros.

(b)   a high intensity center peak, with equally spaced zeros and smaller peaks on each side.

(c)   a dark area in the center, with equally spaced zeros and smaller peaks on each side.

QUESTION 26*

The zeros on the left side of the diffraction pattern are separated by 2.5 centimeters. What is the diameter of the hair?

(a)   10 microns

(b)   20 microns

(c)   35 microns

(d)   100 microns

(e)   You cannot tell from just this experiment without more information.