Solved: When light with a wavelength of 221 nm is incident

In converting electrical energy into light energy, a sixty-watt incandescent light bulb operates at about 2.1% efficiency. Assuming that all the light is green light (vacuum wavelength 555 nm), determine the number of photons per second given off by the bulb.

The work function for a silver surface is W0 4.73 eV. Find the minimum frequency that light must have to eject electrons from this surface.

Light with a wavelength of 95 nm shines on a selenium surface, which has a work function of 5.9 eV. The ejected electrons have some kinetic energy. Determine the maximum speed with which electrons are ejected.

The photons emitted by a source of light do not all have the same energy. Is the source monochromatic? (A monochromatic light source emits light that has a single wavelength.)

Which colored light bulbred, orange, yellow, green, or violetemits photons with (a) the least energy and (b) the greatest energy? (See Example 1 in Chapter 24.)

Does a photon emitted by a higher-wattage red light bulb have more energy than a photon emitted by a lower-wattage red bulb?

Radiation of a given wavelength causes electrons to be emitted from the surface of metal 1 but not from the surface of metal 2. Why could this be? (a) Metal 1 has a greater work function than metal 2 has. (b) Metal 1 has a smaller work function than metal 2 has. (c) The energy of a photon striking metal 1 is greater than the energy of a photon striking metal 2

In the photoelectric effect, electrons are ejected from the surface of a metal when light shines on it. Which one or more of the following would lead to an increase in the maximum kinetic energy of the ejected electrons? (a) Increasing the frequency of the incident light (b) Increasing the number of photons per second striking the surface (c) Using photons whose frequency f0 is less than W0/h, where W0 is the work function of the metal and h is Plancks constant (d) Selecting a metal that has a greater work function

In the photoelectric effect, suppose that the intensity of the light is increased, while the frequency of the light is kept constant. The frequency is greater than the minimum frequency f0. State whether each of the following will increase, decrease, or remain the same: (a) The current in the phototube (b) The number of electrons emitted per second from the metal surface (c) The maximum kinetic energy that an electron could have (d) The maximum momentum that an electron could have

One propulsion method that is currently being studied for interstellar travel uses a large sail. The intent is that sunlight striking the sail will create a force that pushes the ship away from the sun (Figure 29.11), much as the wind propels a sailboat. To get the greatest possible force, the surface of the sail facing the sun (a) should be shiny like a mirror, (b) should be black, or (c) could be either shiny or black, since the same force will be created for either type of surface

In the Compton effect, an incident X-ray photon of wavelength is scattered by an electron, and the scattered photon has a wavelength of . Suppose that the incident photon is scattered by a proton instead of an electron. For a given scattering angle , is the change   in the wavelength of the photon scattered by the proton greater than, less than, or the same as the wavelength of the photon scattered by the electron? (Hint: Use Equation 29.7 for a proton instead of an electron.) 8.

In a Compton scattering experiment, an incident X-ray photon is traveling along the x direction. An electron, initially at rest, is struck by the photon and is accelerated straight ahead in the same direction as the incident X-ray photon. Which way does the scattered photon move? (a) Along the y direction (b) Along the y direction (c) Along the x direction (Hint: Use the principle of conservation of momentum to guide your reasoning.)

The speed of a particle is much less than the speed of light. Thus, when the particles speed doubles, the particles momentum doubles, and its kinetic energy becomes four times greater. However, when the momentum of a photon doubles, its energy becomes (a) two times greater (b) four times greater (c) one-half as much (d) one-fourth as much.

Review Conceptual Example 4 as background for this question. The photograph shows a device called a radiometer. The four regular panels are black on one side and shiny like a mirror on the other side. In bright light, the panel arrangement spins around in a direction from the black side of a panel toward the shiny side. Do photon collisions with both sides of the panels cause the observed spinning?

Determine the de Broglie wavelength for (a) an electron (mass 9.1  1031 kg) movin

A stone is dropped from the top of a building. As the stone falls, does its de Broglie wavelength increase, decrease, or remain the same?

