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In this installment in the history of atom theory, physics professor (and my dad) Dean Zollman explains how Niels Bohr built on the work of others to craft his model of the atom – Kim

By Dean Zollman

Dean ZollmanWhen asked to visualize or draw an atom, most of us would probably draw a small central nucleus with electrons orbiting in circles or ellipses. Some of the electrons would be close to the nucleus while others would be farther away. An example is shown in the drawing below. This view of the atom is a representation of the Bohr Model. While it is no longer considered the most correct one, it has appealed to many people for over 100 years. So, it is frequently used when we want to represent something that we cannot see (and even have difficulty comprehending).

Bohr model of the atom

A schematic illustration of the Bohr Model of the atom (By Sharon Bewick, via Wikimedia Commons under a Creative Commons Attribution-Share Alike 3.0 Unported license )

The Bohr Model builds on the concepts that we have discussed in the previous two posts. It incorporates Max Planck’s ideas that the energy of light is related to its frequency and to Albert Einstein’s concept that light comes in small packets of energy called photons. The model also brings in Ernest Rutherford’s discovery that the atom has a very small but very massive center which has a positive electrical charge. Thus, the model includes many of the important discoveries of the early 20th century.

Niels Bohr (1885-1962) was born in Copenhagen and raised in a family with many intellectual advantages. His father, Christian, was a very accomplished physiologist; his mother, Ellen, was a member of a prominent family in Denmark.

Bohr and his dissertaton

An illustration from a report about Niels Bohr’s doctoral defense. The report was published in the Copenhagen newspaper Dagbladet in May 1911. (Scanned from Niels Bohr: A Centenary Volume edited by A.P. French and P.J. Kennedy)

Bohr attended the University of Copenhagen and received a doctorate in 1911. At the time, Bohr was studying physics at the university, a large fraction of the work in physics was focused on using the recently discovered electron to explain a variety of phenomena. Thus, Bohr’s master’s and PhD studies were about an electron theory of metals. Because he had created a theory involving electrons, Bohr decided to begin his postdoctoral work with the discoverer of the electron, J.J. Thomson. So, he moved to the Cavendish Laboratory in Cambridge.

The collaboration with Thomson did not work out well, and Bohr was rather frustrated with his time in Cambridge. However, he soon met Ernest Rutherford who had recently discovered the structure of the atom and the presence of a nucleus. Rutherford was impressed with Bohr and soon invited him to join the research group at the University of Manchester.

So Why Is This Element So Stable?

Bohr immediately began making significant contributions to work in Rutherford’s lab. One of his early research activities was to understand how alpha particles, which were emitted in some radioactivity, slowed down as they interacted with matter. His collaborator for this work was Charles G. Darwin (1887 –1962), grandson of the Charles Darwin. Issues of stability of the atom were critical to their work as they were to then current models of the atom. As we discussed several months ago, Rutherford had devised a planetary model of the atom. However, this model had a fundamental problem. Based on the laws of electricity and magnetism, the atom was not stable. The electron in orbit should very rapidly radiate energy and end up in the nucleus.

Niels Bohr and Margrethe Nørlund

Niels Bohr and Margrethe Nørlund at the time of their engagement in 1910 (public domain, via Wikimedia Commons)

Bohr was also concerned about stability from a different perspective. At a conference in 1922, he described his thoughts as he began thinking about the atom 10 or so years earlier. “My starting point was not at all the idea that an atom is a small scale planetary system and as such governed by the laws of astronomy. I never took things as literally as that. My starting point was rather the stability of matter, a pure miracle when considered from the standpoint of classical physics. By stability, I mean that the same substances always have the same properties.” (Quoted in Pullman, The Atom in the History of Human Thought)

In short, Bohr wondered why all iron (or hydrogen or whatever) atoms were the same as all others of the same element. The laws of physics as they were known in 1912 did not require such consistency in nature. (But nature would have certainly been chaotic without the consistency.)

By June 1912, Bohr was spending all of his research time on a model of the atom. At this time Bohr’s concerns were radioactivity, the periodic table and how atoms bound together to make molecules. He was not yet interested in the spectra of light emitted by the atoms.

However, some other researchers were interested in the light emission process. They were approaching it by applying the results of Planck and Einstein to atomic models that were available. In 1910, Arthur Hass (1884-1941) used Planck’s idea that the energy of an electron vibrating in an atom similar to the Thomson Model was proportional to its frequency. (Recall that the Thomson Model has electrons moving in a uniform positive charge rather than in orbits.)

