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Why do Lewis dot diagrams hold a maximum of 8 electrons in the outermost energy level?

Answer 1

The short answer is that there is a general "octet rule" where eight valence electrons tends to be stable for atoms without access to #d# orbitals because they are occupying all allowed quantum states. For #n <= 2#, this holds.

The clever solution comes from a little bit of quantum mechanics, even though general chemistry should have covered this.

QUANTUM NUMBERS

Let us consider the quantum numbers #n#, #l#, #m_l#, and #m_s#:

There must be two electrons occupying distinct quantum states.

Next, two electrons cannot share precisely the same four quantum numbers; rather, they must occupy distinct quantum states in accordance with the Pauli Exclusion Principle.

Now, if we look at the second energy level, #n = 2#, we have the #\mathbf(2s)# and #\mathbf(2p)# orbitals available as valence orbitals. Notice how many quantum numbers we have available:

#l = 0:# (#2s# orbital)

#l = 1:# (#2p# orbital)

QUANTUM STATES ALLOWED FOR THE ELECTRON

In the same subshell, #n# and #l# are automatically the same, and the only quantum numbers that can be different are #m_l# and #m_s#; therefore, the two possible values of #m_s# correspond to two distinct quantum states.

It also follows that since the orbital shapes are different for #l = 0# vs. #l = 1#, and since different #m_l# correspond to different vector projections of #l#, this corresponds to four distinct quantum states---one for #m_l = 0# and three for #m_l = 0, pm1#.

FOR THE 2S AND 2P ORBITALS, WHY EIGHT?

That means in total, we have the four allowed states for the electron for different #m_l#, and two allowed states for the electron for different #m_s# in each of four distinct #m_l# states.

Overall, it follows that for #n = 2# and #l = 0, 1#, we have #m_l = 0# and #m_l = 0,pm1# and #m_s = pm"1/2"#, so we have eight allowed quantum states for the electron.

Therefore, the maximum number of electrons that the #2s# and #2p# valence orbitals can hold altogether is eight.

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Answer 2

Wyatt Adkins

The maximum of 8 electrons in the outermost energy level of Lewis dot diagrams is based on the octet rule, which states that atoms tend to gain, lose, or share electrons to achieve a stable electron configuration resembling a noble gas with a full outer shell of 8 electrons.

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Answer from HIX Tutor

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