Bohr’s Model of the Atom Draws Critics

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In this installment of the history of atom theory, physics professor (and my dad) Dean Zollman discusses the problems physicists had with Bohr’s model – and they could get downright catty. – Kim

By Dean Zollman

Dean ZollmanIf you look at a description of the Bohr model of the atom in most textbooks or many popularized accounts, you could easily get the impression that it was an immediate success. Physicists were troubled by some of its assumptions, but it worked, so they moved on. However, like several other developments that I have discussed in these posts, the history is more complex. Many physicists were not just unhappy with some of the assumptions, they were sure the entire model was absolutely wrong.

Basically the Bohr model of the atom was an attempt to use the classical physics of Newton, Maxwell, and others but incorporate the quantum ideas of Planck and Einstein. Thus, it was the beginning of a revolution but not as great as the revolution that was to come soon. As a result of Bohr’s quantum-classical blended model, five major concerns arose.

  1. An accelerating charged particle will emit continuous radiation. An electron moving in a circle is accelerating. Yet in Bohr’s model the orbiting electrons did not radiate. If it did, the electron would spiral quickly into the nucleus. (I discussed this one in a previous post.) Bohr had no logical reason for the nonradiating electron, but without it, atoms would not exist.
  2. In the early 20th century, electromagnetic radiation such as radio waves was created by shaking electrons back and forth. The frequency of the shaking determined the frequency of the wave. For radio, microwaves, etc., we still do that. A radio station that broadcasts at 99.5 megahertz shakes electrons in its antenna 99,500,000 times per second. Scientists in 1913 expected that light was emitted in the same way, so an electron in an atom would vibrate to emit light. However, in the Bohr model nothing vibrated; the light just appeared as the electron changed orbits.
  3. Even worse, these “quantum jumps” in orbit seemed to occur without a cause. Once an electron was in orbit with an energy higher than the lowest possible energy, it would at some time move to a lower energy, but Bohr could not ascribe a cause to that event.
  4. Then, physicists asked: how does the electron “know” where it is going? When it leaves one orbit, it gives off a photon of light. The energy of that photon is determined by the energy that the electron will have when it lands in the lower orbit. It seems that the electron knows what will happen to it before the event is finished.
  5. And, finally, what happens to the electron in between the time it leaves one orbit and the time it gets to the second orbit?

So, there were some rather good reasons to wonder if Bohr was making up a story that just did not fit with the known laws of physics. However, for many people something was more important than these concerns. The Bohr model worked in a way no other model of the atom had. Bohr had been able to reproduce the equation for the spectral lines that had been discovered by Balmer. He had also explained several recently observed effects. That was enough for some physicists, but not for all.

Arnold Sommerfeld

Arnold Sommerfeld in 1897 (public domain via Wikimedia Commons)

Arnold Sommerfeld (1888-1951) at Ludwig Maximilian University in Munich did see the positive side of Bohr’s model. He and his colleagues made modifications to the model by assuming that the electron would move in elliptical orbits rather than circles. (Then, the electrons are moving in a manner similar to the planets around the sun.)

This change made the connection between the model and recent accurate measurements even better than the model with circular orbits. Thus. These refinements to create the Bohr-Sommerfeld model gave the model more credibility than it had before.

Bohr-Sommerfeld model of the atom The Bohr-Sommerfeld model of the atom (by Pieter Kuiper, public domain via Wikimedia Commons)

Paul Ehrenfest

Paul Ehrenfest (public domain via Wikimedia Commons)

However, not everyone was happy with this turn of events. Paul Ehrenfest (1880-1933) wrote to Sommerfeld to congratulate him on this work. His statement was somewhat a back-handed compliment. He said, “Even I consider it horrible that this success will help the preliminary, but still completely monstrous, Bohr model on to new triumphs, I nevertheless heartily wish physics at Munich further success along this path!” Earlier Ehrenfest had written to Hendrik Lorentz (1853-1928), “Bohr’s work on the quantum theory of the Balmer formula, has driven me to despair. If this is the way to reach the goal, I must give up doing physics.” Clearly, Ehrenfest was not a fan of the Bohr model.

One of the least diplomatic critics of Bohr was Johannes Stark (1874-1957). In 1919, Stark received the Noble Prize for two discoveries. One of these discoveries, which bears his name, is that spectral lines will split into more than one line when the atoms that emit them are in an intense electric field. Other physicists were able to use the Bohr-Sommerfeld model of the atom to explain why this splitting occurs. That did not, however, stop Stark from taking an intellectual shot at Bohr.

