^* Planck’s constant—6.63 × 10^–34 Joule-seconds (a Joule is a unit of energy, just as a mile is a unit of length)—is a measure of size of the discrete packets, or quanta, of energy emitted in the world of the atom. The significance of its smallness is indicative of the small scale at which quantum effects occur.
This measure lay at the core of the new quantum theory that Max Planck discovered at the turn of the twentieth century. The speed of light—three hundred million meters per second—was the signature of relativity theory, which describes nature in the large. At the other end of the scale, Bohr demonstrated how Planck’s constant shaped the world of the atom—nature in the small. Planck’s constant determines the Planck length—1.61 × 10^–35 meters—the smallest conceivable length in physics. It is the length at which quantum effects take over. The Planck length is a combination of Planck’s constant, the universal gravitational constant from Newton’s law of gravity (6.67 ×10^–11 (meter)³/[kilogram × (second)²]), and the velocity of light. To get some idea of its smallness, if a single atom were expanded until it was the size of the entire universe, the Planck length would be just four feet long.