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Niel Bohr’s Nuclear Model: The Nuclear Model That Changed Physics

Niel Bohr said that before 1913 no one expected that the lines of color you get from burning hydrogen would tell you anything about physics even though the colors follow a pattern. Just like butterflies have patterns with the colors on their wings, “but nobody thought that one could get the basis of biology from the coloring [on the] wings of a butterfly.[1]

However, in February of 1913, 27-year-old Niels Bohrread a book about the spectral lines of hydrogen and everything clicked.  Within a few weeks, Bohr created a model that changed Physics.



Table of Contents

Niels Bohr’s Early Life

The Accidental Discovery of Bouncing Alpha Particles

Bohr’s Journey and His Nuclear Model

Bohr’s Theory Gets More Validation

References


Niel Bohr’s Early Life

Niel Bohr
Niels Bohr

When 25-year-old Niels Bohr arrived in England in September of 1911 he was so excited that he wrote his fiancée that he “rejoiced” when he “happened to read the address ‘Cambridge’ over the door.[2]”.  Bohr was thrilled to be able to work in a top-notch department under the incomparable JJ Thomson, who had discovered the electron 14 years earlier, and his dizzying array of influential students. 

Instead, it was a total disaster.  The fellow students did not want to talk to a mumbling Dane with too much energy and weird ideas.  It didn’t help that on the first day Niels Bohr went to Thomson with a copy of one of Thomson’s books, opened it up, and told the Nobel Prize winner in halting English: “this is wrong”[3]

Bohr actually thought that the conversation went well and then left a copy of his poorly translated Ph.D. thesis and started his research. A few weeks later Bohr started to realize that things weren’t so great and wrote his brother, “Thomson has so far not been as easy to deal with as I thought on the first day… he has not yet had time to read my paper and I do not know if he will accept my criticism.[4]”For the next three months, Bohr was miserable and mostly alone.

Then, on December 6, 1911, Bohr’s life changed when JJ Thomson had his annual dinner for his current and former students.  This was a strangely raucous affair, with formal attire and a 10-course meal as well as people standing on tables to shout limericks and “poems” about physics at Cambridge: “Oh my darlings! Oh my darlings! Oh my darlings ions mine! You are lost and gone forever, when just once you recombine.” 

So, yeah, Physicists were dorks then too.  And for dessert, they served plum pudding!  This was also a dorky physics joke because the accepted view of atoms, called the “plum pudding” model came from JJ Thomson[5] who imagined that the negative electrons were like the raisons (or if you are a Brit, the plums) in a sea of positive pudding. 

The Accidental Discovery of Bouncing Alpha Particles

However, this was a slightly controversial dorky joke as Thomson’s former student Ernest Rutherford was there and 9 months earlier Rutherford had proposed a new model for the atom which Rutherford thought was, “superior to J.J.’s[6].”Rutherford was only 40 years old but had already discovered alpha and beta radiation, discovered the half-life of radiation and used that to make a method to determine the age of the earth, and determined that radiation can change the atomic number of material, for which he won a Nobel Prize, and had accidentally determined that alpha particles can bounce off thin pieces of metal. 

The accidental discovery of the bouncing alpha particles was what made Rutherford decide that the plum model didn’t work as the scattering of alpha particles, “must be the result of a single collision, and when I made calculations I saw that it was impossible … unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus.[7]” 

This is why on March 7, 1911, Rutherford published an article where he assumed that atoms were composed with, “a positive charge Ne at its center, and surrounded by a distribution of negative electricity Ne uniformly distributed within a sphere of radius R.[8]” By the way, Rutherford wasn’t wedded to the “uniformly distributed electrons” as he also mentioned the work of a Japanese scientist named Hantaro Nagaoka who had made a “Saturn” model of the atom where the electrons were in a ring around a positive center[9] (Rutherford wasn’t particularly concerned with the electrons).  Rutherford’s “model” was almost immediately disliked and ignored. 

