Niels Bohr

J.J. Thomson

One day, in late September 1911, as Bohr was crossing the Great Belt, he wrote to his fiancee, "I am taking off with all my silly fierce spirit".

Financed by a stipend from the Carlsberg Foundation (a Danish institution) for a year's study abroard, he was on his way to Cambridge to start postdoctoral research under J.J. Thomson, the director of the Cavendish. In his baggage he carried the poor translation of his Ph.D thesis, which he had helped prepare a little earlier.

Bohr knew of Thomson's ideas on atomic structure, since these are mentioned in one of Thomson's books which Bohr had quoted several times in his thesis. When asked why he had gone there for postdoctoral research, he replied : "First of all I had made this great study of the electron theory. I considered Cambridge as the center of physics and Thomson as a most wonderful man." In other words, Bohr looked forward above all to discuss with Thomson matters related to his thesis.

Several physicists have given an account of Bohr's first meeting with Thomson. It went about as follows. Bohr entered Thomson's office, carrying one of Thomson's books, opened it on a certain page, and politely said : "This is wrong". This first encounter with Thomson did not lay the basis for the relationship Bohr had hoped for. Later, Bohr reminisced

It was a disappointment that Thomson was not interested to learn that his calculations were not correct. That was also my fault. I had no great knowledge of English and therefore I did not know how to express myself. I could say only that this is incorrect. He was not interested in the accusation that it was not correct.

Thomson was a genius who actually showed the way to everybody. Then some young man could make things a little better.

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

Then, while still attached to Cambridge, Bohr met Rutherford.

Rutherford

In the autumn of 1911, only months after Rutherford's discovery of nuclear atom, Bohr met Rutherford for the first time. It happened in Manchester, in early November, in the course of a visit by Bohr to a friend of his late father. Bohr's recollection of that occasion :

He invited Rutherford and I talked with Rutherford. We didn't talk about Rutherford's own discovery of the nucleus. I told Rutherford that I would like to come up, work and also get to know something about radioactivity. He said I should be welcome, but I had to settle with Thomson. So I said I would, when I came back to Cambridge.

Later, arrangements were made for Bohr's transfer to Manchester. These were confirmed in an exchange of letters in January 1912.

It was because Rutherford's discovery of the nucleus led to the most important discovery by Bohr of the structure of the atom as a whole. Bohr later say of him : "To me he had almost been like a second father.' It was because of his exposure to Rutherford's independent ways of making scientific judgements, his style of leadership, guiding others while vigorously continuing his own researches, and his concern for his younger collaborators.

On 24 July 1912 Bohr left Manchester for his Denmark. His postdoctoral period had come to an end. Bohr's stay in Manchester had lasted three months.

Message from England

A courier from Stockholm had arrived in Copenhagen with a communication from England to the Danish general staff, to the effect that an important message for Prof. Bohr was to come via the general staff offices. It was requested to ascertain whether Bohr would be willing to receive that message, which was to be written on a piece of ultramicrofilm hidden in a hollowed-out section of a key attached to a bunch of other keys. Only after receipt of a signal that Bohr would accept the message would the bunch of keys be sent to Copenhagen.

Gyth was charged with contacting Bohr. He was an officer in the information division of the Danish general staff who at the same time was deeply involved with the Danish resistance movement. Thus came about Gyth's visit to Bohr, the beginning of a secret operation codenamed '213'.

Bohr declared himself willing to accept the message. But it took another three weeks before a sufficiently well qualified courier was found to bring the material from Stockholm to Copenhagen.

After receipt of the keys, Gyth managed to locate the microdot which was the size of a pinhead. He put it under a microscope and transcribed it.

"I have heard in a roundabout way that you have considered coming to this country if the opportunity should offer. I need not tell you how delighted I myself should be to see you again."

"Indeed I have in my mind a particular problem in which your assistance would be of the greatest help. Darwin and Appleton are also interested in this problem and I know they too would be very glad to have your help and advice."

