Having established the “house rules” governing the hydrogen atom’s behavior, Bohr set to work calculating what these would imply in terms of observable phenomenon. He did so by applying nothing more than Newton’s laws, Maxwell’s equations, and the conservation of energy. Throwing in a sprinkle of algebra for good measure, he first made an estimate for the size of the hydrogen atom. When in the ground state, he predicted it would have a radius of about 1 × 10-10 meters—in very good agreement to the value estimated by numerous experiments before.
QUANTUM QUOTE
Then it is one of the greatest discoveries.
—Albert Einstein’s reaction when he heard about certain predictions of Bohr’s model
Next, he tackled the mysterious line spectrum of hydrogen. Could his model be used to shed any light on this? He began by calculating the energy levels for the electron when it is orbiting the proton with its permissible quantities of angular momentum. Next, he calculated the frequency of light that would be emitted when an electron jumped between any two of these energy levels. From this, it was a simple matter to derive a formula for the wavelengths emitted for jumps from any arbitrary energy level down to any other.
Amazingly, when he took the special case of all jumps into the first excited state, the wavelengths predicted by his formula agreed almost exactly with values observed by Balmer. Bohr’s formula was truly remarkable since it led to the right answer using nothing but fundamental physics (aside, of course, from his enlightened postulates).
This was an even greater achievement than that of Balmer. After all, Balmer had begun with the right answer (the known wavelengths) and worked backward to find a mathematical formula that just so happened to match. Bohr arrived at the answer beginning with basic principles. Although we still need to come to grips with his starting postulates, this achievement was clearly a great leap forward in our understanding of the atom.
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