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It is not that it necessarily affects the behavior of the electron, but it is to even out the magnetic field created by the positive nucleus with the negative electrons. If electrons are in the same orbital, the spins must be opposite. If they are in different orbitals, they must be parallel, therefor they must be the same spin. Take the p orbitals- first you would fill px with one spin up, then py with spin up, then pz with spin up, and once those are full, you would go back and add spin down to px, then py, then pz, as necessary. When the electrons are paired, the atom is more stable.
Electron spin is a property that relates to the direction an electron rotates about its axis. It was discovered by shining a beam of silver atoms in a magnetic field. Because the electrons spin in different directions, their magnetic properties change. This caused atoms to split into two beams.
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