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Chapter 38: Q. 22 (page 1114)
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Find the radius of the electron’s orbit, the electron’s speed, and the energy of the atom for the first three stationary states of
The muon is a subatomic particle with the same charge as an electron but with a mass that is times greater: Physicists think of muons as "heavy electrons," However, the muon is not a stable particle; it decays with a half-life of into an electron plus two neutrinos. Muons from cosmic rays are sometimes "captured" by the nuclei of the atoms in a solid. A captured muon orbits this nucleus, like an electron, until it decays. Because the muon is often captured into an excited orbit , its presence can be detected by observing the photons emitted in transitions such as and .
Consider a muon captured by a carbon nucleus . Because of its long mass, the muon orbits well inside the electron cloud and is not affected by the electrons. Thus, the muon "sees" the full nuclear charge and acts like the electron in a hydrogen like ion.
a. What is the orbital radius and speed of a muon in the ground state? Note that the mass of a muon differs from the mass of an electron.
b. What is the wavelength of the muon transition?
c. Is the photon emitted in the transition infrared, visible, ultraviolet, or ray?
d. How many orbits will the muon complete during s? Is this a sufficiently large number that the Bohr model "makes sense, " even though the muon is not stable?
The maximum kinetic energy of photoelectrons is 2.8 eV. When the wavelength of the light is increased by 50%, the maximum energy decreases to 1.1 eV. What are (a) the work function of the cathode and (b) the initial wavelength of the light?
Which metals in Table 38.1 exhibit the photoelectric effect for (a) light with and (b) light with ?
The electrons in a cathode-ray tube are accelerated through a potential difference and then shot through a 33-nm-diameter circular aperture. What is the diameter of the bright spot on an electron detector behind the aperture?
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