For one, it made solids, well, not very solid.  For example, if a typical atom was the size of a cathedral, the atom (with 99.9997% of the weight) would be the size of a fly[10]!  Moreover, “Rutherford’s atom” had a significant problem: opposite charges attract, so what keeps the negative electrons from being sucked into the positive nucleus?  Even if the electrons were spinning around the nucleus like planets then they would be accelerating charges (spinning is a form of acceleration), which should, according to Maxwell’s laws, be creating electromagnetic waves, which would cause the electrons to lose energy and spiral into the nucleus. 

In other words, according to the laws of classical physics, Rutherford’s atom should just implode.  Not surprisingly, JJ Thomson was particularly displeased with this model and the students at Cambridge followed suit, all except Bohr.  In 1962, Bohr was asked if he was the only person in Cambridge who “responded well” to Rutherford’s atom.  He replied, “yes, but you see I did not even respond to it. I just believed it[11]

At the dinner in December of 1911, Bohr realized starkly that he was working for the wrong man.  Here was the physics, and the physicist, that he needed.  It didn’t hurt that “Papa” Rutherford was a big, loud and exuberant New Zealander, described by a contemporary as, “always a charming blend of boy, man, and genius”!

Bohr sheepishly told JJ Thomson that he wanted to spend some time in Manchester to “know something about Radioactivity,” and Thomson was perfectly happy to let him go, but had him stay in Cambridge for the winter term.  By March, 1912, Bohr was in a laboratory in Manchester and now wrote his brother that the new lab was, “full of characters from all parts of the world working with joy under the energetic and inspiring influence of the ‘great man’.[12]

Bohr’s Journey and His Nuclear Model

However, after a few weeks he told Rutherford that he would “like to concentrate on the theoretical things,” and basically never experimented at any laboratory again. (Rutherford usually hated theoreticians but he made an exception for Bohr, partially because he thought Bohr was brilliant and partially because Bohr was a very good soccer player – and Rutherford respected that).

At the time Bohr was very interested to hear from Rutherford about the Solvay conference that he had gone to in October of 1911.  At the conference, it became clear that quantum ideas were here to stay, as the scientist Marcel Brillouin said at the conference, “From now on we will have to introduce into our physical and chemical ideas a discontinuity, something that changes in jumps, of which we had no notion at all a few years ago.[13]” (Of course, Max Planck and Albert Einstein had these thoughts for more than a few years by this time.) 

But how to introduce quantum ideas, and how to make it work with atoms?  No one, even Einstein, knew.  Einstein started to joke that quantum ideas would drive you crazy and told a friend that “the h-disease…looks ever more hopeless.[14]”  Rutherford wasn’t too interested in what he heard at the Solvay conference and, “just said it is odd.[15]” But Bohr once again just believed, and by mid-July, Bohr wrote Rutherford, in the reverse of Einstein, that you needed quantum theories to describe atoms as, “it seems hopeless[16]” with only classical mechanics. 

Niels Bohr
Niels Bohr first worked with Rutherford at
Manchester in 1912. This photo shows the young Niels and Margrethe Bohr, ca. 1914

By the end of July, Bohr returned to Denmark and to his fiancée Margrethe Nøland.  While Bohr had been depressed in Cambridge, he had written to Margrethe worried that she might not like his work and she replied, “Oh, dear Niels, I cannot at all describe to you how much I love you and how much I love your work, and I cannot distinguish you from it and I cannot at all describe to you how much I long for the future, for being allowed to help you a little sometime, if only I can.[17]” 

Niels Bohr was eager for her help and wrote asking her to,“help me try to lead a great and active life. My head is so full of plans, and they are all, all of them, based on you,[18]” to which she readily agreed.  They married in August, and Niels would dictate all of his papers and Margrethe would edit and be a source of logic and sanity. 

Even after they had six sons together and he got an assistant nothing could be published without Margrethe’s approval.  Anyway, soon after marriage, in September, 1912, he, “went into the country with my wife and we wrote a very long paper on these various things.”  However, it didn’t go very well, and Bohr wrote Rutherford that he was facing “some serious trouble” with the work and nothing productive happened for months. 

