Bohr and The Atom

Niels Bohr’s Early Career

In March of 1912 Niels Bohr (1885–1962) arrived in Manchester to begin working with Rutherford. Previously, he had worked with Thomson in Cambridge. Unfortunately, their relationship had been strained from the start, and never really flourished as Bohr had hoped. Writing to his brother Harald, Bohr said:

“… Thomson has so far not been as easy to deal with as I thought the first day. …”

Perhaps, Bohr’s initial encounter with Thomson was to blame, where upon entering Thomson’s office, Bohr proclaimed:

“This is wrong.”

He was referring to something in a book Thomson had written. Of course, Bohr never meant to be insulting, rather he was simply trying to engage in a scientific discussion with his very limited (at the time) command of English. The situation was undoubtedly exacerbated by Thomson’s inability to tolerate criticism.

Later in life, Bohr would reflect on his time with Thomson:

“The whole thing was very interesting in Cambridge but it was absolutely useless.”

His circumstances significantly improved under Rutherford:

“Rutherford is a man you can rely on; he comes in regularly and enquires how things are going and talks about the smallest details – Rutherford is such an outstanding man and really interested in the work of all the people around him.”

Bohr’s time with Rutherford was brief, lasting only about four months. During this time Rutherford was cautiously encouraging of Bohr’s efforts, although quite preoccupied with his own endeavors of book writing and new research interests. In fact, Bohr’s main scientific influence wasn’t Rutherford. Instead, the new physics Bohr learned came from two other researchers under Rutherford: Georg von Hevesy (1885–1966), and Charles Galton Darwin (1887–1962). Regardless, Rutherford’s model of the atom would inspire and provide Bohr with a tremendous stepping-stone to his own work on atoms, which he would ultimately be forever known. Bohr writing to Harald from Manchester:

“Perhaps I have found out a little about the structure of atoms.”

What an understatement this turned out to be.

Bohr’s Atom

Rutherford’s model was a big step forward towards understanding the atom. From the experimental data he and his researchers collected, the most plausible picture of the atom was one where a very compact nucleus resides at the center surrounded by electrons flying all around it. More precisely, we can imagine the electrons orbiting the central nucleus similar to the way the planets orbit the sun. Unfortunately, this version of an atom is unstable.

According to the known physics at the time (classical physics) electrons moving in such a fashion would emit light, which is a loss of energy for an electron. This energy loss shows up in the form of a lower potential energy for the electron, which means it moves closer to the nucleus.

To understand the potential energy a negatively charged electron “feels” for the positively charged nucleus, imagine a rubber band that has been fixed to a wall at one end, while at the other end we begin to stretch it outward. As we keep stretching, there will be a point where we will feel the tension in the rubber band resist being stretched further by pulling inward against us. At this point the potential energy is very high, but if we stop stretching, and begin to let the rubber band move inward, the resisting tension goes down along with the potential energy.

We can imagine the potential energy between an electron and the nucleus as resulting from an invisible “rubber band” with the electron connected to one end, and the nucleus connected to the other while fixed at the center of the atom. What prevents the electron from being completely pulled into the nucleus is that the inward pulling of the “rubber band” and the outward stretching of the centrifugal force equal each other.

The real problem is that the electron continues to emit light, thus losing energy, and moving closer, and closer to the nucleus, until it finally collides with the nucleus and destroys the atom. Such was the fate of Rutherford’s – classical physics – version of the atom. Bohr wasn’t bothered at all.

The failures of classical physics were already very familiar to Bohr from his PhD work. So seeing it fail in the realm of atoms was not much of a surprise to him:

“This seems to be nothing else than what was to be expected as it seems rigorously proved that the [classical physics] cannot explain the facts in problems dealing with single atoms.”

How did Bohr reconcile the seemingly unquestionable Rutherford atom with the instability predicted by classical mechanics? By introducing a new hypothesis, which he says:

“… there will be given no attempt of a mechanical [classical physics] foundation …”

Bohr’s hypothesized that the binding energy of the electron – the energy required to remove an electron from the very atom that holds it – can only come from a set of discrete, rather than continuous values. In other words, he quantized the binding energy of the atom. Reflecting on this later in life, Bohr remarked:

“It was in the air to try to use Planck’s ideas in connection with such things.”

