Monthly Archives: November 2013

Development of Quantum Physics VIII – Tiny Jumping Planets, Everywhere

The previous article introduced the following problem: Atoms can absorb and emit radiation of certain energies only. There’s a quite simple formula for the hydrogen atom which is able to describe the absorption and emission lines in its spectrum. But how do atoms have to be built in order to produce the observed spectra? In our case: How does a hydrogen atom look like? We already found out that it has to have a nucleus, in which almost all of the atom’s mass is concentrated, and also a comparatively huge electron shell.

After much effort, Neils Bohr was able to construct a model of the hydrogen atom which seemed to fit the experimental data. It’s this very model which I’d like to discuss in this article.

Niels Bohr (around 1922)
(Source: www.nobelprize.org)

(I’ll spare the mathematical backgrounds of Bohr’s model here, although they are quite easy to understand. But I’ll write a seperate article about them for the interested reader.)

You can find all the other articles of this series here.

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Bohr’s atom model is also known as the “planetary model”. There’s a simple reason for this: In Bohr’s model, the electron circles around the atom’s nucleus like a tiny planet orbiting a central star. (For the sake of simplicity, we will only deal with the hydrogen atom – so our atom consists of just one electron and a nucleus.) If we treated our system of particles really thoroughly, we would have to describe a situation in which the electron and the nucleus circle a common barycenter, but we can make our lives a lot easier if we assume that the atomic nucleus sits in the center of the electron’s circular orbit motionlessly. In doing so, we don’t make a big error in describing the situation properly, because more than 99.9 % of the atom’s mass is concentrated in the nucleus. Our simplification is legitimate and sufficiently exact.

Well, the radial force, which always points towards the central nucleus (centripetal force) and keeps the electron on its curved trajectory, is the Coulomb force. This is just the technical term for the electromagnetic attraction between the negatively charged electron and the positive nucleus (= one proton).

From the relation “centripetal force equals Coulomb force” alone, we can derive an expression for the radius of the electron’s orbit. By now, every radius is allowed. (The distance between electron and nucleus can be, for example, 5 (arbitrary) units of length or 38 units or 26.1 units or every other value imaginable.)

Now, let’s introduce some quantum physics – suddenly it gets a bit trickier!
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