"All I want to do is to assure you that if you decide to come, you will have a very warm welcome and an opportunity of service in the common cause"

"Yours sincerely, J. Chadwick. Physics Laboratories - The University of Liverpool"

Bohr declined the invitation. At Bohr's request, Gyth returned the next day to pick up a reply to Chadwick. He saw to it that this letter was reduced to 2 x 3 mm size. Next, it was wrapped in metal foil and handed to a courier. Then it went to a dentist who inserted the message in a hollow tooth of the courier, then covered it with a filling.

"In spite of the times, it was possible to continue undisturbed both the experimental and the theoretical work."

"I have to the best of my judgment convinced myself that in spite of all future prospects, any immediate use of the latest marvelous discoveries of atomic physics is impracticable."

But two weeks later he called Gyth again. Further reflection had led him to believe he saw a method for practical uses of fission. He had committed his idea to paper and asked Gyth if he could help him once again to get his message to the British. Gyth obliged and this time the letter was sent in secret, but less dramatic ways.

The escape

In mid-September Bohr was informed by Swedish diplomatic sources in Copenhagen that arrest of refugees was imminent. In the following days, it became increasingly clear that Bohr own fate was also at risk. All this led him to contact the Danish underground, especially the biochemist Kaj Linderstrøm-Lang. Linderstrøm-Lang arranged for an escape route to Sweden.

On 29 September 1943 Bohr and his wife left Carlsberg on foot to walk to a small house in the Musikby, part of the Sydhavn quarter, where they arrived in the early evening. That was the place of assembly for about a dozen people who, together with the Bohrs, were to make the illegal crossing over the Øresund in the same boat. Toward ten o'clock everyone left the little house, crawling on all fours part of the way, to get to the beach. Everybody boarded a little fishing boat that brought them on to the Øresund. Linderstrøm-Lang, who kept an eye on the Bohrs, all the way from Carlsberg to the boat, now departed.

A good hour later, all passengers were transferred to a large trawler. In the early hours of 30 September they were safely delivered in the harbour of Limhamn. From there, they were transported to Malmø, three miles to the north, where everyone was bedded down in the detention rooms of a police station. Bohr immediately contacted the rector of the University of Lund asking him to request an interview with the Swedish minister of foreign affairs in Stockholm. In the early afternoon of the same day, Bohr arrived by train in Stockholm. His wife stayed behind to await the arrival of the sons who came over shortly afterward with their families. At the station, Bohr was met by Prof. and Mrs. Klein -- who would be the Bohr's hosts -- by an intelligence officer of the Swedish general staff and by captain Gyth.

Gyth brought Bohr to the Kleins by taxi. In high Le Carre style, they first drove to a building used by the Swedish intelligence service, went up to the roof, walked over roofs to another building, then went down and took another taxi. Soon after arrival at the Klein home, a police officer arrived, with whom Gyth arranged security measures. One policeman to be present at all times in the home, one to be stationed in front of the houses, one to patrol nearby streets. That done, Gyth told Bohr of the British desire to have him come quickly.

For his own reasons, Gyth had had to flee to Swedien earlier in September. A few hours after Bohr's arrival, he had been told what had happened. At once he arranged for a communication to England of Bohr's escape. Almost immediately he received word that the British wanted Bohr to come over as soon as possible. The next day, an unarmed Mosquito bomber would be at Bohr's disposal at Stockholm's airport.

However, Bohr did not want to leave at once. First, he intended to intervene with the Swedish government on behalf of the Jews in Denmark. As it happened, for a few days, bad weather over the British Isles made his departure impossible anyway. Lasting thorugh 3 October, Bohr proposed modes of action to the Swedish minister of foreign affairs, King Gustaf V, the crown prince, and a number of other prominent Swedes. Meanwhile, Gyth had arranged for Bohr and his wife who had arrived in Stockholm to move to more spacious quarters provided by a member of the Danish embassy staff. Surveillance continued, now also including an armed Danish officer who during the night guarded the bedroom.

The time had now come for Bohr to fly to England. At ten o'clock on the evening of 4 October, Bohr said goodbye to his family.