This concept led John W. Nicholson (1881-1955) to consider a similar idea but using a model of the atom in which all electrons were in orbit outside the positive charge but all at the same distance from the nucleus. Nicholson was interested in explaining the light in stars’ spectra that seemed to have no counterpart on earth. After some work, Nicholson concluded that his model worked best if he required that the angular momentum of the electrons was equal to an integer times Planck’s constant divided by 2 pi.

(A short physics lesson: Angular momentum is a quantity that is useful for any object moving in an orbit. It is equal to mass x speed x radius. Nicholson could equally well have stated a requirement on the energy. It was simpler in terms of the equations to use angular momentum.)

Nicholson concluded that the light in the spectra is created by the atoms when they “run down” (lose energy) by “discrete amounts.” This is the beginning of using Balmer’s discovery of the nature of the spectrum from gases to understand the quantum nature of the atom.)

Bohr built on Nicholson’s idea by adopting the requirement that the angular momentum can have only certain discrete values related to Planck’s constant. However Bohr’s atom has many orbits for the electrons. In the fall 1912, he returned to the University of Copenhagen. He was however still not interested in light emitted by atoms. At the beginning of 1913 Bohr wrote to his brother, “[My] calculations would be valid for the final, chemical state of atoms, whereas Nicholson’s would deal with the atoms sending out radiation, …” And, to Rutherford he wrote “I do not at all deal with the question of calculation of the frequencies corresponding to the lines of the visible spectrum.”

Niels Bohr and Albert Einstein

Niels Bohr and Albert Einstein at the 1930 Solvay Conference in Brussels (Photograph by Paul Ehrenfest public domain via Wikimedia Commons)

Let’s Add Some Light

At this time, Bohr had apparently not heard of or had forgotten about Balmer’s famous formula which described the values for the frequencies of the light emitted by the hydrogen atom. Fortunately, H.M. Hansen (1886-1956), a spectroscopy specialist at the University of Copenhagen, reminded Bohr of Balmer’s work. Bohr thought of the emission of light in terms of the electron changing orbits outside the positive nucleus. As the electron moved from one orbit to another closer to the nucleus, it lost energy. That energy appears as light emitted by the atom. Further, that energy was related to the frequency of light by the equation that Planck had invented. He invoked Einstein’s results by assuming that each change in orbit resulted in the emission of one photon (quantum) of light.

Bohr's Model

A schematic showing the process of light emitted by an atom in Bohr’s Model (by Brighterorange, GFDL, CC-BY-SA-3.0, or CC BY-SA 2.5-2.0-1.0, via Wikimedia Commons)

Later, Bohr recalled, “As soon as I saw Balmer’s formula, the whole thing was immediately clear to me.” Balmer’s formula can be written as

Frequency of light = (speed of light) R (1/m2 – 1/n2)

To Balmer, R was a number that he determined experimentally, and m and n were integers. Not only was Bohr able to derive the form of Balmer’s formula, but he determined the value of the until then mysterious R in terms of fundamental measurements such as the mass and charge of the electron, Planck’s constant, and pi.

Photon in a Bohr atom

An animation of a photon of light being emitted and absorbed by a Bohr atom (by Kurzon, CC BY-SA 3.0, via Wikimedia Commons)

Today, Bohr’s work is presented in most texts in a couple of straight forward steps. First Bohr established the rule for the value of the angular momentum. Thus, he established a model of the atom that required the electrons to be in various orbits around, but not all orbits were possible – only those that met his condition on the angular momentum. Then, he derived Balmer’s formula. As is almost always the case, the story was more complex than that.

Bohr’s model of the atom established that the orbits of electrons are restricted to certain values. We can talk about these values in terms of angular momentum, energy or distance from the nucleus – all of them are equivalent. Most importantly, only certain values are allowed. Today we say that the orbits of the electrons are quantized. This fundamentally changed the way that we look at matter. Next time we will look further into Bohr’s atom and some of its refinements. Somewhat later we will consider the models that eventually replaced it.

(Unless otherwise stated quotations from Bohr were taken from Niels Bohr: A Centenary Volume edited by A.P. French and P.J. Kennedy.)

Dean Zollman is university distinguished professor of physics at Kansas State University where he has been a faculty member for more than 40 years. During his career he has received four major awards — the American Association of Physics Teachers’ Oersted Medal (2014), the National Science Foundation Director’s Award for Distinguished Teacher Scholars (2004), the Carnegie Foundation for the Advancement of Teaching Doctoral University Professor of the Year (1996), and AAPT’s Robert A. Millikan Medal (1995). His present research concentrates on the teaching and learning of physics and on science teacher preparation.


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