During Stark’s Nobel Lecture, he stated Planck’s hypothesis “forms the starting point of Bohr’s theory of the emission of serial lines. Although I myself once stood on the threshold of this theory, and although the final formulae give a series of frequency relationships in the spectral series which agree well with observed facts, I am nevertheless unable to believe it, because in its provisions it postulates suppositions which contradict, not only Maxwell’s theory, but the very spirit of physics. This criticism is directed not at Planck’s quantum of action, but at the hypotheses of Bohr which are bound up with it.”

In other words, Planck’s ideas are OK, but Bohr misused them and must be wrong. I have not found any record of Stark’s thoughts when Bohr was the recipient of the Nobel Prize three years later.

Stark’s choices in politics were also not very wise. With Philipp Lenard (1862-1947) he led the Deutsche Physik (German physics, sometimes called Aryan Physics) movement during the Nazi period in Germany.

There were also many critics of Bohr’s model in England, including J.J. Thompson (1856-1940), the discoverer of the electron, and John William Nicholson (1881-1955), who developed his own atomic model.

All of the criticisms were eventually silenced when Bohr’s model was replaced by modern quantum theory. We will get to that in a couple of months. But, first we will look at an explanation for why the electrons do not radiate while moving in an orbit. This hypothesis partially helped give a foundation to one of Bohr’s assumptions and laid more of the groundwork for quantum theory. It even involves a French prince.

(Several of the quotations in this post are reproduced from a series of papers written or co-written by Helge Kragh.)

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.

Previously

What Are Things Made of? Depends on When You Ask.

Ancient Greeks Were the First to Hypothesize Atoms

The Poetry of Atoms

Atom Theory in Ancient India

Religion, Science Clashed over Atoms

Medieval Arabic Scholarship Might Have Preserved Scientific Knowledge

Rediscovering a Roman Poet – and Atom Theory – Centuries Later

Reconciling Atom Theory with Religion

Did Atom Theory Play a Role in Galileo’s Trouble with the Inquisition?

Did Gifted Scientist’s Belief in Atoms Led to His Obscurity?

Does Atom Theory Apply to the Earthly and the Divine?

A Duchess Inspired by Atoms

Separating Atoms from Atheism

Isaac Newton: 300 Years Ahead of His Time

Issac Newton and the Philosopher’s Stone

When Chemistry and Physics Split

Redefining Elements

Mme Lavoisier: Partner in Science, Partner in Life

With Atoms, Proportionality and Simplicity Rule

Despite Evidence of Atoms, 19th Century Skeptics Didn’t Budge

Mission of the First International Scientific Conference: Clear up Confusion

Rivalry over the First Periodic Table

The Puzzle of Dark Lines amid Rainbow Colors

The Colorful Signature of Each Element

Light Waves by the Numbers

Even Scientific Dead Ends Can Contribute to Knowledge

Discovery of the Electron Took Decades and Multiple Scientists

‘Wonders of the X-ray’

The Accidental Discovery of Radioactivity

Marie Curie: A Determined Scientist

Pierre and Marie Curie Extract Radium – and Pay a High Price

Scientists Delve into Radioactivity and Make Their Own Discoveries

The First Attempts to Visualize Atoms

Did Busy Work Lead to Models for Atoms?

Why Does Ice Melt? The Answer Lies in Physics.

Einstein Explains How a Dim Light Can Release More Energy Than a Bright One

How Bohr’s Famous Model of the Atom Was Created

Bohr’s Model of the Atom Answers Fundamental Questions – but Raises More

When a Saint Chooses God over Family

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In the sixth century, Irish Saint Columbanus got an A on the faith test, but I can’t help but feel sorry for his mother.

His calling to serve God meant leaving all women behind – even her. If we are to believe his hagiographer, Columbanus quoted Matthew: “He that loveth father or mother more than me is not worthy of me: and he that loveth son or daughter more than me is not worthy of me” (King James version).

He was proving he loved God more than anything or anyone else, so much that he sacrificed his relationship with his own family. And he confirmed her second worst fear, saying that they would never see each other again in this life. Assuming she was a faithful medieval woman, her worst fear would be for him to wind up in hell and be separated from him forever.

