Theories of the Universe
Chunks of Uncertainty
Angular momentum can be thought of as momentum moving in a circle. It's what keeps a ball moving on the end of a rope as you spin it over your head. In classical physics it is defined by the mass and the speed at which it is spinning. In quantum mechanics, the angular momentum, like everything else, is quantized.
All quantum physicists will agree that they can't explain quantum theory and that it doesn't make sense. So why would they use something to define the fundamental structure of the universe if they don't understand what it is? Well, physicists who work in the field use the straightforward formulas handed down to them by the brilliant minds that developed them, but often don't understand why they work or even what they mean. But what is known about it has produced remarkably accurate results. And that's why it's used. Some even feel that quantum mechanics offers some of the most accurate numerical predictions that science has ever developed. And until something else comes along, the mathematical system used to define the quantum world is all that is available. For now, let's pick up where we left off in the last section and follow the unfolding of quantum cosmology.
Waves of Matter
One of the reasons de Broglie wanted to develop a mechanical model was to show that the theories developed so far could be verified by experimental means. Up until then, the Rutherford-Bohr atomic model was just theory; no one really knew whether the atoms looked like that. If he could show that his predictions could be confirmed by experiment, it would solidify the new ground on which quantum theory was developing.
Neils Bohr came up with a description of how light was radiated from inside an atom. He also has shown why an atom was stable. His explanation of what the structure of the atom was like was close to but not quite like the one envisioned by Rutherford that we touched upon earlier. Remember that he theorized that the atom's structure was very much like a planetary system with the electrons orbiting the nucleus the way planets orbit the Sun. Bohr adopted this basic configuration, but couldn't imagine the electrons orbiting the nucleus as some cosmic cloud that was indefinable. So he had arranged the orbiting electrons into layers or shells. Have you seen Russian nesting dolls or Chinese stacking boxes? In those you have one complete doll or box contained within another. Every time you open up one there's a smaller one inside. The shells Bohr described were just like that, except that each shell had a specific number of electrons.
Bohr was able to calculate mathematically the diameter of each electron orbit along with the maximum number of electrons in each shell. The angular momentum of the electron in orbit was counteracted by the attraction of the nucleus. In other words, since unlike electrical charges attract each other, the positive charge inside the nucleus attracted the negative charge of the electron. This theory explained the structure of the atom and why it remained stable.
A French Prince Discovers Matter Waves
When you create a standing wave with a jump rope, each point on the rope where there is no movement, a resting place, is called a node. It's the point at the end of each wave and also the point between the waves that are moving up and down. For example, there are two nodes on the lowest frequency standing wave (a half wave), the two endpoints of the rope. The next higher frequency, (a whole wave) has three nodes, the ones on each end and a third in the middle, which is the point that separates the crest from the trough. The next higher frequency (1 1/2 waves) has four nodes, the two end points and two in the middle and so on. Get the idea? As the number of nodes on the rope increases, the frequency of the standing wave increases. If this were a vibrating violin string, the pitch would also increase.
In 1923, a graduate student at the Sorbonne in Paris, Prince Louis de Broglie (1892-1987), introduced the remarkable idea that particles may exhibit wave properties. He had been strongly influenced by Einstein's arguments that light had a dual nature. He was also deeply impressed by Einstein's particles of light that could cause the photoelectric effect (knock electrons out of metal) while also producing the interference patterns caused by waves as in the double slit experiment. He proposed one of the great unifying principles in quantum physics. He was convinced that the wave/particle duality discovered by Einstein in his theory of light quanta was a general principle that extended to all forms of matter. In other words, the propagation of a wave is associated with the motion of a particle of any kind—photon, electron, proton, or any other.
De Broglie wished to develop a mechanical explanation for the wave/particle duality of light and to extend this to all forms of matter. He needed to find a mechanical reason for the photons in the wave to have an energy that was determined by the frequency of that wave.
De Broglie noticed a connection between the angular momentum of the electron in a Bohr orbit and the number of nodes in a standing wave pattern (remember you created those with the jump rope in the last section). The orbiting electrons could only have one unit of h (Planck's constant) or two units, etc. Could these discontinuous changes in the electron's angular momentum, these changes in the amount of h allowed, be due somehow to a similar change in standing wave patterns?
De Broglie realized that the Bohr orbit could be seen as a circular violin string, like a snake swallowing its own tail. Would the orbit size predicted by his standing matter waves correspond to Bohr's calculated electron shells? What would his wave do if confined to a circle? Well, what he discovered was that his matter waves fit Bohr's orbits exactly. And when he calculated the wavelength of the lowest orbit, he discovered another astonishing mathematical connection between the wave and the particle. The momentum of the orbiting electron equaled Planck's constant divided by the wavelength.
Excerpted from The Complete Idiot's Guide to Theories of the Universe © 2001 by Gary F. Moring. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.
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