Guest author, Thomas Kennedy, features a twice-monthly series, Quantum Leap, wherein he guides readers through the fascinating world of quantum mechanics. This is issue 012.
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*This issue is continued from Issue 011, “Orbits“
Bohr and a German physicist, Arnold Sommerfeld, expanded the original Bohr model to explain these variations. According to the Bohr-Sommerfeld model, not only do electrons travel in certain orbits, but the orbits have different shapes and the orbits could tilt in the presence of a magnetic field. Orbits can appear circular or elliptical, and they can even swing back and forth through the nucleus in a straight line.
The orbit shapes and various angles to the magnetic field could only have certain shapes, similar to an electron in a certain orbit. As an example, the fourth orbit in a hydrogen atom can have only three possible shapes and seven possible traits. These added states allowed more possibilities for different spectral lines to appear. This brought the model of the atom into closer agreement with experimental data.
The conditions of the state of the orbit got assigned quantum numbers. The three states discussed so far consist of: orbit number (n), orbit shape (l) and orbit tilt (m).
In 1924 an Austrian physicist, Wolfgang Pauli predicted that an electron should spin (kind of like a top) while it orbits around the nucleus. The electron can spin in either of two direction. This spin consisted of a fourth quantum number: electron spin (s).
Pauli gave a rule governing the behavior of electrons within the atom that agreed with experiment. If an electron has a certain set of quantum numbers, then no other electron in that atom can have the same set of quantum numbers. Physicists call this “Pauli’s exclusion principle.” It provides an important principle to this day and has even outlived the Bohr-Sommerfeld model for which Pauli designed it.
In 1924, a Frenchman named Louis de Broglie thought about particles of matter. He thought that, if light can exist as both particles and waves, why couldn’t atom particles also behave like waves? In a few equations derived from Einstein’s famous equation (E=mc2), Broglie showed how matter waves would behave, if they existed at all. (Experiments later proved him correct.)
In 1926, the Austrian physicist, Erwin Schrödinger, had an interesting idea: Why not go all the way with particle waves and try to form a model of the atom on that basis? His theory worked similar to harmonic theory for a violin string, except that the vibrations traveled in circles.
The world of the atom, indeed, began to appear very strange. It proved difficult to form an accurate picture of an atom, because nothing in our world really compares with it.
Schrödinger’s wave mechanics did not question the makeup of the waves, but he had to call it something. He gave it a symbol – the Greek letter, “psi”.
In 1926, the German physicist, Max Born, had an idea about Schrödinger’s ‘psi’. Born thought that they resembled waves of chance. These ripples moved along waves of chance, made up of places where particles may occur and places where no particles occurred. The waves of chance ripple around in circles when the particle appears like an electron in an atomic orbit; they ripple back and forth when the electron orbit goes straight through the nucleus; and they ripple along in straight lines when a free particle moves through interatomic space. You can think of them as waves when traveling through space and as particles whenever they travel in circles. However, they cannot exist as both waves and particles at the same time.
Just before Schrödinger proposed his theory, a German physicist, Werner Heisenberg, in 1925, had a theory of his own called matrix mechanics, which also explained the behavior of atoms. The two theories seemed to have entirely different sets of assumptions, yet they both worked. Heisenberg based his theory on mathematical quantities called “matrices” that fit with the conception of electrons as particles, whereas Schrödinger based his theory on waves. Actually, the results of both theories appeared, mathematically, the same.
In 1927, Heisenberg formulated an idea, which agreed with tests, that no experiment can simultaneously measure the position and momentum of a quantum particle. Scientists call this the “Heisenberg uncertainty principle.” This implies that, as one measures the certainty of the position of a particle, the uncertainty in the momentum gets correspondingly larger. Or, with an accurate momentum measurement, the knowledge about the particle’s position gets correspondingly less.
The visual concept of the atom now appeared as an electron “cloud” which surrounds a nucleus. The cloud consists of a probability distribution map, which determines the most probable location of an electron. For example, if one could take a snap-shot of the location of the electron at different times, and then superimpose all of the shots into one photo, then it might look something like the image at right.*
*Thanks to the work of Jim Walker for his contribution to this series.
Next Issue: “Chemistry”
Watch for Issue #13 of Thomas’ “Quantum Leap”, on April 30, 2010.
You can access all previous issues of “Quantum Leap”, here.
thanks T, the calculus relation makes it a little comprehensible. will catch the next issue.
[...] Guest author, Thomas Kennedy, features a twice-monthly series, Quantum Leap, wherein he guides readers through the fascinating world of quantum mechanics. This is issue 013. ====================================================== *This issue is continued from Issue 012, “Uncertainty“ [...]
Possibly. I don’t know how I could easily get hold of a copy to check. Nevertheless, the main point is that he had a complete formulation of non-relativistic QM without spin before anyone else, and that still stands.