I would like to think Columbanus struggled with his decision, but his fear of sin was strong. See my post on English Historical Fiction Authors for more.

Saint Columbanus

Medieval image of Saint Columbanus (public domain, via Wikimedia Commons)

Sin Is Good for the Bottom Line

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If medieval Christians obeyed the Church on when they could have intimacy, the religion would have died out.

Even husbands and wives could only “meet” on certain days. Forbidden were Sundays, Wednesdays, and Fridays; that time of the month; during pregnancy plus a month or more after the birth; 40 days before Christmas; 40 days before and eight days after Easter; eight days after Pentecost; the eves of great feasts; and five days before Communion (maybe that’s why it was only once a year for most people).

One layman probably spoke for many when he said God gave men and women those parts below the waist so that married couples could have relations and so what if the motive was pleasure.

I’m not sure how the Church came up with its list of “no sex allowed” days. If I were a cynical person, I would say it would be a good way to drum up revenue.

If you sinned, you had to confess, then do penance, usually prayer, fasting, abstaining from meat and wine, or some combination. Or you could give alms in the form of money or land.

So while the Church could abhor relations outside matrimony and married couples meeting with each other on the wrong days, it could also make a tidy sum from the sinners.

This is why the current draft of Queen of the Darkest Hour has an uncle deciding to introduce his nephew to his favorite harlot and distract him from the queen’s maid: “Yes, it is different. You’re using a whore instead of ruining a virgin, and that’s better than making an enemy of the queen. Besides, the Church would have little funds if men did not swive whores and repent. I’ll give you some coins for penance afterward.”

Source

Daily Life in the World of Charlemagne by Pierre Riché

The Seven Deadly Sins and the Four Last Things - Lust

The Seven Deadly Sins and the Four Last Things – Lust by Hieronymus Bosch, 1485, oil on panel (public domain via Wikimedia Commons)

Lessons Learned from Rereading Grimm’s Folk Tales

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The folk tales collected by the brothers Grimm deal with the most powerful motives of all of us: love, envy, revenge, greed, hunger. All in a few pages. Perhaps that is why they continue to fascinate me long into adulthood.

For the past few weeks, I’ve been reading a recent translation of the stories. For research. Really. My characters would have told stories like these to entertain each other and teach their kids moral truths.

Forget the Disney versions. The punishments for the villains are brutal, and sometimes the villain is moronic enough to pronounce their own sentence, thinking the description of their actions is hypothetical. And there are a few real downers where everyone dies.

The tales have their share of humor, often at the expense of the not-so-bright. The guy or gal who’s nicknamed “Clever” often isn’t. Or they are devious.

Sometimes the damsel in distress is rescued by the prince, but many times the heroine is saving the hero. And she is a heck of a lot more loyal, even when her beloved has forgotten her (usually because he’s been bewitched). As adult, I often find myself on the side of the bride who wants to end a marriage she’s been forced into, even though there’s only one way to do that.

Despite the magic and supernatural, I feel like I know these people sometimes. The guy who chronically complains, even about the way things are done in heaven. The wife who paces around the mill pond where her husband disappeared, sometimes calling his name, sometimes sobbing softly. The hero or heroine who brave all for love.

And those moral lessons hold true today:

  • Your wits are a powerful weapon.
  • Stupidity and greed will make you suffer and might kill you.
  • Treachery and rudeness will come back to bite you.
  • Your kind heart, hard work, fidelity, and courage will always triumph, no matter what other people say.
Illustration for

Illustration for “Snow White and Rose Red,” by Hermann Vogel (public domain image via Wikimedia Commons)

Bohr’s Model of the Atom Answers Fundamental Questions – but Raises More

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In this installment on the history of atom theory, physics professor (and my dad) Dean Zollman explains the science behind Bohr’s Model of the Atom. As so often happens in science, Bohr’s work contributed to our knowledge of matter in its tiniest parts, but more questions arose. – Kim

By Dean Zollman

Dean ZollmanLast time, I discussed the historical perspective on the development of the Bohr Model of the Atom. This discovery is critical to the development of the modern quantum view of matter. So, this time I deviate some from the historical approach and discuss the physics of Niels Bohr’s model. Understanding the ideas that go into the model is not complex. Bohr’s genius was putting all of the parts together and adding one critical assumption.