After he had left, Gyth and the hosts broke open a bottle of champagne to celebrate the successful conclusion of this part of the adventure. Shortly after midnight, the bell rang. There stood Bohr. His plane had taken off alright but after a short while had to return because of engine malfunction. Bohr had taken a taxi back.

Since all security personnel had been dismissed, Gyth decided to guard the bedroom himself armed with the host's old revolver.

All was peaceful until in the early morning hours he heard soft steps on the stairs. Somebody approached the apartment door. Gyth stood at the ready, the revolver in one hand, a heavy candelabrum in the other.

Then, the morning newspaper dropped through the mail slot. Looking out of the window some moments later, Gyth saw an old newspaper lady wearing felt slippers so as not to wake her customers.

That evening, Bohr took off again via Stockholm's Bromma airport.

Bohr's plane flight to Britain had its hairy moments. When the plane reached the Kattegat near occupied Denmark, it increased altitude to avoid Nazi fighters and it became necessary to use the oxygen mask. By intercom, the pilot instructed Bohr, who was lying in the bomb bay separated from the cabin, to turn on the oxygen. But he got no response.

So the pilot took the plane down to near sea level. When it landed at a military airport in Scotland, in the early hours of 6 October, Bohr was in fine shape, telling that he had slept most of the way, which meant that he had been unconscious because of lack of oxygen.

Bohr spent the rest of that night in the home of the airport commander. The following morning he was flown to London's Croydon airport, where he was met by Chadwick and the secret service officer who had supervised his escape to Britain. They saw to it that Bohr was installed in the Savoy hotel.

Institute of Advanced Study

On 1948, Bohr arrived in Princeton after a trip by sea from Denmark. For about a week, he had had no opportunity to discuss scientific matters. He was quite pent up. Wolfgang Pauli and I were walking in a corridor of the Institute for Advanced Study when Bohr first came in. When he saw us, he practically pushed us into an office, made us sit down, said, 'Pauli, schweig' (Pauli, shut up). Then he talked for about two hours before either of us had a chance to interrupt him. Had Bohr's words been recorded, it would have constituted a fascinating document on the development of quantum theory.

A few weeks later, Bohr came to my office at the Institute of which I then was a temporary member. He was in a state of angry despair and kept saying 'I am sick of myself,' several times. I was concerned and asked what had happened. He told me he had just been downstairs to see Einstein. They had got into an argument about the meaning of quantum mechanics, but Bohr had been unable to convince Einstein of his views.

Bohr model

Spectrum

When Newton let sunlight pass through a prism, he had observed an aggregate of rays indued with all sorts of colors. This spectrum of colors appeared to him to be continuous. Nevertheless, the resolving power of his experimental arrangement was not sufficient to show that the solar spectrum actually consists of a huge number of discrete lines interspersed with darkness.

The first observation of discrete spectra is apparently due to Thomas Melvill, who was born the year before Newton died. He found that the yellow light produced by holding kitchen salt in a flame shows unique refraction, that is, the light is monochromatic. Actually, no single atomic or molecular spectrum is monochromatic. But in the case of kitchen salt, the yellow so-called D-line is much more intense than all other lines. Moreover, it was found subsequently that the D-line is in fact a doublet, a pair of close-lying lines. It would also be clear later that the D-line stems from the heated sodium atoms contained in the salt molecules.

As to the solar spectrum, the discovery of some of its discrete features dates from the early nineteenth century, when Wollaston and then Fraunhofer observed dark lines in this spectrum. Fraunhofer noted that one of these lines has precisely the same frequency as the D-line seen when heating kitchen salt. This coincidence comes about because the radiating power of any substance as seen in its "emission spectrum" equals to its absorbing power as seen in its dark line "absorption spectrum". Thus Fraunhofer's dark D-line could eventually be explained by the fact that the outer layers of the sun contain sodium, which picks out for absorption the D-line frequency generated in the sun's interior.

