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Let's stop and review for a moment. What exactly is the Bohr Model of the Atom?
The Bohr model has the following features:
1) There is a nucleus (this was Rutherford's discovery).
2) The electrons move about the nucleus in "stationary states" which are stable, that is, NOT radiating energy.
3) When an electron moves from one state to another, the energy lost or gained is done so ONLY in very specific amounts of energy, not just any old amount.
4) Each line in a spectrum is produced when an electron moves from one stationary state to another.
Today, we call this model an example of a "quantized" atom. The term "quantum" was introduced by Planck to describe a small bundle of energy. So a quantized atom being stimulated is shooting out trillions of quanta (plural) of energy per second.
One way to think about the quanta of energy streaming out is to think of a machine gun shooting out thousands of bullets per second. It SEEMS like a stready, unbroken stream of metal, but it is not. Each bullet is a "quantum."
Another example is water coming out of a hose. It SEEMS like a steady, unbroken stream of water, but we know it is just trillions and trillions of tiny, individual water molecules. The idea is the same with the energy quantum.
Still another example is a stream of gas shooting out a nozzle. It SEEMS like a steady, unbroken stream of gas, but in reality it is trillions and trillonsof individual gas molecules all moving in the same direction. Get the idea now??
Last example. In 1905, Albert Einstein wrote an article in 1905 titled "On a Heuristic Point of View about the Creation and Conversion of Light." In it he uses Planck's idea of a quantum to explain something called the photoelectric effect. He wound up showing that certain equations governing energy behavior are exactly the same as those for a gas in the same volume. By analogy, then, energy could be treated the same way as a gas -- as a collection of particles moving around within the volume. He wrote:
From this we then conclude:
Monochromatic radiation of low density behaves -- as long as Wein's radiation formula is valid -- in a thermodynamic sense, as if it consisted of mutually independent energy quanta . . . .
Two paragraphs later, in referring to "monochromatic radiation," he uses the phrase "discontinuous medium consisting of energy quanta."
Feature #4 above is Bohr's explanation of the mechanism for the production of lines in the hydrogen spectrum. The story surrounding this is interesting. At least, I think so.
Bohr was married, as I said, in August, 1912. He and his wife did not honeymoon in Norway as planned, but returned more-or-less immediately to Manchester. The new term was beginning and Bohr was behind schedule in finishing some work that Rutherford had assigned to him. Bohr finished that work and eventually the term ended, ending Bohr's year-long government grant for study.
Bohr even fell behind schedule in writing the paper I am discussing. He wrote a note to Rutherford on November 4, 1912 apologizing for the time he was taking "to finish my paper on the atoms and send it to you." By January 1913, Bohr and his wife were back in Copenhagen where he assumed his new position as assistant to the physics professor. This slowed down the work on the atomic model paper, but it was not abandonded.
The next event in this story (which is not the complete one, only highlights) is a January 31, 1913 letter to Rutherford in which Bohr excluded the "calculation of frequencies corresponding to the lines of the visible spectrum." However, the paper Bohr mailed to Rutherford on March 6, 1913 contained the correct mechanism for the production of the lines of the spectrum. What happened?
The letter shows Bohr HAD been thinking about spectra. It was probably here (in the first week of February 1913) that (according to Bohr's recollection in 1954) he was asked by Hans Marius Hansen (a yound Danish physicist) how Bohr's new atomic model would explain the hydrogen spectrum. Bohr's reply was that he had not seriously considered the issue, believing the answer to be impossibly complex. (Remember that by 1913, several thousand lines, of different elements, were known AND many of these lines exhibited bizarre splittings - called the Zeeman effect -- in magnetic fields. No one, and I mean no one, had any answers for what was going on.)
Hansen disputed Bohr's position and insisted Bohr look up Balmer's work. Bohr did so and soon had the answer for how the lines are produced. In the 1954 interview mentioned above, Bohr said:
"As soon as I saw Balmer's formula, the whole thing was immediately clear to me."
Up to that point, Bohr had not been aware of the Balmer formula. However, it was quickly incorporated into his paper and the final product was shipped off to Rutherford.
So what is the mechanism that makes the lines in the spectrum? On page 11, after discussing the mechanism from p. 8 onward, Bohr said:
" . . . that the lines correspond to a radiation emitted during the passing of the system between two different stationary states."
Later, on p. 14, he wrote:
"We are thus led to assume that the interpretation of the equation (2) is not that the different stationary states correspond to an emission of different numbers of energy-quanta, but that the frequency of the energy emitted during the passing of the system from a state in which no energy is yet radiated out to one of the different stationary states, . . . ."
So, in other words, each line is equal to the DIFFERENCE in energy as an electron moves between two stationary states. And, if you read Bohr's paper, at the bottom of page 8, you will see two equations where he writes Wτ2 minus Wτ1. This subtraction, of course, yields an answers which we call a "difference."
This is also the reason why the harmonics (see back to problem #2) were not observed. Harmonics are observed when an object (such as an electron) resonates at a specific frequency, called the fundamental. Overtones of twice the frequency, three times the frequency and so on are also observed. Here the frequency of the line in the spectrum had to do with energy gained or lost as the electron moved from one stationary state to another.The line is an energy DIFFERENCE!! The fundamental frequency of the electron was not involved at all with the lines!! No one until Bohr, not even Planck or Einstein, had thought to challenge the idea that spectral lines were produced by electrons emitting the specific frequenceies of each line.
By the way, exactly how an electron moves between two stationary states is never discussed by Bohr. How does the electron know to go to another stationary state of a specific energy amount? Why that amount and not some other amount? How does the electron know to stop at the right energy amount? Maybe Bo knows, but Bohr certainly didn't.
Bohr sent a second draft to Rutherford about two weeks after the first since he had "found it necessary to introduce some small alterations and additions." He then traveled to Manchester to persuade Rutherford that the paper would harmed greatly by any reduction in length. On May 10, Bohr returned the final, corrected proof to Rutherford and this became the published version.
In August 1914 (slightly more that a year after Bohr's paper was published), Rutherford said:
"N. Bohr has faced the difficulties [of atomic structure] by bringing in the idea of the quantum. At all events there is something going on which is inexplicable by the older mechanics."
Of course, Rutherford was completely correct. The "older mechanics" had to give way to the "quantum mechanics." Bohr would lead a revolution in thinking during the 1920s and 1930s that continues to be profitably mined even today.
At age eighty, J.J. Thomson, stooped by age, but still sharp of mind, wrote:
"At the end of 1913 Niels Bohr published the first of a series of researches on spectra, which it is not too much to say have in some departments of spectroscopy changed chaos into order, and which were, I think, the most valuable contributions which quantum theory has ever made to physical science."
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