Bohr had a large foundation on which to build. He knew:

  • Newton’s basic laws of motion.
  • Light is a form of energy, so when an atom emits light, it must decrease its own energy.
  • Planck and Einstein had showed that light came in energy packets (photons). The value of the energy is a constant, called Planck’s constant, time the frequency of the light.
  • Rutherford had discovered the atom is composed of a positive charge (nucleus) at the center and negative charges (electrons) around the positive charge.
  • Positive and negative charges attract each other and energy can be stored in the electrical attraction.
  • Each atom emits a spectrum of light, and that spectrum is unique to each element.
  • Balmer had been able to describe the spectrum of hydrogen with a not-too-complex equation. (As I mentioned last time, Bohr learned or rediscovered this fact somewhat late in his research on an atomic model.)

To these concepts, Bohr added:

  • The electron can occupy only certain orbits around the nucleus.
  • While in these orbits, the electrons does not emit or absorb light.
  • Light is emitted or absorbed when electrons changes orbits.

These ideas built on those of others, but Bohr applied them in a unique way.

Why Don’t Things Fall Apart?

Limiting the electrons to certain orbits was the critical step. Bohr knew that an electrical charge moving in a circle should radiate light continuously. Such a process would result in all colors of light being emitted, and the electron crashing into the nucleus in a very short time. He needed a reason for the atom to be stable.

To create that situation, he assumed that the electron could have only certain values for its angular momentum. The angular momentum for an object traveling in a circle is its mass times speed times radius of the circle. Bohr’s assumed that this quantity had to be an integer number times Planck’s constant divided by 2 pi. While moving in these allowed orbits, electrons do not emit any electromagnetic energy.

When moving from one orbit to another, however, the electrons absorb or release energy. If the electron moves to an orbit farther from the nucleus, it absorbs an amount of energy equal to the energy of a photon in one of the absorption lines. This energy is also the difference in the energy of the electron in the orbits. When the electron jumps to an orbit closer to the nucleus, it releases an amount of energy equal to the energy of a photon in one of the emission lines. Allowed orbits restrict the possible jumps to just a few. Consequently, the light spectrum emitted by atoms would be discrete. Since Bohr’s model uses the same orbits to explain both emission and absorption of energy, it predicts emission and absorption lines that have identical energies.

In proposing that electrons move only in allowed orbits, Bohr was suggesting that the energy of the electron can be measured, or quantized. In any given orbit, an electron has a certain amount of kinetic energy associated with its motion and electrical potential energy associated with the electrical force of attraction exerted by the nucleus. If electrons move only in allowed orbits, their energy takes on selected, or discrete, values. Bohr saw the same quantization of energy in the atom that Planck saw in the radiation emitted by solids and Einstein saw in the photoelectric effect. At the atomic level, energy appears in discrete amounts.

Measuring How Light Is Absorbed or Emitted

To make these ideas quantitative, Bohr combined this idea with the equations for energy of an orbiting electrical charge and Newton’s Laws. After some algebra, he had an equation for the values of the possible energies that an electron orbiting a hydrogen nucleus could have. The light was emitted or absorbed when the electron moved from one orbit to another. So the energy of the photon was equal to the difference between those energies. To obtain the frequencies of light emitted or absorbed by hydrogen atoms, Bohr applied the Planck-Einstein energy of a photon.

Bohr atom

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

The energies associated with each allowed orbit provide a useful way of describing what happens as atoms absorb or emit light. The energy-level diagram below provides a convenient way to describe the energy emitted or absorbed by a hydrogen atom. The lowest red line is called the n = 1 energy and corresponds to the energy of an electron when it is moving in the smallest orbit, the orbit closest to the nucleus. This is often referred to as the ground state of the electron because it represents the smallest energy the electron can have. The n = 2 line corresponds to the energy the electron has in the next orbit, n = 3 in the third orbit, and so on. Collectively, the energy levels above ground state are called excited states. The energy of the electron increases as we move to higher excited states.

Energy level diagram 1

An energy level diagram for the emission of ultraviolent and visible light from hydrogen. (Created with a program from the Visual Quantum Mechanics project, Dean Zollman, principal investigator)

The distance between states is proportional to the energy difference between states. So, for example, the energy difference between n = 3 and n = 2 is smaller than that between n = 2 and n = 1. The blue arrows in the energy level diagram indicate that the electron has changed energy from an excited state to a lower energy state. At the top of the diagram is the spectrum of hydrogen. The lines indicate the colors that would be emitted by these changes. All of the photons emitted by changes to the n = 1 energy are in the ultraviolet and are drawn in gray on the right side of the spectrum. The transitions to the n = 2 energy are visible and shown by their approximate colors. These are the spectral lines that Balmer saw.

