FIGURE 3–1 Temperatures of some familiar objects, on a scale of powers of 10.

BOX 3–1

de Broglie Waves

It has been known since the work of Max Planck and Albert Einstein that one must sometimes think of light as consisting of (massless) particles, now called photons. This idea complements the more common notion that light is a wave. Likewise, quantum mechanics teaches us that atoms, as well as all particles, also possess wavelike properties. This wave-particle duality of both light and atoms is the cornerstone of quantum mechanics, yet it remains one of its most unsettling aspects.

The quantum-mechanical wavelength of massive particles in thermal equilibrium is inversely proportional to the square root of their temperature. It is exceedingly small at normal (room) temperatures, a small fraction of a nanometer or so. As atoms get colder, though, their wavelength becomes longer—for the temperatures we will discuss here, these wavelengths can be hundreds of micrometers. Another way to say this is that at ever-lower temperatures, quantum mechanics becomes progressively more dominant.

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