An electron and a neutron have different masses. Is it possible, according to Equation 29.8, that they can have the same de Broglie wavelength? (a) Yes, provided the magnitudes of their momenta are different. (b) Yes, provided their speeds are different. (c) No; two particles with different masses always have different de Broglie wavelengths

In Figure 29.1b, replace the electrons with protons that have the same speed. With the aid of Equation 27.1 for the bright fringes in Youngs double-slit experiment and Equation 29.8, decide whether the angular separation between the fringes would increase, decrease, or remain the same, relative to the angular separation produced by the electrons

A beam of electrons passes through a single slit, and a beam of protons passes through a second, but identical, slit. The electrons and the protons have the same speed. Which one of the following correctly describes the beam that experiences the greatest amount of diffraction? (a) The electrons, because they have the smaller momentum and, hence, the smaller de Broglie wavelength (b) The electrons, because they have the smaller momentum and, hence, the larger de Broglie wavelength (c) The protons, because they have the smaller momentum and, hence, the smaller de Broglie wavelength (d) The protons, because they have the larger momentum and, hence, the smaller de Broglie wavelength (e) Both beams experience the same amount of diffraction, because the electrons and protons have the same de Broglie wavelength.

Assume that the position of an object is known so precisely that the uncertainty in the position is only y 1.5  1011 m. (a) Determine the minimum uncertainty in the momentum of the object. Find the corresponding minimum uncertainty in the speed of the object in the case when the object is (b) an electron (mass 9.1  1031 kg) and (c) a Ping-Pong ball (mass 2.2  103 kg). Rea

Suppose that you are target shooting at a stationary target. A bullet leaving the barrel of a gun is analogous to an electron passing through the single slit in Figure 29.14. With this analogy in mind and assuming that the magnitude of the bullets momentum is not abnormally large, what would target shooting be like if Plancks constant had a relatively large value instead of its extremely small value of 6.63 1034 Js? (a) It would be more accurate because there would be less uncertainty in where the bullet hits the target. (b) It would be less accurate because there would be greater uncertainty in where the bullet hits the target. (c) There would be no difference.

Sunlight, whose visible wavelengths range from 380 to 750 nm, is incident on a sodium surface. The work function for sodium is W0 2.28 eV. Find the maximum kinetic energy KEmax (in joules) of the photoelectrons emitted from the surface and the range of wavelengths that will cause photoelectrons to be emitted.

Will electrons with a greater value of KEmax be emitted when the incident photons have a relatively greater or a relatively smaller amount of energy?

In the range of visible wavelengths, which wavelength corresponds to incident photons that carry the greatest energy?

What is the smallest value of KEmax with which an electron can be ejected from the sodium?

An electron and a proton have the same kinetic energy and are moving at speeds much less than the speed of light. Determine the ratio of the de Broglie wavelength of the electron to that of the proton.

How is the de Broglie wavelength related to the magnitude p of the momentum?

How is the magnitude of the momentum related to the kinetic energy of a particle of mass m that is moving at a speed that is much less than the speed of light?

Which has the greater de Broglie wavelength, the electron or the proton?

An astronomer is measuring the electromagnetic radiation emitted by two stars, which are both assumed to be perfect blackbody emitters. For each star she makes a plot of the radiation intensity per unit wavelength as a function of wavelength. She notices that the curve for star A has a maximum that occurs at a shorter wavelength than does the curve for star B. What can she conclude about the surface temperatures of the two stars? (a) Star A has the greater surface temperature. (b) Star B has the greater surface temperature. (c) Both stars, being perfect blackbody emitters, have the same surface temperature. (d) There is not enough information to draw a conclusion about the temperatures.

Photons are generated by a microwave oven in a kitchen and by an X-ray machine at a dentists office. Which type of photon has the greater frequency, the greater energy, and the greater wavelength?