Then in mid-February, 1913, Bohr discussed his ideas with a colleague and was asked how it worked with the spectral formulae.  Bohr was intrigued, he had forgotten that there were equations for how light was emitted from various glowing gasses[19]!  Specifically, back in 1885, a 60-year-old schoolteacher named Johann Balmer had noticed that the frequency of light from glowing hydrogen followed a geometric pattern, where the frequency depended on the difference of the reciprocal of two integers squared. 

Amazingly, Bohr did not know (or had forgotten) about this empirical law (meaning a law based only on experiment with no theoretical backing) until he read it February 1913[20]!  Years later he recalled, “as soon as I saw Balmer’s formula, the whole thing was immediately clear to me.[21]

In less than 4 weeks, Niels and Margrethe Bohr banged out one of the most influential papers of all times!  In this model, Bohr assumed that the electrons spin in a circle (or shell) around the nucleus, where the electron is limited in that it can only be at certain set distances from the nucleus where the lowest energy, corresponding to the closest to the nucleus, is now called the “ground state”. 

What about the problem of the spinning electron radiating energy and therefore spiraling into the nucleus?  Oh, he just declared that it didn’t happen! Really.  This was described by Bohr’s biographer as, “one of the most audacious postulates ever seen in physics. He simple declared that the ground state is stable, thereby contravening all knowledge about radiation available up till then![22]” Bohr then made two more radical assumptions. 

First, he assumed that the electron was spinning around the nucleus with an energy equal to an integer times “Planck’s constant” times the frequency of spinning divided by 2.  Why divided by 2?  Well, he gave an awkward explanation (years later, he said it was confusing because of the “stupidity of the way of writing it”[23]), but it basically has to do with averaging the energy in the atom with the zero energy once free.  He might have divided by 2 because then the results worked amazingly well with the hydrogen spectrum, and he backtracked to find a reason that seemed to make sense.

With this assumption, and equations for electrical force and energy, Bohr could determine the position of the electron as a function of fundamental constants (like the charge and mass of an electron, and Planck’s constant) and got that the radius of electrons as a constant – times an integer squared.  So, the possible radiuses would be r, 4r, 9r, 16r, or I think you get the pattern. As the distances depended on an integer squared and the energy depends on one over the distance, the energy depends on one over an integer squared.

Bohr’s Theory Gets More Validation

Niels Bohr
Niels Bohr & Albert Einstein: Photograph by Paul Eh renfest (1925), courtesy AIP Emilio Segre Visual Archives

Bohr then made one more assumption, even more drastic than the others: Bohr decided that the energy of the light (radiation) came not from the energy of the electron but the change in energy when it jumped in a “quantum leap” from one shell to another.  This was an absolutely new and radical idea, so crazy that when Einstein heard about it, Einstein admitted that, “he had once similar ideas, but did not dare publish them.[24]” 

With these assumptions, it was a basic physics problem to determine the change in energy from dropping from one radius to another, whereupon Bohr not only got an equation from fundamental ideas that fit the hydrogen spectrum, he also derived the constant in front, called the Rydberg constant, from fundamental constants. This is the highest goal of a theorist, to derive an empirical formula from theory. 

But Bohr wasn’t done yet, he had an extra validation, and I am going to give a small backstory because it is so amazing, I just need to share.  So, in 1879 a pregnant 23-year-old woman named Williamina Fleming was abandoned by her husband.  Desperate, she found a job as a maid to Elizabeth (Lizzy) Pickering the wife of Edward Pickering, a professor of astronomy at Harvard.

One day, Edward Pickering complained to his wife that his employees were so bad that his maid could do a better job[25] and his wife agreed and suggested that he should give Williamina Fleming a chance.  Pickering was amazed to find that Fleming was a naturally fantastic astronomer, and by 1881, hired her as his assistant.  In 1886, Pickering was given money by the widow of Henry Draper for “the Henry Draper Catalogue” to use photographic spectroscopy to catalogue as many stars as possible. 

