Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

| 46 | Concept Questions The maximum speed of the electrons emitted from a metal surface is vA when the wavelength of the light used is . However, a smaller maximum speed vB is observed when a wavelength is used. (a) In which case is there a greater maximum kinetic energy KEmax ? (b) In which case is the frequency of the light greater? (c) Is wavelength greater or smaller than ? Explain your answers.
Problem The work function of a metal surface is . The maximum speed of the electrons emitted from the surface is when the wavelength of the light is . However, a maximum speed of is observed when the wavelength is . Find the wavelengths and . Be sure your answers are consistent with your answers to the Concept Questions.

| 47 | Concept Questions Heat is a form of energy. One way to supply the heat needed to warm an object is to irradiate the object with electromagnetic waves. (a) How is the heat Q needed to raise the temperature of an object by degrees related to its specific heat capacity cspecific heat and mass m? (b) Is the energy carried by an infrared photon greater than, smaller than, or the same as the energy carried by a visible photon of light? Explain. (c) Assuming that all the photons are absorbed by the object, is the number of infrared photons needed to supply a given amount of heat greater or smaller than the number of visible photons? Explain.
Problem 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 , while the wavelength of blue visible light is . Find the number of infrared photons and the number of visible photons needed to raise the temperature of the glass plate by 2.0 C°, assuming that all photons are absorbed by the glass. Verify that your answers are consistent with your answers to the Concept Questions.

| 48 | Concept Questions 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 in Figure 29-10 that the direction of the incident photon is in the +x direction and that the scattered photon emerges at an angle of , which is in the −y direction. (a) Before the scattering, the total momentum has an x component. Does it have a y component? (b) After the scattering, the total momentum has an x component. Does it have a y component? (c) Does the momentum of the scattered electron have an x component? (d) Considering your answer to Question (b), and considering the fact that the scattered photon is moving along the −y axis, does the momentum of the scattered electron have a y component? In each case justify your answer.
Problem In Figure 29-10 the incident photon has a wavelength of . The scattered photon emerges at . Find the x and y components of the momentum of the scattered electron. Check that your answers are consistent with your answers to the Concept Questions.

| 49 | Concept Questions Consider a Young’s double-slit experiment that uses electrons. In versions A and B of the experiment the first-order bright fringes are located at angles and , where is greater than . In these two versions, the separation between the slits is the same but the electrons have different momenta. (a) In which version is the wavelength of an electron greater? (b) In which version is the momentum of an electron greater? Explain your answers.
Problem In a Young’s double-slit experiment the angle that locates the first-order bright fringes is degrees when the magnitude of the electron momentum is . With the same double slit, what momentum magnitude pB is necessary, so that an angle of degrees locates the first-order bright fringes?

| 50 | Concept Question Particle A is at rest, and particle B collides head-on with it. The collision is completely inelastic, so the two particles stick together and move off after the collision with a common velocity. The masses of the particles are different, and no external forces act on them. (a) What is the total linear momentum of the two-particle system before the collision? Express your answer in terms of the masses and the initial velocities, (b) What is the total linear momentum of the system after the collision? Express your answer in terms of the masses and the final velocity of the particle. (c) No external forces act on the two-particle system during the collision. What does this fact tell you about the total linear momentum of the system? (d) How is the de Broglie wavelength of a particle related to the magnitude of its momentum?
Problem The de Broglie wavelength of particle B before the collision is . What is the de Broglie wavelength of the object that moves off after the collision?

| 51 | Concept Question A photon of known wavelength strikes a free electron that is initially at rest, and the photon is scattered straight backward. (a) How is the kinetic energy KE of the recoil electron related to the energies E and E of the incident and scattered photons, respectively? (b) If the wavelength of the incident photon is known, how can the photon’s energy E be determined? (c) How can the wavelength of the scattered photon and, hence, its energy E′ be found if we know the wavelength of the incident photon and the fact that the photon is scattered straight backward?
Problem 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?

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