Chapter 40: Q. 1 (page 1174)
FIGURE Qshows the de Broglie waves of three equal-mass particles. Which one is moving most slowly? Explain.
The wave is shown in part (c) one is moving most slowly.
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The electrons in a rigid box emit photons of wavelengthduring the transition.
a. What kind of photons are they—infrared, visible, or ultraviolet?
b. How long is the box in which the electrons are confined.
Even the smoothest mirror finishes are “rough” when viewed at a scale of . When two very smooth metals are placed in contact with each other, the actual distance between the surfaces varies fromat a few points of real contact to . The average distance between the surfaces is. The work function of aluminum is . What is the probability that an electron will tunnel between two pieces of aluminum that are apart? Give your answer as a power ofrather than a power of.
An electron has a probability (a chance) of tunneling through a potential barrier. If the width of the barrier is doubled, will the tunneling probability be? Explain.
For the quantum-well laser of Figure 40.16, estimate the probability that an electron will be found within one of the GaAlAs layers rather than in the GA As layer. Explain your reasoning.
Consider a particle in a rigid box of length L. For each of the states and :
a. Sketch graphs of . Label the points and .
b. Where, in terms of L, are the positions at which the particle is most likely to be found?
c. Where, in terms of L, are the positions at which the particle is least likely to be found?
d. Determine, by examining your graphs, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than . Explain your reasoning.
e. Calculate the probability that the particle will be found in the left one-third of the box
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