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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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Sketch the n=4 wave function for the potential energy shown in FIGURE EX40.13.
An electron is confined in a harmonic potential well that has a spring constant of . What is the longest wavelength of light that the electron can absorb?
A typical electron in a piece of metallic sodium has energycompared to a free electron, where is the work function of sodium.
a. At what distance beyond the surface of the metal is the electron’s probability density of its value at the surface?
b. How does this distance compare to the size of an atom?
The graph in FIGURE EX40.16 shows the potential-energy function U(x of a particle. Solution of the Schrödinger equation finds that the n=3 level has and that the n=6 level has .
a. Redraw this figure and add to it the energy lines for the n=3 and n=6 states.
b. Sketch the n=3 and n=6 wave functions. Show them as oscillating about the appropriate energy line.
Consider a quantum harmonic oscillator.
a. What happens to the spacing between the nodes of the wave function as |x| increases? Why?
b. What happens to the heights of the antinodes of the wave function as |x| increases? Why?
c. Sketch a reasonably accurate graph of the n=8 wave function of a quantum harmonic oscillator.
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