The next year Pickering then put Williamina Fleming in charge of the project, and she hired an army of women to study the stars.  (Pickering specifically wanted women as they were cheaper than men and he wanted to prove to the world that women could make scientific discoveries).  Pickering called them his “computers” but his rivals called them his “harem”.  Anyway, while cataloguing more than 10,000 stars, Fleming noticed that the spectrum from a star called zeta Puppis was very strange, it seemed to have only half the hydrogen lines and Pickering and Fleming published an article called, “Stars having peculiar spectra” in 1896. 

Pickering decided that these “Pickering series lines” (as they were known) were hydrogen that followed a ½ integer transition levels.  Fast forward to 1913, when Bohr realized that these spectral lines could be explained as being from ionized Helium (helium with only one electron), where the helium having two protons instead of one would multiply the possible frequencies by 4 and one would no longer need 1/2s in the equation!

By March 6th, 1913, Niels Bohr sent his paper to Rutherford and asked him to publish it in England.  Rutherford had mixed feelings writing back that, “your ideas… are very ingenious and seem to work well; but the mixture of Planck’s ideas with the old mechanics makes it very difficult to form a physical idea of what is at the basis of it all.[26]” (Yeah, that is the problem with quantum mechanics isn’t it?).  After a quick visit in April with Rutherford to hash out the details, Bohr published his first of three papers on this model in July of 1913, and it was the talk of the town for every physicist.

Niels Bohr’s brother Harold was in Germany and reported that everyone asked him for a copy of the paper but most people found it too radical for their tastes.  A scientist named Carl Runge sighed, “Well, [Bohr is] such a nice man, and so intelligent. But this man has become completely crazy. This is the sheerest nonsense.[27]”But not everyone hated Bohr’s theory, several younger scientists were very excited.  Bohr’s only friend from Cambridge, Georg de Hevesy, happened to be in Berlin at the time and Albert Einstein told Hevesy that if Bohr’s theory was right it “is of the greatest importance.[28]

”  According to Hevesy, when Hevesy told Einstein about the results with helium, “the big eyes of Einstein looked still bigger[29]” and Einstein remarked, “than the frequency of light does not depend at all on the frequency of the electron!… this is an enormous achievement. The theory of Bohr must be right.[30]”Einstein recalled that in 1913, “all my attempts… to adapt the theoretical foundation of physics to this [quantum] knowledge [had] failed completely …[which is why Bohr’s theory] appeared to me like a miracle – and appears to me as a miracle even today. This is the highest form of musicality in the sphere of thought.[31]

It is important to realize that no one, including Bohr, thought this was a complete theory, it was obviously a makeshift theory that barely worked for atoms with one electron.  However, it was a revelation because it gave a new path forward and the idea that radiation is due to the quantum *change* in energy of electrons is a fundamental concept of Physics that is still used to this day. 

Still, Bohr knew that spinning electrons *do* release radiation, so what was going on in the electrons of the atom?  By 1927, with the help of Heisenberg’s Uncertainty principle, Bohr came up with his answer: you can’t ask that question!  You can’t ask what electrons are or what they do, you can only ask what can you measure about an electron.  This viewpoint, currently called the Copenhagen Interpretation, is the most commonly taught interpretation of quantum mechanics, and Einstein *hated* it.  It quickly became a great public debate between the two men, eventually involving God playing dice, a disappearing moon, a dead-alive cat, spooky action at a distance and more!  I will discuss the history of the great Einstein-Bohr debates.

