de Broglie Waves in the Bohr AtomSection 15.5 in the text (page 542) discusses the de Broglie wavelength of a particle and describes how this idea related to the Bohr theory of hydrogen. In particular, Figure 15.16 shows how a standing wave with a wavelength that, when multiplied by any integer, equals the circumference of a Bohr orbit, connects the de Broglie wavelength to the Bohr orbital radius. That figure shows n = 7: seven de Broglie wavelengths wrapped around a circle with the radius of the seventh Bohr orbit. This wave is stable, and we say it is the result of constructive interference: the wave reinforces itself exactly at every point in space. This is a dynamic situation: the wave is "waving," something that is hard to show in a static picture. Moreover, if the electron momentum is not just right so that its de Broglie wavelength doesn't exactly wrap around the circumference, we get no standing wave; descructive interference results, and the electron cannot exist as part of a stable H atom if it has that momentum. The two QuickTime movies below show animations of a wave with n = 4, a standing wave, and with n = 3.2, an unstable wave. Note in the n = 3.2 movie (which shows the wave wrapped three times around the circle) that the wave (shown wrapped around the circle three times) doesn't "join up with itself," which a characteristic of destructive interference.
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