Originally posted by Marianna
pauli's exclusion principle-
no two electrons can have the set of quantum numbers
thus it explains why the n'th shell has 2n^2 electrons at max, and also why the periodic table is structured like so
if u really want the details:
n - principal quantum number: progresses from 1, 2, 3, ...
for each n, we can divide the electrons in terms of:
l - angular quantum no.: takes values of 0, 1, 2, ..., (n-1)
e.g. in the 4th shell l can take values of 0, 1, 2, 3
for each l, we have:
ml - magnetic quantum no.: takes values of -l, -(l-1), ..., -1, 0, 1, ..., (l-1), l.
e.g. the 3rd subshell (l = 2): ml = -2, -1, 0, 1, 2
for each ml, we have:
ms - spin quantum no.: takes values of -1/2, +1/2:
i.e. there are two electrons in any magnetic quantum state.
so say n = 6 (6th shell)
we have l = 0, 1, ..., 5
at l = x, we have (2x+1) magnetic spin states, each with two electrons.
so if l = x, we have (4x+2) electrons.
thus, at n=6, we have (4*0 + 2) + (4*1 + 2) + ... + (4*5 + 2)
= 2 + 6 + 10 + 14 + 18 + 22 = 72 = 2*(6^2) electrons possible.
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there you go. You don't need it this complicated. I just feel a bit bored...