A laser emits a beam of light whose photons all have the same frequency. When the beam strikes the surface of a metal, photoelectrons are ejected from the surface. What happens if the laser emits twice the number of photons per second? (a) The photoelectrons are ejected from the surface with twice the maximum kinetic energy. (b) The photoelectrons are ejected from the surface with the same maximum kinetic energy. (c) The number of photoelectrons ejected per second from the surface doubles. (d) Both b and c happen. (e) Both a and c happen.

The surface of a metal plate is illuminated with light of a certain frequency. Which of the following conditions determine whether or not photoelectrons are ejected from the metal? 1. The number of photons per second emitted by the light source 2. The length of time that the light is turned on 3. The thermal conductivity of the metal 4. The surface area of the metal illuminated by the light 5. The type of metal from which the plate is made (a) 1 and 2 (b) 5 (c) 3 and 5 (d) 4 (e) 2 and 3

Does a photon, like a moving particle such as an electron, have a momentum? (a) No, because a photon is a wave, and a wave does not have a momentum. (b) No, because a photon has no mass, and mass is necessary in order to have a momentum. (c) No, because a photon, always traveling at the speed of light in a vacuum, would have an infinite momentum. (d) Yes, and the magnitude p of the photons momentum is related to its wavelength by p  h/, where h is Plancks constant. (e) Yes, and the magnitude p of the photons momentum is related to its wavelength by p  h, where h is Plancks constant. (29

Two particles, A and B, have the same mass, but particle A has a charge of q and B has a charge of 2q. The particles are accelerated from rest through the same potential difference. Which one has the longer de Broglie wavelength at the end of the acceleration? (a) Particle A, because it has the greater momentum, and, hence, the longer de Broglie wavelength (b) Particle B, because it has the greater momentum, and, hence, the longer de Broglie wavelength (c) Particle A, because it has the smaller momentum, and, hence, the longer de Broglie wavelength (d) Particle B, because it has the smaller momentum, and, hence, the longer de Broglie wavelength (e) Both particles have the same de Broglie wavelength.

Suppose that the momentum of an electron is measured with complete accuracy (i.e., the uncertainty in its momentum is zero). The uncertainty in a simultaneous measurement of the electrons position __________. (a) is also zero (b) is infinitely large (c) is some finite value between zero and infinity (d) cannot be measured, because one cannot measure the position and momentum of a particle, such as an electron, simultaneously

The dissociation energy of a molecule is the energy required to break the molecule apart into its separate atoms. The dissociation energy for the cyanogen molecule is 1.22 1018 J. Suppose that this energy is provided by a single photon. Determine the (a) wavelength and (b) frequency of the photon. (c) In what region of the electromagnetic spectrum (see Figure 24.9) does this photon lie?

An AM radio station broadcasts an electromagnetic wave with a frequency of 665 kHz, whereas an FM station broadcasts an electromagnetic wave with a frequency of 91.9 MHz. How many AM photons are needed to have a total energy equal to that of one FM photon?

Ultraviolet light with a frequency of 3.00 1015 Hz 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?

Light is shining perpendicularly on the surface of the earth with an intensity of 680 W/m2 . Assuming that 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.

Ultraviolet light is responsible for sun tanning. Find the wavelength (in nm) of an ultraviolet photon whose energy is 6.4 1019 J.

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.

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?

Multiple-Concept Example 3 reviews the concepts necessary to solve this problem. Radiation with a wavelength of 238 nm shines on a metal surface and ejects electrons that have a maximum speed of 3.75 105 m/s. Which one of the following metals is it, the values in parentheses being the work functions: potassium (2.24 eV), calcium (2.71 eV), uranium (3.63 eV), aluminum (4.08 eV), or gold (4.82 eV)?

An owl has good night vision because its eyes can detect a light intensity as small as 5.0 1013 W/m2 . 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?

A proton is located at a distance of 0.420 m from a point charge of 8.30 C. 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 were carried off by a photon. What would be its wavelength?

