Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an online homework management program such as WileyPLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
In working these problems, ignore relativistic effects.
ssm Solution is in the Student Solutions Manual.
This icon represents a biomedical application.
Section 29.3 Photons and the Photoelectric Effect

| 1 | ssm Ultraviolet light with a frequency of strikes a metal surface and ejects electrons that have a maximum kinetic energy of 6.1 eV. What is the work function (in eV) of the metal?

| 2 | Two sources produce electromagnetic waves. Source B produces a wavelength that is three times the wavelength produced by source A. Each photon from source A has an energy of . What is the energy of a photon from source B?

| 3 | An FM radio station broadcasts at a frequency of 98.1 MHz. The power radiated from the antenna is . How many photons per second does the antenna emit?

| 4 | The maximum wavelength that an electromagnetic wave can have and still eject electrons from a metal surface is 485 nm. What is the work function W0 of this metal? Express your answer in electron volts.

| 5 | ssm Ultraviolet light is responsible for sun tanning. Find the wave length (in nm) of an ultraviolet photon whose energy is .

| 6 | Light is shining perpendicularly on the surface of the earth with an intensity of 680 W/m2. Assuming all the photons in the light have the same wavelength (in vacuum) of 730 nm, determine the number of photons per second per square meter that reach the earth.

| 7 | Radiation of a certain wavelength causes electrons with a maximum kinetic energy of 0.68 eV to be ejected from a metal whose work function is 2.75 eV. What will be the maximum kinetic energy (in eV) with which this same radiation ejects electrons from another metal whose work function is 2.17 eV?

* | 8 | Multiple-Concept Example 3 provides pertinent information for problems such as this. The maximum wavelength for which an electromagnetic wave can eject electrons from a platinum surface is 196 nm. When radiation with a wavelength of 141 nm shines on the surface, what is the maximum speed of the ejected electrons?

* | 9 | ssm Consult Interactive LearningWare 29.1 at for background material relating to this problem. An owl has good night vision because its eyes can detect a light inten sity as small as . What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of 8.5 mm and the light has a wavelength of 510 nm?

* | 10 | A proton is located at a distance of 0.420 m from a point charge of . The repulsive electric force moves the proton until it is at a distance of 1.58 m from the charge. Suppose that the electric potential energy lost by the system is carried off by a photon that is emitted during the process. What is its wavelength?

** | 11 | ssm www A laser emits photons per second in a beam of light that has a diameter of 2.00 mm and a wavelength of 514.5 nm. Determine (a) the average electric field strength and (b) the average magnetic field strength for the electromagnetic wave that constitutes the beam.

** | 12 | (a) How many photons () must be absorbed to melt a 2.0-kg block of ice at 0 °C into water at 0 °C? (b) On the average, how many H2O molecules does one photon convert from the ice phase to the water phase? Section 29.4 The Momentum of a Photon and the Compton Effect

| 13 | A light source emits a beam of photons, each of which has a momentum of . (a) What is the frequency of the photons? (b) To what region of the electromagnetic spectrum do the photons belong? Consult Figure 24.10 if necessary.

| 14 | A photon of red light () and a Ping-Pong ball () have the same momentum. At what speed is the ball moving?

| 15 | ssm In a Compton scattering experiment, the incident X-rays have a wavelength of 0.2685 nm, and the scattered X-rays have a wavelength of 0.2703 nm. Through what angle in Figure 29-10 are the X-rays scattered?

| 16 | Incident X-rays have a wavelength of 0.3120 nm and are scattered by the “free” electrons in graphite. The scattering angle in Figure 29-10 is . What is the magnitude of the momentum of (a) the incident photon and (b) the scattered photon? (For accuracy, use and .)

| 17 | Refer to Interactive Solution 29.17 at for help in solving this problem. An incident X-ray photon of wavelength 0.2750 nm is scattered from an electron that is initially at rest. The photon is scattered at an angle of in Figure 29-10 and has a wavelength of 0.2825 nm. Use the conservation of linear momentum to find the momentum gained by the electron.

* | 18 | The X-rays detected at a scattering angle of in Figure 29-10 have a wavelength of 0.1867 nm. Find (a) the wavelength of an incident photon, (b) the energy of an incident photon, (c) the energy of a scattered photon, and (d) the kinetic energy of the recoil electron. (For accuracy, use and .)

