Electron Paths and Kepler's Laws ```Name: Nathan Status: student Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: In the physical structure of atoms; how do the electrons move about? If they are orbits, would Kepler's Laws of Planetary motion apply to this movement? Replies: Hi Nathan 1st, what are Kepler's Laws of Planetary Motion? From this URL: http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion Kepler's three laws are: 1. The orbit of every planet is an ellipse with the Sun at one of the two foci. 2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.[1] 3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. Here is a picture of the polar model of an atom: http://www.presentermedia.com/files/clipart/00001000/1474/atom_pc2_md_wm.jpg Here is a picture of the orbits of the planets: http://www.astro.virginia.edu/class/oconnell/astr121/im/ss-orbs-2.jpg So the difference between the two pictures is that the planets (except Pluto which is a little bit off from the other planets) orbit the sun in a plane while atomic electrons orbit the atomic nucleus in several 3 dimensional planes. But here is the real problem: electrons can show characteristics of a discrete particle, like planets, AND electrons can show characteristics of being a wave, like what you see on ponds. Because of this, we really cannot tell where the electron is. So this is where the comparison of orbiting atomic electrons to orbiting planets breaks down. So no, Kepler's laws do not apply to atomic electrons. To look more deeply into defining the orbits of atomic electrons, please see this URL about the Heisenberg Uncertainty Principle: http://en.wikipedia.org/wiki/Uncertainty_principle Because of this dual nature of the electrons, quantum mechanics tells us we can't speak of the location of an electron, but we can only speak of the probability of where it is. Sincere regards, Mike Stewart Nathan, Kepler's Laws are true because gravity at the level of stars and planets is a 1/r^2 (one over the distance-squared) force that is also proportional to the mass of the object in motion. Without the mass proportion, the law that relates planet orbits to each other (orbit radius vs. period) would not be true, but the laws that apply to an individual orbit could still apply. You would see such a thing with a very large negative charge orbiting a very large positive charge at a very large distance. Within an atom, reality is quite different. Concepts of force and distance "fall apart". An electron no longer has a specific position feeling a specific force. It is in a specific state with a specific energy. The electron does not have a path to follow. The electron's state is called an orbit out of convenience and tradition. Only a few states can exist for the electron. The electron can jump between orbits without warning. If "F=ma" were the guiding relationship at the level of single particles and single atoms, then two of Kepler's Laws would apply (orbital shape, area vs. time). Without F=ma holding true, Kepler's Laws do not apply. Ken Mellendorf Dear Nathan: You are right. If electrons were solid little balls zipping around in set orbits they would follow Kepler's Laws and Newton's as well. But it can be proved that if electrons spun around in such neat orbits, all atoms would have collapsed by now. They have not and this is one of the reasons our present concept of the atom does not look like a miniature solar system. R. W. "Bob" Avakian Oklahoma State Univ. Inst. of Technology Click here to return to the Physics Archives

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