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Chapter 38: Q. 24 (page 1114)
In the following Figure is an energy-level diagram for a simple atom. What wavelengths, in nm, appear in the atom鈥檚 (a) emission spectrum and (b) absorption spectrum?
(a) The emission spectrum wavelengths are
(b) The absorption spectrum wavelengths are
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Potassium and gold cathodes are used in a photoelectric effect experiment. For each cathode, find:
a) The threshold frequency.
b) The threshold wavelength.
c) The maximum photoelectron ejection speed if the light has a wavelength of 220 nm.
d) The stopping potential if the wavelength is 220 nm
A 75 kW radio transmitter emits 550 kHz radio waves uniformly in all directions. At what rate do photons strike a 1.5-m-tall, 3.0-mm-diameter antenna that is 15 km away?
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
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?
Through what potential difference must an electron be accelerated from rest to have a de Broglie wavelength of ?
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