|MadSci Network: Physics|
In your question you did not explained what you understand by "spin". This is important because physicists sometimes have very definite meanings for words that people use very loosely every day. I will understand here that you mean by "spin" the rate at which a particle revolves around another particle. I'll come later to a different, but no less interesting meaning of the word "spin" in quantum physics. Imagine a satellite revolving around the Earth. The satellite does not fall to the Earth because it is revolving around the Earth with enough speed and there is nothing to stop it. The gravitational attraction of the Earth is not enough to bring it down, and only keeps it going around in an orbit. The Danish physicist Niels Bohr imagined the above picture for an electron revolving around the nucleus of an atom in 1913. Since the electron is a particle with a negative charge, and the nucleus of an atom has positive charge, the electron must be revolving around the nucleus in order not to fall upon it. He added one condition that makes it very different from the case of the satellite around the Earth. The electron only has certain permitted orbits around the nucleus. Satellites on the other hand can have orbits at any distance from Earth. His theory was very successful in explaining some observed facts of the hydrogen atom. His theory predicts that the electron will revolve in its lowest permitted orbit around the hydrogen nucleus (which is a proton) at the speed of 2.2 X 10^8 centimeters per second (here 10^8 means 10 to the eight power, that's 100000000 or 100 million). Notice that this is about one percent of the speed of light, which is a very high speed for human standards indeed! The electron can have higher, slower permitted orbits around the proton with a speed given by 2.2 X 10^8 / n centimeters per second where n in the above formula is any integer you like from 1 to infinity. The higher the value of n, the higher the orbit of the electron in the atom. The formula reflects the fact that according to Bohr's theory not all orbits are possible. Only those for which the speed is given by the above formula. The number of turns per second of the electron around the nucleus is given by a similar formula: 6.6 X 10^15 / n^3 turns per second (that's 6.6 times 10 to the fifteenth power divided by the cube of n), where again n is any integer from 1 to infinity. Now you may wonder that if n is really high we could have electrons going very slowly, and maybe catch one. It turns out that if an electron is in a very high orbit (n very large) it will be most likely stripped from the atom by any jolt that the atom suffers. The Bohr theory suffers from many severe problems. For example, it cannot explain atoms with more that one electron, and leaves many questions unanswered, like "What happens if two electrons in an atom collide? What if I send an electron straight into the nucleus?" Bohr's theory is still useful to help us understand certain facts of the atom, but generally speaking is quite unsatisfactory, and because of that, physicists no longer use it for serious calculations. Physics has demonstrated that looking at electrons and protons as particles often leads to contradictions. Nobody has seen an electron or a proton yet, so we don't really know what they are or whether they are spinning around something. Protons don't usually revolve around other particles because they are too heavy. Instead lighter particles like electrons revolve around protons. When protons revolve around something, it is because they are part of molecules that rotate around their own center. At very low temperatures, the protons in a hydrogen molecule revolve around each other 7 X 10^12 times per second, which correspond to a speed of 200000 centimeters per second. Much slower than the electrons around the nucleus of an atom. So I promised to explain what physicists actually understand by the spin of an electron. When physicists were trying to understand how electrons behave, they came to the conclusion that electrons could be something that spin, like a top or a football in the air. It turned out that electrons, and protons are not really balls or tops or whatever, but they nevertheless behave as if they were spinning at a certain rate. That rate is called the spin and all protons and electrons have the same value of spin, but it turns out that this spin really cannot be described with a speed of rotation. Vladimir Escalante Ramirez
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