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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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A beam of electrons is incident upon a gas of hydrogen atoms.
a. What minimum speed must the electrons have to cause the emission of 686 nm light from thetransition of hydrogen?
b. Through what potential difference must the electrons be accelerated to have this speed?
A 100 W incandescent lightbulb emits about 5 W of visible light. (The other 95 W are emitted as infrared radiation or lost as heat to the surroundings.) The average wavelength of the visible light is about 600 nm, so make the simplifying assumption that all the light has this wavelength. How many visible-light photons does the bulb emit per second?
An electron confined in a one-dimensional box emits a 200 nm photon in a quantum jump from n=2 to n =1. What is the length of the box?
How would the graph of Figure 38.2 look if classical physics provided the correct description of the photoelectric effect? Draw the graph and explain your reasoning. Assume that the light intensity remains constant as its frequency and wavelength are varied.
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?
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