When light with a wavelength of 221 nm is incident on a certain metal surface, electrons are ejected with a maximum kinetic energy of 3.28 1019 J. Determine the wavelength (in nm) of light that should be used to double the maximum kinetic energy of the electrons ejected from this surface.

A glass plate has a mass of 0.50 kg and a specific heat capacity of 840 J/(kg C). The wavelength of infrared light is 6.0 105 m, while the wavelength of blue light is 4.7 107 m. Find the number of infrared photons and the number of blue photons needed to raise the temperature of the glass plate by 2.0 C, assuming that all the photons are absorbed by the glass. *

A laser emits 1.30 1018 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.

(a) How many photons (wavelength 620 nm) 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? S

A light source emits a beam of photons, each of which has a momentum of 2.3 1029 kg m/s. (a) What is the frequency of the photons? (b) To what region of the electromagnetic spectrum do the photons belong? Consult Figure 24.9 if necessary.

A photon of red light (wavelength 720 nm) and a Ping-Pong ball (mass 2.2 103 kg) have the same momentum. At what speed is the ball moving?

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?

A sample is bombarded by incident X-rays, and free electrons in the sample scatter some of the X-rays at an angle of 122.0 with respect to the incident X-rays (see Figure 29.10). The scattered X-rays have a momentum whose magnitude is 1.856 1024 kg m/s. Determine the wavelength (in nm) of the incident X-rays. (For accuracy, use h 6.626 1034 Js, c 2.998 108 m/s, and m 9.109 1031 kg for the mass of an electron.) 19. mmh

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 180.0 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. 2

In the Compton effect, momentum conservation applies, so the total momentum of the photon and the electron is the same before and after the scattering occurs. Suppose that in Figure 29.10 the incident photon moves in the x direction and the scattered photon emerges at an angle of 90.0, which is in the y direction. The incident photon has a wavelength of 9.00 1012 m. Find the x and y components of the momentum of the scattered electron. *

What is the maximum amount by which the wavelength of an incident photon could change when it undergoes Compton scattering from a nitrogen molecule (N2)?

Figure 29.10 shows the setup for measuring the Compton effect. With a fixed incident wavelength, a wavelength of  1 is measured for a scattering angle of 1 30.0, whereas a wavelength of  2 is measured for a scattering angle of 2 70.0. Find the difference in wavelengths,  2   1. * 2

A photon of wavelength 0.45000 nm strikes a free electron that is initially at rest. The photon is scattered straight backward. What is the speed of the recoil electron after the collision?

An X-ray photon is scattered at an angle of 180.0 from an electron that is initially at rest. After scattering, the electron has a speed of 4.67 106 m/s. Find the wavelength of the incident X-ray photon. Se

A bacterium (mass 2 1015 kg) in the blood is moving at 0.33 m/s. What is the de Broglie wavelength of this bacterium? 2

What are (a) the wavelength of a 5.0-eV photon and (b) the de Broglie wavelength of a 5.0-eV electron?

As Section 17.3 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?

An electron and a proton have the same speed. Ignore relativistic effects and determine the ratio electron/proton of their de Broglie wavelengths.

Recall from Section 14.3 that the average kinetic energy of an atom in a monatomic ideal gas is given by where k 1.38 1023 J/K and T is the Kelvin temperature of the gas. Determine the de Broglie wavelength of a helium atom (mass 6.65 1027 kg) that has the average kinetic energy at room temperature (293 K). 30.

In a Youngs double-slit experiment that uses electrons, the angle that locates the first-order bright fringes is A 1.6 104 degrees when the magnitude of the electron momentum is pA 1.2 1022 kg m/s. With the same double slit, what momentum magnitude pB is necessary so that an angle of B 4.0 104 degrees locates the first-order bright fringes? * 31. s

A particle has a de Broglie wavelength of 2.7 1010 m. Then its kinetic energy doubles. What is the particles new de Broglie wavelength, assuming that relativistic effects can be ignored?