In addition to quantizing the binding energy, Bohr also obtained results showing that an electron’s distance from the nucleus, or the location of its orbit, is also quantized (as is its angular momentum, or orbital momentum).

At the time of Bohr’s theory, over fifty years had passed since the work of Kirchhoff and Bunsen revealed that the spectra of atoms emit a unique fingerprint consisting of discrete spectral lines, which also represent the exact same frequencies that the atom will absorb at. While the experimental side of spectroscopy continued to make significant progress over those years, for theory it was a different story.

Thomson’s discovery of the electron instigated speculation on their role in an atom’s spectrum, but no real progress had been made. It was beginning to appear that a theory would never be found. This sentiment is well expressed by the physicist Arthur Schuster (1851–1934), who in 1882 said:

“It is the ambitious object of spectroscopy to study the vibrations of atoms and molecules in order to obtain what information we can about the nature of forces which bind them together . . . But we must not too soon expect the discovery of any grand and very general law, for the constitution of what we call a molecule is no doubt a very complicated one, and the difficulty of the problem is so great that were it not for the primary importance of the result which we may finally hope to obtain, all but the most sanguine might well be discouraged to engage in an inquiry which, even after many years of work, may turn out to have been fruitless.”

Bohr had provided a draft of his initial ideas on atoms (our previous discussion summarizes the most significant portions) to Rutherford in July of 1912, but never mentioned a single word about atomic spectra. Almost a year would go by until Bohr would seriously considered atomic spectra in the context of his theory. His interest would be sparked by an engaging conversation he had, in early February of 1913, with H.M. Hansen (1886–1956).

Hansen had worked on spectroscopy while in Göttingen. He inquired about Bohr’s efforts on using his theory to predict spectra. Bohr mentioned that he hadn’t really considered it, as progress there seemed unlikely. Hansen insisted that Bohr reconsidered, and pointed him in the direction of an intriguing spectral formula known as the Balmer Formula.

Jumping Electrons: Spectra

In 1849 Johann Balmer (1825–1898) received his PhD in mathematics from the University of Basel, Switzerland. He would remain in Basel his whole life, teaching at a girl’s school, and lecturing at the university. Being an enthusiast of numerology, Balmer believed that pretty much everything (like the number of sheep in a flock, or the number of steps on an Egyptian pyramid, etc.) in life had some sort of special relationship to numbers and formulas. Although a mathematician by training, Balmer made no significant contributions to that field, but rather his major contribution was in physics with his spectral formula for the hydrogen atom.

His accomplishment is nothing short of remarkable. At the time, Balmer knew of only four spectral frequencies for hydrogen that had been experimentally determined by Anders Ångström (1814–1874). Using only these four data points Balmer, at the age of sixty, constructed a formula that predicted the complete frequency spectrum of the hydrogen atom (and also correctly predicts a lower and an upper bound over the range of frequencies). Shortly thereafter, Balmer learned that not only did his formula account for the original four frequencies, it also correctly predicted twelve other known frequencies.

In 1885, he published two papers on his efforts, which immortalized his name forever. Many more spectral frequencies have been determined over the years and Balmer’s formula remains intact. In 1890, Johannes Rydberg (1854–1919) found that Balmer’s formula is actually a special case of a more general formula (that we now call the Rydberg Formula). Although this formula correctly predicted the spectral lines seen in the hydrogen atom, nobody knew why it worked, it just did. For almost thirty more years the atom would keep this secret.

Following Hansen’s suggestion, Bohr looked up Balmer’s formula, he probably found it in the general form written by Rydberg. The formula was widely known, and most likely Bohr had seen it as a student, only to have it slip his mind later. Upon seeing the Balmer formula again, he must have immediately knew how to coax out the physics buried deep within the formula all those years.

