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Chapter 38: Q. 23 (page 1114)
What is the length of a one-dimensional box in which an electron in the state has the same energy as a photon with a wavelength of ?
The length of a one-dimensional box in which an electron in the state has the same energy as a photon with a wavelength of is
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FIGURE Q38.12 shows the energy-level diagram of Element X.
a. What is the ionization energy of Element X?
b. An atom in the ground state absorbs a photon, then emits a photon with a wavelength of 1240 nm. What was the energy of the photon that was absorbed?
c. An atom in the ground state has a collision with an electron, then emits a photon with a wavelength of 1240 nm. What conclusion can you draw about the initial kinetic energy of the electron?
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?
I FIGURE EX38.24 is an energy-level diagram for a simple atom. What wavelengths, in \mathrm{nm}, appear in the atom's (a) emission spectrum and (b) absorption spectrum?
FIGURE EX38.24 n=1-E_{1}=0.00 \mathrm{eV}
In the atom interferometer experiment shown in Figure laser cooling techniques were used to cool a dilute vapor of sodium atoms to a temperature of . The ultracold atoms passed through a series of collimating apertures to form the atomic beam you see circling the figure from the left. The standing light waves were created from a laser beam with a wavelength of
a. What is the rms speed of a sodium atom in a gas at this temperature ?
b. By treating the laser beam as if it were a diffraction grating. cakculate the first-order diffraction angle of a sodium atom traveling with the rms speed of part a.
c. allow far apart are points and if the second sanding wave is from the first?
d. Because interference is observed between the two paths, each individual atom is apparently present at both point and point . Describe, in your own words, what this experiment tells you about the nature of matter.
a. Calculate the de Broglie wavelength of the electron in the states of the hydrogen atom. Use the information in Table 38.2 .
b. Show numerically that the circumference of the orbit for each of these stationary states is exactly equal to n de Broglie wavelengths.
c. Sketch the de Broglie standing wave for the orbit
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