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Atomic Number and Electronic Configuration in a New Universe

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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?

b) Write the electronic configuration of the elemental with atomic number 8 in the periodic table.

c) What is the atomic number of the second noble gas?

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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.

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(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 ...

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