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Chapter 30 | Atomic Physics 1389
30.6 The Wave Nature of Matter Causes Quantization
13.
Figure 30.66 This figure shows graphical representations of the wave functions of two particles, X and Y, that are moving in the positive x-direction. The maximum amplitude of particle X’s wave function is A0. Which particle has a greater probability of being located at position x0 at this instant, and why?
a. Particle X, because the wave function of particle X spends more time passing through x0 than the wave function of particle Y.
b. Particle X, because the wave function of particle X has a longer wavelength than the wave function of particle Y.
c. Particle Y, because the wave function of particle Y is narrower than the wave function of particle X.
d. Particle Y, because the wave function of particle Y has a greater amplitude near x0 than the wave function of particle X.
14. In Figure 30.66, explain qualitatively the difference in the wave functions of particle X and particle Y. Which particle is more likely to be found at a larger distance from the coordinate x0 and why? Which particle is more likely be found exactly at x0 and why?
15. For an electron with a de Broglie wavelength , which of
the following orbital circumferences within the atom would be disallowed? Select two answers.
a. 0.5 b.
c. 1.5 d. 2
16. We have discovered that an electron’s orbit must contain an integer number of de Broglie wavelengths. Explain why, under ordinary conditions, this makes it impossible for electrons to spiral in to merge with the positively charged nucleus.