From a cliff that is 9.5 m above a lake, a young woman (mass 41 kg) jumps from rest, straight down into the water. At the instant she strikes the water, what is her de Broglie wavelength?

The width of the central bright fringe in a diffraction pattern on a screen is identical when either electrons or red light (vacuum wavelength 661 nm) 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?

Particle A is at rest, and particle B collides head-on with it. The collision is completely inelastic, so the two particles stick together after the collision and move off with a common velocity. The masses of the particles are different, and no external forces act on them. The de Broglie wavelength of particle B before the collision is 2.0 1034 m. What is the de Broglie wavelength of the object that moves off after the collision?

An electron, starting from rest, accelerates through a potential difference of 418 V. What is the final de Broglie wavelength of the electron, assuming that its final speed is much less than the speed of light?

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.

An object is moving along a straight line, and the uncertainty in its position is 2.5 m. (a) Find the minimum uncertainty in the momentum of the object. Find the minimum uncertainty in the objects velocity, assuming that the object is (b) a golf ball (mass 0.045 kg) and (c) an electron.

A proton is confined to a nucleus that has a diameter of 5.5 1015 m. If this distance is considered to be the uncertainty in the position of the proton, what is the minimum uncertainty in its momentum? 3

In the lungs there are tiny sacs of air, which are called alveoli. An oxygen molecule (mass 5.3 1026 kg) is trapped within a sac, and the uncertainty in its position is 0.12 mm. What is the minimum uncertainty in the speed of this oxygen molecule? 4

Particles pass through a single slit of width 0.200 mm (see Figure 29.14). 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. Assume that the uncertainty in the position of the particles is one-half the width of the slit, and use the Heisenberg uncertainty principle to determine the minimum range of angles.

The minimum uncertainty y 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 vy is expressed as a percentage of the particles speed vy Assume that relativistic effects can be ignored. Percentage vy vy 100%. * 4

A subatomic particle created in an experiment exists in a certain state for a time of t 7.4 1020 s before decaying into other particles. Apply both the Heisenberg uncertainty principle and the equivalence of energy and mass (see Section 28.6) to determine the minimum uncertainty involved in measuring the mass of this short-lived particle. c

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 29.12a. How fast must a neutron (mass 1.67 1027 kg) be moving to have a de Broglie wavelength of 0.282 nm?

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 2.1 1018 J. What is the energy of a photon from source B?

The de Broglie wavelength of a proton in a particle accelerator is 1.30 1014 m. Determine the kinetic energy (in joules) of the proton.

Find the de Broglie wavelength of an electron with a speed of 0.88c. Take relativistic effects into account.

The work function of a metal surface is 4.80 1019 J. The maximum speed of the electrons emitted from the surface is vA 7.30 105 m/s when the wavelength of the light is A. However, a maximum speed of vB 5.00 105 m/s is observed when the wavelength is B. Find the wavelengths A and B. 48. How

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 4.50 106 m/s?

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 0.900 1011 m. What is the potential difference?

Multiple-Concept Example 3 reviews the concepts necessary to solve this problem. Light is incident on the surface of metallic sodium, whose work function is 2.3 eV. The maximum speed of the photoelectrons emitted by the surface is 1.2 106 m/s. What is the wavelength of the light?

Some scientists have suggested that spacecraft with sails of the kind described in Conceptual Example 4 could be propelled by lasers. Suppose that such a sail is constructed of a highly reflective material thin enough so that one square meter of the sail has a mass of just 3.0 103 kg. The sail is to be propelled by an ultraviolet laser beam (wavelength 225 nm) that will strike its surface perpendicularly. (a) Use the impulsemomentum theorem (Section 7.1) to determine the number of photons per second that must strike each square meter of the sail in order to cause an acceleration of 9.8 106 m/s2 , which is one million times smaller than the gravitational acceleration at the earths surface. Assume that no other forces act on the sail, and that all the incident photons are reflected. (b) Determine the intensity (power per unit area) that the laser beam must have when it strikes the sail. *