The precise quantitative statement of this relation between emission and absorption was first made in a paper by Kirchhoff, published in 1859. Six weeks later he had readied a sequel in which he showed that from this relation, one can derive what we now call Kirchhoff's law, the law which in turn led Planck to the quantum theory.

Thus, the origins of quantum physics ultimately go back to experimental studies of sunlight and kitchen salt.

Analytical spectroscopy

As happens so frequently in the development of new domains in experimental physics, these origins can be traced to the invention of a new experimental tool. In analytical spectroscopy's case, the Bunsen burner.

In order to generate the emission spectrum of a substance, one has in general to heat it. If the heating flame has colors of its own, as with candlelight, then the observation of the spectrum of the substance gets badly disturbed. The virtue of the Bunsen burner is that its flame is non-luminous. And so it came about that analytical spectroscopy started with a collaboration between Kirchhoff and Bunsen, then both professors in Heidelberg. Their tools were simple : a Bunsen burner, a platinum wire for holding the substance to be examined, a prism, and a few small telescopes & scales.

They observed, as others had conjectured earlier, that there is a unique relation between a chemical element and its atomic spectrum. Spectra may therefore serve as business card for new elements. "Spectrum analysis might be no less important for the discovery of elements that have not yet been found". They themselves were the first to apply this insight by discovering the elements cesium and rubidium. Later, ten more new elements had been identified spectroscopically before the century was over : thallium, indium, gallium, scandium, germanium and the noble gases (helium, neon, argon, kyrpton, and xenon).

The discovery in 1869 of helium by means of a mysterious yellow line found in the spectrum of the sun (whence its name) illustrate what Kirchhoff and Bunsen had forseen.

“”Spectrum analysis opens the chemical exploration of a domain which up till now has been completely closed. It is plausible that this technique is also applicable to the solar atmosphere and the brighter fixed stars.

Later, the spectra of these clouds revealed another substance never seen on earth, accordingly named nebulium, assumed to be a new element. It took sixty years before it was realized that this substance actually is a mixture of metastable oxygen and nitrogen. Another hypothesized stellar element, coronium, turned out just to be very highly ionized iron.

Spectral numerology

In the 1860s, shortly after the first quantitative measurements of spectral frequencies, a new game came to town : spectral numerology. It's less ambitious than trying to find the mechanisms for the origin of spectra. Instead, it's the search for simple mathematical relations between observed frequencies.

A textbook published in 1913 contains no less than twelve proposed spectral formulae. All these have long been forgotten, except for one : the Balmer formula for the spectrum of atomic hydrogen.

After receiving a Ph.D in mathematics, Balmer became a teacher at at a girl's school in Basel and later also privatdocent at the university there. He was neither an inspired mathematician nor a subtle experimentalist, but rather an architect. To him, the whole world, nature and art, was a grand unified harmony. It was his aim in life to grasp these harmonic relations numerically.

What Balmer did is incredible. Having at his disposal only the four frequencies measured by Angstrom, he fitted them with a mathematical expression that predicts an infinity of lines.

$V_{ab}=R({\frac {1}{b^{2}}}-{\frac {1}{a^{2}}})$

R is a constant. The index b takes on the values 1,2,3, and so on. The index a also runs through the integers, but is always larger than the index b. Balmer found that he could fit the four Angstrom lines very well when b=2; a=3,4,5,6; R=3.29163 x 10¹⁵Hz

Having come that far, Balmer told the professor of physics at Basel University what he had found. This friend told him that actually another 12 lines were known from astronomical observations. Balmer quickly checked that these also fitted his formula, for a = 2 and b = 5 to 16.

Balmer's formula has stood the test of time as more hydrogen lines kept being discovered.

However, for nearly thirty years, no one knew what the formula was trying to say.

Then Bohr came along.

On the constitution of the atom

“”I do not think you need feel pressed to publish in a hurry your second paper on the constitution of the atom, for I do not think anyone is likely to be working on that subject.

