Suppose you take a trip to a distant universe and find that the periodic table there is derived from an arrangement of quantum numbers different from the one on Earth. The rules in that universe are:
1. principal quantum number n = 1, 2, ... (as on Earth);
2. angular momentum quantum number l = 0, 1, 2, ... n - 1 (as on Earth);
3. magnetic quantum number m_l = 0, 1, 2, ... l (only positive integers up to and including l are allowed);
4. spin quantum number m_s = - 1, 0, +1 (that is, three allowed values of spin).
a) Assuming that the Pauli exclusion principle remains valid in the alternate universe, what is the maximum number of electrons that can populate a given orbital there?
c) What is the atomic number of the second noble gas?
(a) Pauli's Exclusion Principle states that 'no two electrons can have the same four quantum numbers in an atom'. That means even if the first three quantum numbers (n, l, m_l) are same, the fourth quantum number, ms, should differ. As there are three allowed values of spins (m_s = -1, 0, +1) in this new universe, as opposed to two in earth, the maximum number of electrons that can populate a given orbital there ...
This is a very interesting question and the solution requires you to think out-of-the-box. The solution provides strong reasoning and detailed steps on how to derive the answer of a quantum chemistry problem, when the classical quantum rules are changed.