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In 1913 the Danish physicist Niels Bohr formulated a model for the hydrogen atom that said that an electron moves around the proton in a way similar to the way a satellite moves around the Earth. The only difference is that the electron cannot exist in any orbit. Instead its angular momentum given by mvr (m times v times r), where m is the electron mass, v the velocity and r the distance of the electron to the nucleus must be equal to n times hbar where hbar is the Planck constant and n is any integer number from 1 to infinity, i.e., n=1,2,3,4,... When a physical quantity is limited to a discrete set of values, we say that it is "quantized". A satellite on the other hand can take any value for its angular momentum. Bohr postulated that the angular momentum, and thus the energy are quantized, and that an electron can exist in the atom only in states with those energies. Furthermore he posultated that an electron can jump between those states. If it jumps from a higher energy to a lower energy state, it emits the energy difference between the two states as a package of light, called a "photon". It it receives or absorbs a photon of exactly that energy difference, it jumps from the lower to the higher energy state. Bohr's model was very accurate in explaining the observed energy levels of the hydrogen atom, and thus introduced the idea of quantum physics, but it failed badly in predicting energy levels of atoms with more than one electron. His model is also very unsatisfactory in explaining many other phenomena. It left many questions unanswered. For example, what happens if two electrons in an atom come very close to each other? In the case of two satellites, they could send each other to very different orbits, but that does not always happens in an atom. Because all of this, physicists have discarded Bohr's model. Electrons are much better described in modern quantum mechanics as waves, rather than as particles orbiting around an atom with a certain speed. Still today Bohr's model can give some insights on how electrons in atoms behave, but one has to remember its many limitations. You can find the math needed in the Bohr model in any first year undergraduate physics course that treat the Bohr atom model. With the above in mind, I answer your questions directly. If I give a satellite a package of energy to increase its speed, does it jump to a higher orbit?: If you change the direction of its velocity, many things can happen, including that the satellite can fall to Earth. If you don't change the direction of its velocity, and only the magnitude of its velocity, yes, you change its orbit to one with higher energy. However rembemer that orbits can have variable height. Satellite orbits are ellipses. At its highest point the speed of the satellite is lowest and at its lowest point its speed is highest. Does the math for satellite height, speed and mass work for electrons? According to Bohr's theory it does work for the hydrogen atom. But remember that Bohr's theory "quantizes" heights, speeds, energies and momenta with the condition that mvr=n times hbar, with n=1,2,3... This is the only additional mathematical condition that the Bohr model needs. Physical quantities are not quantized for a satellite, but they are continuous. According to modern quantum mechanics, the math for satellites does NOT work for electrons, and experimental observations confirm this assertion. Does a spinning satellite change this math? To a first approximation it does not, because you can consider a satellite as a particle since it is very small compared to Earth. It you consider more accurate approximations, it changes a little the equations of motion. A spinning satellite can alter its orbit a little because it can exchange some angular momentum with the Earth if it is not perfectly round and is heavier in one side. That's why large satellites like the Space Station need continuous guidance. Electrons on the other hand don't really behave like this. In fact we don't know exactly how an electron is made, whether it has "parts", structure, etc. At some point physicists thought that an electron can spin, and when they tried to measure its spin, a big discovery was made. Electrons do have spin, but not in the normal sense of a spinning top. The electron spin alters its motion in the atom in a far more radical way than a spinning satellite can alter its motion around Earth. Vladimir Escalante Ramirez.

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