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Chapter 38: Q. 21 (page 1114)
The diameter of the nucleus is about . What is the kinetic energy, in MeV, of a proton with a de Broglie wavelength of ?
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17. What is the de Broglie wavelength of a neutron that has fallen in a vacuum chamber, starting from rest?
Electrons in a photoelectric-effect experiment emerge from an aluminum surface with a maximum kinetic energy of 1.30 eV. What is the wavelength of the light?
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?
What lie the winding of the Irasuliens? , and in the hydronics ? In what spectral range do these lie?
The first three energy levels of the fictitious element X were shown in FIGURE P38.56. An electron with a speed of 1.4 X 106 m/s collides with an atom of element X. Shortly afterward, the atom emits a photon with a wavelength of 1240 nm. What was the electron's speed after the collision? Assume that, because the atom is much more massive than the electron, the recoil of the atom is negligible. Hint: The energy of the photon is not the energy transferred to the atom in the collision.
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