1.25 Textbook Problem

[simona_krasnegor_1C]

Hey guys! Does anyone have a good way of explaining this problem from the textbook? Thanks!

1.25 Suppose that in some other universe a rule corresponding to the Pauli exclusion principle reads “as many as two electrons in the same atom may have the same set of four quantum numbers.” Suppose further that all other factors affecting electron configurations are unchanged. (a) Give the electron configuration of the element in the other universe that has five protons. (b) What is the most likely charge on the ion of this element? (c) Give the value of Z for the second inert gas in the other universe. Explain your reasoning.

[Sunny Wu 3A]

This was a tricky question, but here's my understanding:

Given n=1, we could have these sets of quantum numbers:
n=1, l=0, ml=0, ms=+1/2
n=1, l=0, ml=0, ms=+1/2
n=1, l=0, ml=0, ms=-1/2
n=1, l=0, ml=0, ms=-1/2

For part a, 4 of the 5 valence e- would go in the n=1 shell, and the last one would go into the n=2 shell, giving us 1s⁴2s¹.

For part b, given the electron configuration from part a, the atom would want to lose it's outermost electron from the n=2 shell, giving it a charge of +1.

For part c, if 4 electrons is the maximum number of electrons the s subshell can hold (2x2), then by that logic the p subshell can hold 12 (2x6). Thus an electron configuration with the n=2 shell filled would be 1s⁴2s⁴2p¹².
Alternatively, you could probably write out all the possible combinations of quantum numbers like earlier and come to the same conclusion.