Atomic Models – The Bohr Model

In 1913, Niels Bohr proposed his famous atomic model. According to this model, electrons can assume only certain orbits around the nucleus. But first things first. Bohr put together the knowledge blocks available to him at that time, and created a kind of a recipe book.

We know from the Rutherford scattering experiment with a gold foil that the atomic nucleus is tiny relative to the electron shell. But how are the electrons moving around the nucleus? A possible, albeit naive, explanation would be comparing an atom to a planetary system. The nucleus would correspond to a sun, and the electron to a planet which is held in a circular orbit by electrical attraction.

The problem with that theory is that an accelerated charge would have to radiate energy like an antenna. The electron would lose energy, and eventually spiral into the nucleus. Such an atom would be unstable from the classical point of view.

Bohr postulated that atoms were stable, but could not explain why. He assumed that electrons could follow only certain discreet orbits. But it follows that only certain discreet electromagnetic radiative transitions are allowed. Transitions are radiationless when the electron jumps one orbit closer to the nucleus. When the electron stays in the smallest orbit, the so-called basic state is reached.

According to Bohr, the permissible orbits are characterized by the angular momentum. The angular momentum must be a multiple of Planck constant h bar.

What about the energy of the electron? Generally speaking, a bound state is characterized by negative energy. The electron receives positive energy and can leave the atom only when this so-called binding energy is overcome. The atom then becomes ionized.
However, we are talking about bound states, in particular the basic state, and the smallest orbit with n=1. The next higher orbit n=2 has more energy, the orbit n=3 has even more energy, and so on.

When talking about transitions in which electromagnetic radiation is released, let us recall the Balmer equation as generalized by Rydberg. We are now able to interpret the difference between the numbers n and m as the difference in energies, for example, between shell No. 2 and shell No. 3. As we can see, Bohr proposed an ingenious interpretation of Rydberg’s findings.

Bohr’s postulate of discrete orbits thus allows a new interpretation of the discrete absorption and emission spectrum. During the transition in hydrogen, for example from shell 3 to shell 2, a photon is released. The opposite happens when the electron jumps from shell 2 to 3: a photon of that frequency is absorbed. The absorbed or emitted light corresponds in each case to the energy difference between two permitted energy levels in the atom.

Bohr’s postulate of certain permitted electron orbits helped to explain why only certain emission and absorption energies of photons were possible in the atom. However, Bohr could not explain why only these electron orbits were permitted.

A step in that direction was made later by Louis de Broglie, who postulated that matter, and electrons in particular, had wave properties. This changed our understanding of an electron, from a particle travelling either left or right, to overlapping waves travelling both left and right. These overlapping waves may form a standing wave, which, however, would need certain constructive interference conditions.

According to de Broglie, a wavelength λ is assigned to each pulse P. A constructive interference between waves travelling right and left is given when a multiple of these wavelengths is equal to the circumference, thus 2πr=lλ , in this example for l=2. This revolutionary idea allows interpreting Bohr’s postulate as a necessary condition for standing waves.

The next step towards quantum physics is the question of what this Oscillating Thing, a term that seems fitting for an electron, is supposed to be; and, in particular, in how many dimensions it is oscillating. That standing wave is certainly not two-dimensional, as in the Bohr atomic model. It is at least three-dimensional; but that’s just the beginning, the dawn of the quantum dimension.