* | 19 | ssm www What is the maximum amount by which the wave length of an incident photon could change when it undergoes Compton scattering from a nitrogen molecule (N2)?

** | 20 | An X-ray photon is scattered at an angle of from an electron that is initially at rest. After scattering, the electron has a speed of . Find the wavelength of the incident X-ray photon. Section 29.5 The De Broglie Wavelength and the Wave Nature of Matter

| 21 | The interatomic spacing in a crystal of table salt is 0.282 nm. This crystal is being studied in a neutron diffraction experiment, similar to the one that produced the photograph in Figure 29-13. How fast must a neutron () be moving to have a de Broglie wavelength of 0.282 nm?

| 22 | A bacterium () in the blood is moving at 0.33 m/s. What is the de Broglie wavelength of this bacterium?

| 23 | ssm As Section 27.5 discusses, sound waves diffract, or bend, around the edges of a doorway. Larger wavelengths diffract more than smaller wavelengths. (a) The speed of sound is 343 m/s. With what speed would a 55.0-kg person have to move through a doorway to diffract to the same extent as a 128-Hz bass tone? (b) At the speed calculated in part (a), how long (in years) would it take the person to move a distance of one meter?

| 24 | How fast does a proton have to be moving in order to have the same de Broglie wavelength as an electron that is moving with a speed of ?

| 25 | A photon has the same momentum as an electron moving with a speed of . What is the wavelength of the photon?

* | 26 | A particle has a de Broglie wavelength of . Then its kinetic energy doubles. What is the particle’s new de Broglie wavelength, assuming that relativistic effects can be ignored?

* | 27 | ssm From a cliff that is 9.5 m above a lake, a young woman () jumps from rest, straight down into the water. At the instant she strikes the water, what is her de Broglie wavelength?

* | 28 | The width of the central bright fringe in a diffraction pattern on a screen is identical when either electrons or red light () pass through a single slit. The distance between the screen and the slit is the same in each case and is large compared to the slit width. How fast are the electrons moving?

* | 29 | Consult Interactive Solution 29.29 at to explore a model for solving this problem. In a television picture tube the electrons are accelerated from rest through a potential difference V. Just before an electron strikes the screen, its de Broglie wavelength is . What is the potential difference?

** | 30 | The kinetic energy of a particle is equal to the energy of a photon. The particle moves at 5.0% of the speed of light. Find the ratio of the photon wavelength to the de Broglie wavelength of the particle. Section 29.6 The Heisenberg Uncertainty Principle

| 31 | Consider a line that is 2.5 m long. A moving object is some where along this line, but its position is not known. (a) Find the min imum uncertainty in the momentum of the object. Find the minimum uncertainty in the object’s velocity, assuming that the object is (b) a golf ball () and (c) an electron.

| 32 | An electron is trapped within a sphere that has a diameter of (about the size of the nucleus of an oxygen atom). What is the minimum uncertainty in the electron’s momentum?

| 33 | ssm www In the lungs there are tiny sacs of air, which are called alveoli. The average diameter of one of these sacs is 0.25 mm. Consider an oxygen molecule () trapped within a sac. What is the minimum uncertainty in the velocity of this oxygen molecule?

| 34 | Review Conceptual Example 7 as background for this problem. When electrons pass through a single slit, as in Figure 29-15, they form a diffraction pattern. As Section 29.4 discusses, the central bright fringe extends to either side of the midpoint, according to an angle given by , where is the de Broglie wavelength of the electron and W is the width of the slit. When is the same size as W, , and the central fringe fills the entire observation screen. In this case, an electron passing through the slit has roughly the same probability of hitting the screen either straight ahead or anywhere off to one side or the other. Now, imagine yourself in a world where Planck’s constant is large enough so you exhibit similar effects when you walk through a 0.90-m-wide doorway. Your mass is 82 kg and you walk at a speed of 0.50 m/s. How large would Planck’s constant have to be in this hypothetical world?

| 35 | ssm www Particles pass through a single slit of width 0.200 mm (see Figure 29-15). The de Broglie wavelength of each particle is 633 nm. After the particles pass through the slit, they spread out over a range of angles. Use the Heisenberg uncertainty principle to determine the minimum range of angles.

* | 36 | The minimum uncertainty in the position y of a particle is equal to its de Broglie wavelength. Determine the minimum uncertainty in the speed of the particle, where this minimum uncertainty is expressed as a percentage of the particle’s speed . Assume that relativistic effects can be ignored.

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