what is the quantum mechanical explanation of the octet rule?

what is the quantum mechanical explanation of the octet rule?


1 Answers

Mukesh Sharma
askIITians Faculty 43 Points
8 years ago

For the first rows in the Periodic table, this can easily be explained by the fact that electrons possess four quantum numbers (usually n, l, ml and ms). These numbers are restricted as such:

By Pauli's exclusion principle all of these numbers can't be the same for any two electrons in an atom.

So in the n=2 shell you can have two possible values for l, one possible value for ml when l=0, three possible values for ml when l=1, and two possible values for ms. This sums to a total of eight possible value vectors: (1+3)·2=8.

In the n=3 shell the eight rule also holds true for l<2, which gives you sort of the same combinatorial all over again.

Since the quantum numbers cannot be the same for any electrons in an atom adding an extra electron to an atom with eight electrons in its outermost shell forces the electron to occupy a state with a higher principal quantum number (n), and since the binding energy of the electron increases with n this is energetically unfavorable to binding with an atom that has more space in its outermost shell.

For further reference n is the principal quantum number (dealing with energy states), l is the orbital quantum number (dealing with sub shells), ml is the orbital magnetic quantum number (direction of l) and ms is the spin quantum number (direction of spin).

Thanks & Regards
Mukesh Sharma
askIITians Faculty

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