— Rutherford to Bohr c. 1912

Shortly after 7 February 1913, Bohr heard of the Balmer formula. Later, by 6 March, he had completed a paper containing its interpretation. On that day, Bohr sent a letter to Rutherford in which he enclosed "the first chapter on the constitution of atoms", asking him to forward that manuscript to "Philosophical Magazine" for publication. Up to that point, Bohr had three published papers to his name : his doctor's thesis, a short sequel thereto, and his paper on alpha-particle absorption. His new paper was to make him a world figure in science and marks the beginning of the quantum theory of atomic structure.

This paper proposed the postulate that an electron inside a hydrogen atom can move only on one or another of a discrete set of orbits --of which there are infinitely many --. This postulate is in violation of the tenets of classical physics, which allows a continuum of possible orbits. Bohr called his orbits "stationary states". Their respective energies, taken in order of increase, will denoted by E_a where a = 1,2,3, and so on. We shall refer a = 1 as the "ground state", the lowest orbit, closest to the nucleus, which has the lowest energy E₁.

According to classical law, an electron in the ground state will not stay there, but will spiral into the nucleus. Bohr circumvented this disaster by introducing one of the most audacious postulates ever seen in physics. He simply declared that the ground state is stable, thereby contravening all knowledge about radiation available up till then.

Now what about the higher stationary states? These are unstable. The electron will drop from a higher to some lower state. Then Bohr assumes, transitions from higher state "a" to lower state "b" are accompanied by the emission of one light quantum with frequency v_ab, given by.

$E_{a}-E_{b}=hv_{ab}$

Next, Bohr returned to his earlier hypothesis which links the kinetic energy W of an atomic state to its frequency v.

$W=Kv$

Bohr now makes an explicit proposal for K

$W_{a}={\frac {1}{2}}ahv_{a}$

This equation associates an integer a to each states. It is the first example of a quantum number.

Then, it is possible to derive the Balmer formula from the last two previous equations combined with a third one, which expresses that the electron is kept in orbit by the balance between the centrifugal force which pulls the electron away from nucleus, and the attractive electric force which pulls it toward the nucleus. At this point, Bohr was able to predict the value of R.

$R_{z}={\frac {2\pi ^{2}mZ^{2}e^{4}}{h^{3}}}$

Let m and -e denote the mass and charge of the electron and Ze the charge of the nucleus (for hydrogen, Z=1). Using the best known experimental values for m,e and h, Bohr obtained R=3.1 x 10¹⁵ "inside the uncertainty due to experimental errors" with the best value of R obtained from spectral measurements.

This expression is the most important equation that Bohr derived in his life. It represented a triumph over logic. Never mind that discrete orbits and a stable ground state violated laws of physics which up till then were held basic. Nature had told Bohr he was right anyway. Of course, it was not to say that logic should not be abandoned, but rather a new logic was called for : the quantum mechanics.

Bohr was also able to derive an expression for r_a, the radius of tha a-th orbit.

$r_{a}={\frac {a^{2}h^{2}}{4\pi ^{2}Zme^{2}}}$

This yields the "Bohr radius" r₁ = 0.55 x 10^-8 cm for stable hydrogen, in agreement with was then known about atomic size. Bohr noted further that the bigger radii of higher states explain why so many more spectral lines had been seen in starlight than in the laboratory.

Further verification

In 1896 Charles Pickering from Harvard had found a series of lines in starlight which he attributed to hydrogen, even though this did not fit Balmer.

In 1912, these same lines were also found in the laboratory by Alfred Fowled in London.

Bohr pointed out that "we can account naturally for these lines if we ascribe them to helium", a singly ionized helium, that is, a one-electron system with Z=2. According to the formula for R_z, this would give a Balmer formula with R replaced by R₂ = 4R.

Fowler objected. In order to fit the data, the 4 ought to be replace by 4.0016.

Bohr remarked in October 1913 that the formulation in his paper rested on the approximation in which the nucleus is treated as infinitely heavy compared to the electron. Later, a calculation shows that, if the true masses for the hydrogen and helium nuclei are used, then the 4 is replaced by 4.00163.

Up to that time, no one had ever produced anything like it in the realm of spectroscopy. Agreement between theory and experiment to five significant figures.