Monday, April 22, 2013

History of Science -- Part Eleven: The Atom

Niels Bohr grew up in a comfortable and respected family that nurtured independent thought. His father, a professor of psychology at Copenhagen University, was interested in philosophy and science and encouraged those interests in his two sons. Niel’s brother, Harald, eventually became an outstanding mathematician. Niels Bohr’s early years were supportive. Unlike Einstein, he was never the rebel.

In college in Denmark, Bohr won a medal for some clever experiments with fluids. But I’ll skip ahead to 1912 when, with his new Ph.D., Bohr went to England as a “postdoc,” a postdoctoral student.

By this time the atomic nature of matter was generally accepted, but the atom’s internal structure was unknown — actually, it was in dispute. Electrons, negatively charged particles thousands of time lighter than the atom, had been discovered a decade earlier by J.J. Thompson. An atom, being electrically neutral, must somewhere have a positive charge equal to that of its negative electrons, and that positive charge presumably had most of the mass of the atom. How are the atom’s electrons and its positive charge distributed?

Thompson had made the simplest assumption, that the massive positive charge uniformly filled the atomic volume and the electrons — one in hydrogen and almost 100 in the heaviest known atoms — were distributed throughout the positive background like raisins in a rice pudding. (I personally call that the chocolate chip cookie theory, since I prefer cookies to pudding.) Theorists tried to calculate how various distributions of electrons might give each element its characteristic properties.

There was a competing model for the atom. Ernest Rutherford at the University of Manchester in England explored the atom by shooting alpha particles (helium atoms stripped of their electrons) through a gold foil. He saw something inconsistent with Thompson’s uniformly distributed positive mass. About one alpha in 10,000 would bounce off at a large angle, sometimes backwards. The rest of the particles seemed to pass through the thin gold without any deflection. The experiment was likened to shooting prunes through rice pudding — collisions with raisins could not knock a fast prune much off track. Rutherford concluded that his alpha particles were colliding with an atom’s positive charge, and that almost all the atom’s mass was concentrated in a small lump, a “nucleus.”

Why, then, didn’t the negative electrons, attracted by the positive nucleus, not just fall into it? For the same reason that the planets don’t crash down into the son. They orbit the sun. Rutherford decided that electrons orbited a small, massive, positive nucleus.

There was a problem with Rutherford’s planetary model: instability. Since an electron is charged, it should radiate as it races around its orbit. Maxwell’s equations had shown that a charge in motion would radiate electromagnetic waves. Calculations showed that an electron should give off its energy as light and spiral down to crash into the nucleus in less than a millionth of a second.

Most of the physics community considered the instability of the planetary model a more serious problem than the rice pudding model’s inability to explain the rare large-angle deflections of Rutherford’s alpha particles. But Rutherford, a supremely confident fellow, knew his planetary model was basically right. Experiments trump philosophy!

When the young postdoc Bohr arrived in Manchester, Rutherford assigned him the job of explaining how the planetary atom might be stable. Bohr’s tenure in Manchester lasted only six months, supposedly because his support money ran out. But eagerness to get back to Denmark to marry the beautiful Margrethe likely shortened his stay. (After all, scientists are human just like the rest of us.) While teaching at the University of Copenhagen in 1913, Bohr continued to work on the stability problem.

How he got his successful idea is not clear. But while other physicists were trying to understand how the quantum of energy and Planck’s constant, ℎ, arose from the classical laws of physics, Bohr took an “ℎ is okay!” attitude. He just accepted quantization as fundamental. After all, it worked for Planck, and it worked for Einstein.

Bohr wrote a very simple formula that stated that “angular momentum,” the rotational motion of an object, could exist only in quantum units. If so, only certain electron orbits were allowed. And, most important, he wrote his formula so that there was a smallest possible orbit. By fiat, Bohr’s formula “forbids” an electron to crash into the nucleus. If his ad hoc formula was correct, the planetary atom was stable.

Without more evidence, Bohr’s quantum idea would be rejected out of hand. But from his formula, Bohr could readily calculate all the energies allowed for a single electron orbiting a nucleus, that is, for the hydrogen atom. From those energies he could then calculate the particular frequencies of light that could be emitted from hydrogen atoms electrically excited in a “discharge,” something like a neon sign only with hydrogen instead of neon.

Those frequencies had been carefully studied for years, though Bohr was initially unaware of that work. Why only certain frequencies were emitted was a complete mystery. The spectrum of frequencies, unique to each element, presented a pretty set of colors. But were they any more significant than the particular patterns of a butterfly’s wings? Now, however, Bohr’s quantum rule predicted the frequencies for hydrogen with stunning accuracy — precise to parts in 10,000. But at this time, while Bohr had light quanta emitted by atoms, he, along with essentially all other physicists, still rejected Einstein’s compact photon.

Some physicists nevertheless dismissed Bohr’s theory as “number juggling.” Einstein, however, called it “one of the greatest discoveries.” And others soon came to agree. No one understood why it worked. But work it did. And for Bohr that was the important thing. Bohr’s pragmatic “ℎ is okay!” attitude toward the quantum brought him quick success.

(Bohr's equations contained the value of ℎ divided by 2π. That is because of the relationship of angular momentum and a circle. There are 2π radians in the circumference of a circle and the electrons orbited in circles. This relationship of ℎ / 2π appears so much in modern formulas, that a special symbol for the value of ℎ / 2π was created called h-bar: "."
ℏ = ℎ / 2π)

Contrast Bohr’s early triumph with his quantum ideas with Einstein’s long remaining “a man apart” in his belief in the almost universally rejected photon. I often wonder how the early experiences of these two men are reflected in their lifelong friendly debate about quantum mechanics.

(That story, however, is several chapters into the future History of Science. For the next episode we will learn of a possible explanation of Bohr’s formula and restrictions on electron orbits.)

Please forgive a little anti-climatic addition to an essay that is really complete, but I must say more about Niels Bohr:

Much later he conceived the principle of complementarity: that items could be separately analyzed as having contradictory properties, like behaving as a wave or a stream of particles. The notion of complementarity dominated his thinking on both science and philosophy. This principle attempts to explain the duality that everyone found so difficult to accept with Einstein’s proposal that light could act like particles.*

This is a history, so I should also add that, during the 1930s, Bohr gave refugees from Nazism temporary jobs at the Institute of Theoretical Physics at the University of Copenhagen, now known as the Niels Bohr Institute, which he founded. He provided them with financial support, arranged for them to be awarded fellowships from the Rockefeller Foundation, and ultimately found them places at various institutions around the world. After Denmark was occupied by the Germans, he had a dramatic meeting in Copenhagen with Heisenberg, who had become the head of the German nuclear energy project.

In 1943, fearing arrest, Bohr fled to Sweden, where he persuaded King Gustav V of Sweden to make public Sweden's willingness to provide asylum. He was then flown to Britain, where he joined the British Tube Alloys nuclear weapons project, and was part of the British team of physicists who worked on the Manhattan Project.

After the war, Bohr called for international cooperation on nuclear energy. He was involved with the establishment of CERN, and became the first chairman of the Nordic Institute for Theoretical Physics in 1957. He was also involved with the founding of the Risø DTU National Laboratory for Sustainable Energy.

He died in 1962 at 77 years of age.

*In physics, complementarity is a fundamental principle of quantum mechanics, closely associated with the Copenhagen interpretation which will be discussed in following chapters. It holds that objects governed by quantum mechanics, when measured, give results that depend inherently upon the type of measuring device used, and must necessarily be described in classical mechanical terms. Further, a full description of a particular type of phenomenon can only be achieved through measurements made in each of the various possible bases — which are thus complementary.

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