Additional Problems

| 37 | A particle has a speed of . Its de Broglie wave length is . What is the mass of the particle?

| 38 | The dissociation energy of a molecule is the energy required to break apart the molecule into its separate atoms. The dissociation energy for the cyanogen molecule is . 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 24-10) does this photon lie?

| 39 | ssm The de Broglie wavelength of a proton in a particle accelerator is . Determine the kinetic energy (in joules) of the proton.

| 40 | What is (a) the wavelength of a 5.0-eV photon and (b) the de Broglie wavelength of a 5.0-eV electron?

| 41 | Recall from Section 14.3 that the average kinetic energy of an atom in a monatomic ideal gas is given by , where and T is the Kelvin temperature of the gas. Determine the de Broglie wavelength of a helium atom () that has the average kinetic energy at room temperature (293 K).

| 42 | A magnesium surface has a work function of 3.68 eV. Electro magnetic waves with a wavelength of 215 nm strike the surface and eject electrons. Find the maximum kinetic energy of the ejected electrons. Express your answer in electron volts.

* | 43 | ssm 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?

* | 44 | 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 . What is the wavelength of the light?

** | 45 | Review Conceptual Example 4 before attempting this problem. A beam of visible light has a wavelength of 395 nm and shines perpendicularly on a surface. Because of the light, there are photons per second striking the surface. By using the impulse–momentum theorem (Section 7.1), obtain the average force that this beam applies to the surface when (a) the surface is a mirror, so the momentum of each photon is reversed after reflection, and (b) the surface is black, so each photon is absorbed and there are no reflected photons.

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