Just as Planck and Einstein had done before, Bohr’s “solution” began with a set of bold postulates. In his case, four of them. Like his predecessors, he could not really explain their underlying basis. But when he took these as his starting point, and then applied the well-established principles of classical physics, he arrived at a model that seemed to give all the right answers—at least for the hydrogen atom.
ATOM TRAP
Although we have presented the quantum story in more or less chronological order, we have jumped around a bit. For example, Rutherford came up with his model of the atom in 1911, more than a decade after Planck had unveiled his quantum hypothesis. So when Bohr quantized the atom, he was really applying the “old” idea of the quantum to the “new” concept of the nuclear atom.
Bohr’s first postulate came straight from the Rutherford school and offered nothing new: assume that the electron moves in a circular orbit about the proton. Just like a planetary system, the electron is not pulled straight into the proton on account of its orbital motion.
And what of the radiation-induced spiral of doom? Bohr simply postulated that—for reasons then unknown—electrons don’t radiate when they occupy certain special orbits. When an electron occupies one of these, he said the atom was in a stationary state (or state for brevity). The particular energy of an electron orbiting in one of these stationary states he called an energy level. The least energetic state he termed the ground state, with the higher lying states referred to as excited states.
DEFINITION
An atom is said to be in a stationary state whenever its electrons are in specific, stable orbits in which they do not radiate. The lowest energy stationary state is called the ground state, while all those with higher energy are called excited states.
The energy level corresponding to each stationary state refers to the orbiting electron’s energy when the atom is in that stationary state.
Third, he postulated that the atom emits light only when it passes from a stationary state of higher energy to another of lower energy. Moreover, he hypothesized that the frequency of light emitted during such a transition was given by the precise energy difference between the two corresponding energy levels divided by Planck’s constant. Of course, you’ll recognize this as the exact same energy-frequency relationship of Planck and Einstein.
Before describing Bohr’s fourth and boldest postulate, we need to introduce you to the concept known as angular momentum. This can be understood by comparing a child’s pinwheel to a giant wind turbine. You can stop a spinning pinwheel with your pinky finger. On the other hand, to stop a spinning wind turbine you’d probably need the Incredible Hulk. The reason is that all rolling, spinning, or orbiting bodies would like to keep rolling, spinning, or orbiting. External forces are required to bring them to a halt.
In technical terms, any object exhibiting circular motion possesses angular momentum, the quantity of which depends on the object’s mass, radius of rotation, and angular speed. Larger, more massive objects have more angular momentum than smaller, lighter objects. (Incidentally, another way of viewing the stability of planetary orbits about the sun is that their angular orbital momentum is conserved—yet another conservation law.)
DEFINITION
Angular momentum is a measure of a rolling, spinning, or orbiting body’s tendency to keep rolling, spinning, or orbiting.
Returning to our atom, an orbiting electron will also have an angular momentum that is determined by its mass, angular speed, and distance from the nucleus. It was on this very quantity that Bohr based his key postulate. He hypothesized that an orbiting electron’s angular momentum was quantized, and that its permissible values were given by whole-number increments of Planck’s constant.
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