A schematic using the Bohr Model

A schematic using the Bohr Model of transitions for orbiting electrons.  (From Nusha, GFDL or CC-BY-SA-3.0, via Wikimedia Commons)

In a sample of hydrogen gas at room temperature, each atom is most likely to have its electron in its ground state. An external source – heat, light, or electricity – can provide energy to these electrons. When we pass white light through a sample of hydrogen gas for example, electrons “select” photons of energy needed to move into excited states.

As shown in the diagram below electrons might move from n = 1 to n = 2, from n = 1 to n = 3, from n = 2 to n = 3, and so forth. Because the energy levels are the same as for emission, the only change in the diagram is the direction of the arrows. The electrons are moving from lower energy to higher energy. The photons with energies equivalent to each of these jumps are absorbed while the others are ignored. Consequently, the light that emerges is the full spectrum minus the photons with frequencies used to move electrons into excited states. We see a discrete absorption spectrum.

Energy level diagram

An energy level diagram for the absorption of ultraviolent and visible light by hydrogen. (Created with a program from the Visual Quantum Mechanics Project, Dean Zollman, principal investigator)

Limitations to Bohr’s Model

One of the successes of Bohr’s model is that he could calculate the energies of all of the levels in the hydrogen atom. The n = 1 (ground state) energy is -13.6 electron volts. (The minus sign is a notation to indicate that the electron is being attracted to the nucleus.) The next one, n = 2, is -3.4 electron volts. In general the energy of the nth level is -13.6 eV/n2. (An electron volt (eV) is a very small unit of energy used in atomic physics.) Bohr was able to obtain these numbers by doing some algebra and getting a result that depends only on constants such as the electrical charges on the electron and proton and Planck’s constant. Likewise, he could determine the radius of the hydrogen atom. He did not need Balmer’s data from observations. So, he had a model that seemed quite complete.

In addition to explaining the discrete spectra found for chemical elements, Bohr’s model also resolves the problem of why atoms do not collapse. The electron can lose only specific amounts of energy equivalent to the jumps in the energy-level diagram. When it reaches lowest energy, the electron can neither lose more energy nor move closer to the nucleus. The stability of the atom is assured. Bohr’s model of the atom moved several pieces of the atomic puzzle into place. It did, however, leave some questions unanswered.

While the concept of allowed orbits explains both the stability of the atom and discrete emission and absorption spectra, it is not based on any known principles of physics. There seems to be no reason for electrons to jump instantaneously from one energy state to another, shunning all energies in between.

Furthermore, additional observations revealed limitations to the model. While it was enormously accurate in describing the hydrogen spectrum, Bohr’s model was far less successful in describing the spectra produced by more complex atoms. Moreover, the intensity of individual spectral lines varied. Some lines were brighter than others – an observation for which Bohr’s model offered no explanation. The resolution to these problems lay in yet another model of the atom – the quantum mechanical model. We will move toward learning about it next time.

1927 Solvay Conference

In 1927, the world’s top physicists met at a Solvay Conference to discuss issues related to quantum physics and the atom. Niels Bohr is on the far right in the second row. Physics was very much a European man’s occupation in those days. The only woman participant was Marie Skłodowska Curie, third from the left on the front row. An American, Arthur Compton, is the third person to the left of Bohr. (Public domain via Wikipedia Commons. For an annotated, interactive version go to Wikimedia Commons.)

Much of the material in this post was adapted from Fascination of Physics by Spears and Zollman. It is used by permission.

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.

Previously

What Are Things Made of? Depends on When You Ask.

Ancient Greeks Were the First to Hypothesize Atoms

The Poetry of Atoms

Atom Theory in Ancient India

Religion, Science Clashed over Atoms

Medieval Arabic Scholarship Might Have Preserved Scientific Knowledge

Rediscovering a Roman Poet – and Atom Theory – Centuries Later

Reconciling Atom Theory with Religion

Did Atom Theory Play a Role in Galileo’s Trouble with the Inquisition?

Did Gifted Scientist’s Belief in Atoms Led to His Obscurity?

