"Perhaps I have found out a little about the structure of atoms."I. Setting the Stage
The Bohr model of the atom deals specifically with the behavior of electrons in the atom. In constructing his model, Bohr was presented with several problems.
Problem #1: charged electrons moving in an orbit around the nucleus SHOULD radiate energy due to the acceleration of the electron in its orbit. The frequency of the emitted radiation should gradually change as the electron lost energy and spiraled into into the nucleus. Obviously this was not happening, because the spectral lines of a given element were sharply defined and unchanging.
Problem #2: the spectral lines did not show overtones (or harmonics). These are lines where the frequency is double, triple and so on of the fundamental frequency. The lines of the spectrum of each element were scattered about with no apparent pattern, other than the purely empirical formula of Balmer (which dates to 1885). However, no one knew what Balmer's formula meant.
J.J. Tomson's model was constructed with full knowledge of problem #1 above. What Thomson did is to extend the positive charge to the same size as the atom (radius = 10¯8 cm.) and allow the electrons to distribute themselves inside. The calculations for his "plum pudding" model, published in 1904, showed that the model did produce electron arrangements that were stable.
However, the Thomson model was conclusively destroyed by Rutherford's 1911 nucleus paper. (In the future -- 1913 and years later -- other discoveries will be made that the Thomson model fails to account for, but the Rutherford model does. Of course, Thomson, Rutherford, Bohr, etc. were not aware of these. There were even efforts in 1914 and 1915 to use the Thomson Model, but these efforts went nowhere.)
The nuclear model of Rutherford's was supported by evidence that could not be refuted. However, if electrons rotated around a nucleus, they would either rip the atom apart or self-destruct. Bohr's answer to the above problems appeared in print for the world to see in July 1913. However, as you can see from Bohr's letter to his brother, the journey to the answer started much earlier.
Bohr wrote out his ideas to date in a memo to Rutherford sometime in June/July 1912. This memo (with one missing page) still exists and if you were a qualified scholar, you could go visit it and read it!! Bohr leaves Manchester right after writing the memo and goes to Copenhagen and is married on August 1, 1912.
The critical part of Bohr's thinking was the making of two assumptions. Bohr himself described these assumptions on page 7 of his famous paper:
"(1) That the dynamical equilibrium of the systems in the stationary states can be discussed by help of the ordinary mechanics, while the passing of the systems between different stationary states cannot be treated on that basis.Making the assumptions at all was a bit shaky, but in September 1913, at a meeting of the British Association for the Advancement of Science, Sir James Jeans remarked:
(2) That the latter process is followed by the emission of a homogeneous radiation, for which the relation between the frequency and the amount of energy emitted is the one given by Planck's theory."
"The only justification which can be offered for the moment with regard to these hypotheses is the very important one that they work in practice."
II. Assumption #1: Electrons Move, yet are Stable
Bohr describes "stationary states" (He never uses the word the modern term "orbit.") on page 5:
"According to the above considerations, we are led to assume that these configurations will correspond to states of the system in which there is no radiation of energy states which consequently will be stationary as long as the system is not disturbed from outside."As an electron moves in a "stationary state" it emits no radiation whatsoever. This violated a branch of science called electrodynamics (having to do with movement of charged particles and their amount of energy), but the fact is that the atom is stable and DOES NOT emit radiation in the manner predicted. It is this branch which predicts the electron will lose energy and crash into the nucleus (this is the problem #1 mentioned at the top of the file).
In this assumption is some of Bohr's daring nature. While he realized electrodynamics is useless (second part of his sentence), he proposed to use "mechanics" to describe the motion of an electron in its orbit (first part of the sentence). Mechanics deals with things like inertia, momemtum and other features of movement not involving electrical charges. He was willing to throw out well-supported scientific ideas that didn't work, but was also willing to keep other ideas that allowed him to make calculations.
The justification for Bohr deciding to assume mechanics held in the atom, but electrodynamics didn't? The results he got had two features: 1) they concurred with already known results and 2) offered an explanation for why some results were found and not others.
III. Assumption #2 - Incorporation of Planck's Constant
The "latter process" in assumption #2 is described at the end of assumption #1 -- "the passing of the systems between different stationary states"
What Bohr proposed is that the atom will emit (or gain) energy as it moves from one stationary state to another. However, the amounts of energy will not be any old amount, but only certain, fixed values. Those values will be the DIFFERENCES in energy between the stationary states.
Bohr says on p. 7:
"The second assumption is in obvious contrast to the ordinary ideas of electrodynamics but appears to be necessary in order to account for experimental facts."The experimental facts refered to are the lines in the spectrum of hydrogen.
What Planck had discovered in 1900 was a fundamental limitation on nature. Energy is not emitted or absorbed in a continuous manner, but rather in small packets of energy called quanta. Emission and absorption occured in a DIScontinuous manner. In other words, an atom moved from one energy state to another state in steps. In the mathematical description of this process there occured a new constant of nature, discovered by Planck and named after him.
Planck's constant, symbolized by h, was involved in governing HOW MUCH energy a given quantum had. The amount of energy was directly dependent on the frequency of the radiation according to the following equation:
E = hν
This famous equation was first announced by Planck in 1900.
Bohr argued that Planck's constant should be used to help account for the stability of the atom. This reversed the technique of others who were trying to use atomic models to determine the physical significance of h. Bohr also realized that, if he was correct, his theory should produce a constant with the units of length. This constant would characterize the distance of the electron from the nucleus.
Bohr said on page 2:
The principal difference between the atom-models proposed by Thomson and Rutherford consists in the circumstance the forces acting on the electrons in the atom-model of Thomson allow of certain configurations and motions of the electrons for which the system is in a stable equilibrium; such configurations, however, apparently do not exist for the second atom-model. The nature of the difference in question will perhaps be most clearly seen by noticing that among the quantities characterizing the first atom a quantity appears -- the radius of the positive sphere -- of dimensions of a length and of the same order of magnitude as the linear extension of the atom, while such a length does not appear among the quantities characterizing the second atom, viz. the charges and masses of the electrons and the positive nucleus; nor can it be determined solely by help of the latter quantities.What Bohr wass pointing out is that Rutherford's model (with its constants of mass and charge) cannot produce a unit of length, but with the introduction of h, such a length constant could be produced. If you write h2 / me2, you get a value with the units of length and of the proper magnitude. Here are the numbers (modern values):
. . . it seems necessary to introduce in the laws in question a quantity foreign to the classical electrodynamics, i. e. Planck's constant, or as it often is called the elementary quantum of action. By the introduction of this quantity the question of the stable configuration of the electrons in the atoms is essentially changed as this constant is of such dimensions and magnitude that it, together with the mass and charge of the particles, can determine a length of the order of magnitude required.
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).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.
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.
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:Two paragraphs later, in referring to "monochromatic radiation," he uses the phrase "discontinuous medium consisting of energy quanta."
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 . . . .
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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