Concept: Pauli's Exclusion Principle puts a hard mathematical limit on the capacity of a single spatial orbital.
Formula: None required.
Solution: - According to Pauli's Exclusion Principle, no two electrons can have the exact same set of four quantum numbers.
- If two electrons are in the same exact orbital, they share identical \( n, l \), and \( m \) values.
- The only quantum number left to differentiate them is the spin quantum number (\(s\)), which only has two possible states: \( +1/2 \) (spin up) and \( -1/2 \) (spin down).
- Therefore, a maximum of 2 electrons can occupy a single orbital.
Why other options are incorrect: 1 is an incomplete orbital. 3 or more violates the Pauli Exclusion Principle, as it would require two electrons to have identical spins.
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