Does Atom Theory Apply to the Earthly and the Divine?

A Duchess Inspired by Atoms

Separating Atoms from Atheism

Isaac Newton: 300 Years Ahead of His Time

Issac Newton and the Philosopher’s Stone

When Chemistry and Physics Split

Redefining Elements

Mme Lavoisier: Partner in Science, Partner in Life

With Atoms, Proportionality and Simplicity Rule

Despite Evidence of Atoms, 19th Century Skeptics Didn’t Budge

Mission of the First International Scientific Conference: Clear up Confusion

Rivalry over the First Periodic Table

The Puzzle of Dark Lines amid Rainbow Colors

The Colorful Signature of Each Element

Light Waves by the Numbers

Even Scientific Dead Ends Can Contribute to Knowledge

Discovery of the Electron Took Decades and Multiple Scientists

‘Wonders of the X-ray’

The Accidental Discovery of Radioactivity

Marie Curie: A Determined Scientist

Pierre and Marie Curie Extract Radium – and Pay a High Price

Scientists Delve into Radioactivity and Make Their Own Discoveries

The First Attempts to Visualize Atoms

Did Busy Work Lead to Models for Atoms?

Why Does Ice Melt? The Answer Lies in Physics.

Einstein Explains How a Dim Light Can Release More Energy Than a Bright One

How Bohr’s Famous Model of the Atom Was Created

A New Home with an Unburied Saint Joseph Statue

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I meant to write this post almost a week ago, and I have Saint Joseph to thank for my tardiness.

Before my husband and I moved, I wrote a post for English Historical Fiction Authors about the various origin stories for burying a Saint Joseph statue to sell property. Then we resumed packing.

The post for EHFA ran on time. The post I was planning for Outtakes didn’t get written. We were at that stage in the packing where we were lucky if we labeled the boxes with the rooms they should go to. No time for the sorting what to keep or trash and write detailed lists as we did at the start of the process.

So we are now in our new home busily unpacking boxes and Saint Joseph’s statue is watching over this chaos from the mantle. Did he sell our house? I don’t know, but both times I’ve buried him, the property sold just in time to avoid our paying two mortgages.

St. Joseph statuette

Help Wanted: Where Was Cumeoberg?

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Cumeoberg was an Avarian fortress, or an old name for a mountain, or a mountain-top fortress, and the site of a nonbattle in Charlemagne’s 791 war against the Avars. And it is a setting for a scene in my work still in progress, Queen of the Darkest Hour.

The problem: I have multiple options for where it might have been. I know it was somewhere near the Austrian city now named Tulln, called Comagena in Roman times, and in today’s Wienerwald, a huge forested area near Vienna.

So, was in on a rise just south of Tulln? Was it on a mountain near today’s Königstetten? Or does it overlook today’s Klosterneuburg?

I’ve flipped though books without arriving at any certain answer. The reason for all this labor is that even after nine years away from my days at a daily newspaper, I still live in dread of The Call.

If the caller was polite, they would start with, “Thank you for the nice article.” And on the other end, I would be waiting for the But, as in “but you spelled my name wrong.” Callers who were less than polite would start with, “Don’t you people have proofreaders?”

Odd to think that in fiction—where we confess from the get-go that we’re making things up—that we novelists want to be accurate. But that’s why we often get caught in research rabbit holes, even for one scene.

For now, my best guess is that Cumeoberg was on a mountain near Königstetten, but dear reader, if you’ve heard otherwise, let me know in the comments or by email at kim [at] kimrendfeld [dot] com.

Sources (somewhat contradictory)

Charlemagne: Translated Sources, P.D. King

A History of Charles the Great (Charlemagne) by Jacob Isidor Mombert

The History of France: From the earliest period to the present time by Thomas Wright

Charlemagne and the Avars

Albrecht Altdorfer’s 1518 The Victory of Charlemagne over the Avars near Regensburg (public domain via Wikimedia Commons)

How Bohr’s Famous Model of the Atom Was Created

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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.

Previously

What Are Things Made of? Depends on When You Ask.

Ancient Greeks Were the First to Hypothesize Atoms

The Poetry of Atoms

Atom Theory in Ancient India

Religion, Science Clashed over Atoms

Medieval Arabic Scholarship Might Have Preserved Scientific Knowledge

Rediscovering a Roman Poet – and Atom Theory – Centuries Later

Reconciling Atom Theory with Religion

Did Atom Theory Play a Role in Galileo’s Trouble with the Inquisition?

