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AnswerIn fact, electrons do leave their shells. Around atoms they only exist in shells (quantum energy states) but can change energy states by moving from one shell to another. They can also completely leave one atom and take up residence with another or even remain free. This is the nature of electricity. If electrons were permanently bound to the shells on one atom, out lights and computers simply wouldn't work. AnswerThe question wording needs some clarification. There are two issues of concern here - the electron spin, and the "orbit" around the nucleus. These will be addressed separately.

Electron Spin

In the classical sense, the electron was once considered to spin about its axis in the same way the earth rotates around its axis. Classical mechanics yields to quantum physics here, because the electron does not actually spin about its axis in the same the earth does. Instead, we measure the angular momentum of the electron, which is a quantum factor.

The spin of an electron is always 1/2, and can be measured and confirmed experimentally. This value is constant (although it can be said to be "up" or "down"). The scalar value of the electron spin never changes from 1/2.

Electron Orbitals

An electron travels around the nucleus in confined quantum regions, or shells. Unlike a planet that orbits the sun in a predictable elliptical orbit, an electron's trajectory within its shell is random and unpredictable. Consider a spherical cloud around the nucleus. That cloud is made up of one or two electrons, and there is a known probability that you will find an electron on any point on the surface of that shell.

As a thought experiment, if you were able to take a video of a single hydrogen atom, you would observe the nucleus at the center comprising one proton (and one neutron in deuterium), surrounded by a distant, thin opaque sphere. The sphere is not solid, it is just a single electron buzzing around the nucleus so quickly that, in the time your camera had a chance to register one frame of the image, the electron had buzzed all around the nucleus so many times that the sphere appears to you to be semi-solid.

By strict definition, only two electrons can occupy the same shell at one time, due to a phenomenon called the Pauli Exclusion Principle. In many atoms, several shells have exactly the same energy levels, and so in quantum parlance we combine shells of identical energy levels together, and consider them as a single shell. There are n2 shells with identical energy levels for each orbital number, so therefore there is 1 shell for the first orbital, 4 shells for the second orbital, 9 shells for the third orbital, and so one. Since each shell can contain no more that 2 electrons, there are 2 electrons allowed in the first orbital, 8 in the second, 18 in the third, and so on.

AnswerThe nucleus carries a positive charge and the electron carries a negative charge.

Better answers are more complicated, but this should be a start.

[This answer is incorrect - spin has nothing to do with charge]

More informationWhen we talk about electron spin, lots of folks get the impression that electrons "rotate" about an "axis" in the same way the earth does to make day and night. It's not really like that. Spin is actually a quantum mechanical characteristic rather than a "physical spin" like the revolution of planetary bodies. Hey, we assign color as a quantum mechanical characteristic, but that doesn't mean that what we assign a color to actually has "color" or is a certain "color" as in being possessed of a certain hue.
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Related Questions

Particles with a negative charge that move in shells around the nucleus?

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