137 - Arthur I. Miller [22]
(b)
(b) This figure shows the Balmer series.
Since the late nineteenth century scientists had been aware that when light illuminated a collection of atoms, they emitted light in response. When the light the atoms emitted was passed through an instrument that separated its frequencies—a spectroscope—lines appeared. Dubbed spectral lines, these lines were unequally spaced and bunched up more and more as their frequency increased. Most strikingly the series of lines were different for each sort of atom. In fact, an atom’s spectral lines were its fingerprint, its DNA. Scientists had made a stab at writing equations to describe these lines, but there was no theory of the atom to explain the equations. Bohr’s was the first to succeed.
According to Bohr’s theory atoms emitted light when an electron moved from an upper to a lower orbit. The light that was emitted by an electron had the same frequency as a spectral line that had been observed. An oddity of the theory was that the electron’s transition from one orbit to another could not be visualized—it disappeared and appeared again like the Cheshire cat’s smile. In this sense the electron’s quantum jumps were discontinuous.
Bohr’s was a magnificent theory and it worked more than adequately. When applied to the hydrogen atom, the difference between the spectral lines observed in the laboratory and the spectral lines deduced from his theory was only 1 percent.
Scientists were impressed not only by its accuracy but also by its iconic visual imagery: the atom as a miniscule solar system with the electrons revolving in circular orbits around a central “sun,” or nucleus. It was a momentous fusion of large and small, of the universe and the atom, the macro-and microcosmos.
Bohr’s theory depicted the simplest element, hydrogen, as a single electron orbiting a positive charge—its nucleus. The atom had no total electrical charge; it was electrically neutral, just as atoms are in nature. Helium, the next element in the periodic table of the chemical elements, differs from hydrogen in that it has two electrons that orbit around a nucleus that has two units of positive electric charge. Because helium does not react chemically—it cannot bond with any other element—Bohr deduced that the innermost orbit needed to be filled up with two electrons. He went on to infer that the next orbit can take on eight electrons.
Atoms depicted according to Bohr’s atomic theory. (Kramers and Holst [1923]).
As another of the pioneers of atomic physics, Max Born, head of the Institute for Atomic Physics at the University of Göttingen, put it:
A remarkable and alluring result of Bohr’s atomic theory is the demonstration that the atom is a small planetary system…. The thought that the laws of the macrocosmos in the small reflect the terrestrial world obviously exercises a great magic on mankind’s mind; indeed its form is rooted in the superstition (which is as old as the history of thought) that the destiny of men could be read from the stars. The astrological mysticism has disappeared from science, but what remains is the endeavor toward the knowledge of the unity of the laws of the world.
Pauli’s work on Bohr’s theory
No one had attempted to apply the Bohr theory to anything more complex than the hydrogen atom. Pauli set out to do so.
He began the year after he arrived in Munich and decided to apply Bohr’s theory to the next simplest atomic system to the hydrogen atom, that is, two protons orbited by a single electron—the hydrogen-molecule ion, H+2. The mathematics he had to grapple with was extremely complex. The problem gnawed at him. It took over his life. He ended up thinking about it night and day.
The