Question

Why are electrons in the outer shell of an atom can have a maximum of 8 electrons?

Answer 1

The state of an electron in an atom (which you can think of as an available "slot" in an orbital that the electron is filling) is described by four "quantum numbers":

nn, the principal quantum number, which is the most important for determining the energy level and the distance from the nucleus.ℓℓ, the angular momentum quantum number, which tells how much orbital angular momentum the electron has.mm, the magnetic quantum number, which tells the component of the electron's orbital angular momentum in the z^z^ direction.msms, the spin quantum number, which tells the quantum spin state of the electron. 

There's something called the Pauli exclusion principle, which says that no two identical fermions (e.g., electrons) can share the same quantum state. So, in this case, it means that no two electrons in the same atom can have all four quantum numbers the same. This is why electron shells can "fill up".