References

[1] Niels Bohr Oral History (October 31, 1962) American Institute of Physics – Session I

[2]Neils Bohr to Margrethe Nolund (Sept 1911) found in Crease, R and Mann C The Second Creation (1996) p. 22

[3] Found in Pais, A Niels Bohr’s Times (1991) p. 120

[4] Found in Pais, A Niels Bohr’s Times(1991) p. 120

[5]“atoms consist of a number of negatively electrified [electrons] enclosed in a sphere of uniform positive electrification” Thomson, JJ “On the Structure of the Atom…” The London, Edinburgh and Dublin Phil. Mag vol. 7 (1904)

[6] Rutherford, E. to Boltwood, B, December 1910, recalled in Geiger, Reeves, Richard A Force of Nature: The Frontier Genius of Ernest Rutherford p. 80

[7] Rutherford, Ernest “Forty Years of Physics” in Background to Modern Science, (1938) p 48 

[8] Rutherford, E “The Scattering of alpha and beta particles by Matter and the Structure of the Atom” Philosophical Magazine vol. 21 (1911) p. 671

[9] Rutherford, E “The Scattering of alpha and beta particles by Matter and the Structure of the Atom” Philosophical Magazine vol. 21 (1911) p. 671

[10] Bryson, Bill “A Short history of nearly everything” p. 141

[11] Niels Bohr Oral History (October 31, 1962) American Institute of Physics – Session II

[12]A. Douglas Stone, Einstein and the Quantum: The Quest of the Valiant Swabian (Princeton University Press, 2015), 183.

[13] Brillouin, W from Solvay, E., Langevin, P., Broglie, M. D. D., &Institut international de physique Solvay (1912). La théorie du rayonnement et les quanta: rapports et discussions de la réunion tenue à Bruxelles du 30 octobre au 3 novembre 1911. Paris: Gauthier-Villars. p.

[14] Albert Einstein to Lorentz (Nov 23, 1911) translated in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press p. 228

[15] Niels Bohr Oral History (October 31, 1962) American Institute of Physics – Session III

[16] Bohr to Rutherford (July 2, 1912) found in Pais, A Neils Bohr’s Times p. 137

[17] Margrethe Noland to Niels Bohr (Feb 9, 1912) found in Aaserud, F. Heilbron, J Love, Literature and the Quantum Atom (2013)

[18] Niels Bohr to Margrethe Noland (1912) found in Aaserud, F. Heilbron, J Love, Literature and the Quantum Atom (2013)

[19] According to Pais, A Niels Bohr’s Times (1991) p. 144 on February 7, 1913, Bohr sent Hevesy a list of ideas “used as the foundation of my calculations” and did not include spectral lines.

[20]Later Bohr recalled that it was talking to this professor was when he found, “that there was this very simple thing about the hydrogen spectrum.”  Niels Bohr Oral History (October 31, 1962) American Institute of Physics – Session III

[21] Niels Bohr Oral History (October 31, 1962) American Institute of Physics – Session III

[22]Pais, A Niels Bohr’s Times (1991) p. 144

[23] Bohr said that confusion about the factor of 2 was due to, “the stupidity of the way of writing it”  Niels Bohr Oral History (October 31, 1962) American Institute of Physics – Session I

[24] Hevesy to Rutherford (1913) found in Stachel, J Einstein from ‘B’ to ‘Z’ (2002) p. 369

[25] “Williamina Paton Stevens Fleming (1857-1911)” Harvard University Librarty Open Collections Program: Women Working, 1800-1930https://library.harvard.edu/collections/women-working-1800-1930

[26] Rutherford to Bohr (March 20, 1913) found in Pais, A Niels Bohr’s Times (1991) p. 153

[27] Richard Courant oral interview (1962) found in Kragh, H Niels Bohr and the Quantum Atom (2012) p. 123

[28] Hevesy to Rutherford (1913) found in Stachel, J Einstein from ‘B’ to ‘Z’ (2002) p. 369

[29] Hevesy to Rutherford (1913) found in Stachel, J Einstein from ‘B’ to ‘Z’ (2002) p. 369

[30] Hevesy to Bohr (1913) found in Stachel, J Einstein from ‘B’ to ‘Z’ (2002) p. 370

[31] Einstein, A “The Advent of Quantum Theory,” Science, vol. 113 (1951) p. 83

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