Why do Lewis dot diagrams hold a maximum of 8 electrons in the outermost energy level?
1 Answer
The short answer is that there is a general "octet rule" where eight valence electrons tends to be stable for atoms without access to
The cool answer is derived from a bit of quantum mechanics (though you should have been taught this in General Chemistry).
THE QUANTUM NUMBERS
Let us consider the quantum numbers
#n#  the principal quantum number, defining the energy level, taking on integer values#1, 2, . . . , n# , e.g.#2s# has#n = 2# .#l#  the angular momentum quantum number, defining the orbital shape, taking on integer values#0, 1, . . . n# , e.g.#2s# has#l = 0# , while#2p# has#l = 1# .#m_l#  the orbital angular momentum quantum number. In other words, projection of#l# , taking on the values#0, pm l# , e.g.#m_l# for#l = 1# is#0, pm1# .#m_s#  the magnetic quantum number, taking on values for the possible spins of the electron, e.g.#pm "1/2"# .
TWO ELECTRONS MUST OCCUPY DIFFERENT QUANTUM STATES
Next, according to the Pauli Exclusion Principle, two electrons must occupy different quantum states. That is, no two electrons can share exactly the same four quantum numbers.
Now, if we look at the second energy level,

#l = 0:# (#2s# orbital)#m_l = 0# #m_s = +"1/2", "1/2"#

#l = 1:# (#2p# orbital)#m_l = 1, 0, +1# #m_s = +"1/2", "1/2"#
ALLOWED QUANTUM STATES FOR THE ELECTRON
In the same subshell,
It also follows that since the orbital shapes are different for
WHY EIGHT FOR THE 2S AND 2P ORBITALS?
That means in total, we have the four allowed states for the electron for different
Overall, it follows that for
Therefore, the maximum number of electrons that the