As the atomic number increases, the number of electrons in a neutral atom a.decrease b.increase c.remain the same is undetermined  

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The key to answering this question is that as you increase the atomic number you are forming a "neutral" atom.  In order to be neutral, an atom has to have an equal number of positive charges (protons in the nucleus) and negative charges (electrons around the nucleus).

So every time you increase the atomic number by one proton, you also have to increase the number of electrons by one.

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