Did Gifted Scientist’s Belief in Atoms Led to His Obscurity?

Does Atom Theory Apply to the Earthly and the Divine?

A Duchess Inspired by Atoms

Separating Atoms from Atheism

Isaac Newton: 300 Years Ahead of His Time

Issac Newton and the Philosopher’s Stone

When Chemistry and Physics Split

Redefining Elements

Mme Lavoisier: Partner in Science, Partner in Life

With Atoms, Proportionality and Simplicity Rule

Despite Evidence of Atoms, 19th Century Skeptics Didn’t Budge

Mission of the First International Scientific Conference: Clear up Confusion

Rivalry over the First Periodic Table

The Puzzle of Dark Lines amid Rainbow Colors

The Colorful Signature of Each Element

Light Waves by the Numbers

Even Scientific Dead Ends Can Contribute to Knowledge

Discovery of the Electron Took Decades and Multiple Scientists

‘Wonders of the X-ray’

The Accidental Discovery of Radioactivity

Marie Curie: A Determined Scientist

Pierre and Marie Curie Extract Radium – and Pay a High Price

Scientists Delve into Radioactivity and Make Their Own Discoveries

The First Attempts to Visualize Atoms

Did Busy Work Lead to Models for Atoms?

Why Does Ice Melt? The Answer Lies in Physics.

Einstein Explains How a Dim Light Can Release More Energy Than a Bright One

When a Tale about Fashion Becomes Subversive

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When I read Notker the Stammerer’s biography of Charlemagne, composed about 70 years after the emperor’s death, I get the feeling that he didn’t let facts get in the way of his story.

Notker the Stammerer

A 10th century illustration of Notker (public domain, via Wikimedia Commons)

I suspect he fabricated the tale about Charlemagne and his noblemen going on hunt in the clothes they were all wearing right at the moment. Charlemagne had a sheepskin cloak, while the others were adorned in silks and other fragile finery to trek through thorns and rain.

The tale is moralistic about vanity—and subversive. Lay noblemen were expected to flaunt their wealth and chose clothes with pricey materials. The more reliable Einhard has Charlemagne favoring a tunic fringed with silk and a vest of expensive otter and marten furs. The king’s swords had silver and gold hilts. For special occasions, he had embroidered garments, jeweled shoes, a golden buckle for his cloak, and a diadem.

To have a king to wear a sheepskin cloak, something a commoner would have, is a tad rebellious. But Notker does have a point: there are times when the humble item is of great value. See my post on English Historical Fiction Authors about the durability and practicality of this piece of medieval fashion.

Sources

The Monk of Saint Gall: The Life of Charlemagne

Einhard: The Life of Charlemagne

The Kindness of a Parisian Stranger

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Before my first trip out of the States in 1987, I was warned that the Parisians would be rude. I heard things like “Once you get out of Paris, the French are friendly.” And my first glimpses of the city made me think, “Oh, this is like New York, but they speak French.” For a Jersey girl, that’s no big whoop.

My arrival into France was less than ideal. The airline had lost my luggage and my ears felt like they were stuffed with cotton. On top of that, I had jet lag. Then I noticed a tear in my skirt.

So I must have been a pathetic sight in that little store where I was looking for needle and thread.

I found what I needed, approached the woman at the counter, and said in French what I thought was “I would like to buy these.” The shopkeeper, old enough to be my mother, gave me a puzzled look. I repeated it.

After a moment, a look of understanding dawned on her, and she said the word I had meant to say. At that moment, this teenage American realized that I had said I wanted to sell her something already in her shop.

I felt like an idiot, but this Parisian was very kind. When I removed the wad of money from my pouchette, she maternally explained francs, and that this purchase would cost only a few of them.

This was not at all the rudeness I was expecting. Perhaps, it was that I was 19, female, and harmless looking. Perhaps, it was at least an attempt – clumsy but sincere – to speak the language. Or perhaps it is that there are kind people everywhere.

So as I hear the news from Paris, my heart breaks for this magnificent city and the people who live in it.

Eiffel Tower

By Tristan Nitot (standblog.org) (GFDL, CC-BY-SA-3.0 or CC BY-SA 2.5, via Wikimedia Commons)

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