Movement of the Electron Around the Nucleus
You raise some really good questions:
The answer is: although it is convenient to think of the electron moving around the nucleus along circular paths, the correct description is a quantum mechanical one. This is tough to visualize, and hence people have stuck to the flawed picture of electrons moving along orbits. Incidentally, the orbit picture (Bohr's model) gives the right answers for many physical properties, including the energy needed for the electron to jump from one energy (orbit) level to another one. This switch in energy (orbit) levels occurs when the electron gains or loses energy through the absorption or emission of a photon (which is a light particle with a certain amount of energy, also called a quantum of energy).
In the more accurate quantum picture, the motion of the electron is described by probability functions and there is no fixed orbit. Different paths have different probabilities, and one can calculate average energy levels. These energy levels turn out to have exactly the same values as the energy levels calculated using the orbital (Bohr) model. However, the probability picture avoids the problem of an orbiting object losing energy through radiation.
I hope this provides a little inside. For more information, you can search the Internet for the key phrase "Bohr Model." I found, for example, this Web site related to the topic: http://csep10.phys.utk.edu/astr162/lect/light/bohr.html
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