According to Bohr, an electron can change quantum states by “jumping” from one to another. If an electron jumps from a higher to lower energy quantum state, it will emit a single photon, which will show up in the atom’s frequency spectrum. In other words, an atom’s frequency spectrum is due to all the “excited” electrons “jumping” from higher to lower energy quantum states, whereby they emit photons. If an electron goes from a lower to higher energy quantum state it will absorb a single photon. Realize that given two quantum states, the energy, or frequency, of the photon emitted when the electron “jumps down”, is the same energy, or frequency, of the photon absorbed when the electron “jumps up”. Therefore, over fifty years later, Bohr’s model finally explained the conclusion Kirchhoff made from his experiments about a substance, like an atom: it will emit and absorb at the same frequency.

The Great Debate: Schrödinger and Bohr

In September 1926, Bohr invited Schrödinger to Copenhagen to lecture on and discuss wave mechanics in more detail. No sooner had Schrödinger stepped off the train than Bohr began debating the physical interpretations of quantum mechanics. the next several days, Bohr became even more relentless with discussions, beginning early in the morning and continuing late into the night. Further, to eliminate the possibility of any distractions, Bohr arranged for Schrödinger to stay at his home. The most detailed account of this visit comes from Heisenberg, who at that time was Bohr’s assistant at the institute. He recalled, “although Bohr as a rule was especially kind and considerate in relations with people, he appeared to me now like a relentless fanatic ….”

Schrödinger interpreted his wave equation literally, viewing a quantum object, like an electron, as a wave rather than a particle. For him, the wavefunction was really a matter wave, describing where various portions of an electron were actually scattered throughout space. Also, he insisted upon the possibility of some sort of visualizable construct of the inner workings of the atom.

In total opposition to this stood Bohr. He was in agreement with Born that the wavefunction was describing a quantum probability and not some sort of real physical wave. During their discussion, Bohr favored the particle concept for quantum objects, but later he would require both particle and wave concepts for a complete description – a full realization of Einstein’s “fusion concept” of 1909. However, their biggest point of contention was those jumping electrons in Bohr’s atomic model.

As far as Schrödinger was concerned, the whole idea of electrons hopping from one stable, or stationary, discrete quantum state to another was ridiculous: “You surely must understand, Bohr, that the whole idea of quantum jumps necessarily leads to nonsense. … In other words, the whole idea of quantum jumps is sheer fantasy.”

Who could blame him? Bohr’s atomic model offered no “real” explanation as to why electrons didn’t fall into the nucleus as classical physics would have it. It simply imposed the concept of the stationary quantum state, which was the “magic orbit” that freed the electron from this tragic fate. And if this wasn’t disturbing enough, one had to further accept that an electron could jump between these stationary quantum states by simply absorbing or emitting a photon without any regard for what’s actually governing this process.

Bohr acknowledged that these were difficult concepts to accept but felt that Schrödinger’s biggest problem with it all came back to his need for a working visual:

“it does not prove that there are no quantum jumps. It only proves that we cannot imagine them, that the representational concepts with which we describe events in daily life and experiments in classical physics are inadequate when it comes to describing quantum jumps. Nor should we be surprised to find it so, seeing that the processes involved are not the objects of direct experience.”

Schrödinger continued to insist that removing the discrete quantum states by adopting his wave picture of an electron would resolve the “quantum weirdness.” Bohr pointed out that both Planck’s Radiation Law and Einstein’s work on the interaction of light and matter required discrete quantum states. Surely, was Schrödinger going to tear down the very foundation of quantum mechanics? Moreover, Bohr contended that experiments had already confirmed this discrete nature of the atom in a variety of ways. To this a frustrated Schrödinger replied: “If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.”

After a few days, Schrödinger fell ill and stayed in bed with a feverish cold; perhaps Bohr had finally worn him down. Mrs. Bohr took care of him, bringing him tea and cake by his bedside, all the while Bohr sat on the edge of the bed, continuing to argue, “But surely Schrödinger, you must see ….”

But he couldn’t see. Although the discussions had a huge impact on both of them, in the end no resolution could be found. Nonetheless, Bohr and Schrödinger remained friends.

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