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According to the Pauli Exclusion Principle, how many electrons can occupy an atomic orbital?

  1. One, with any spin

  2. Two, with opposite spin direction

  3. Only those of the same spin direction

  4. Zero, no electrons can occupy it

The correct answer is: Two, with opposite spin direction

The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of quantum numbers. This principle implies that an atomic orbital can hold a maximum of two electrons, but they must have opposite spin direction. In atomic physics, electrons are described by four quantum numbers, which collectively define their unique state within an atom. Since two electrons can occupy the same orbital, they must differ in at least one of these quantum numbers—specifically, in their spin quantum number, which can be either +1/2 or -1/2. Therefore, the correct understanding of how many electrons can occupy an atomic orbital, within the guidance of the Pauli Exclusion Principle, is that it can accommodate two electrons with opposite spins. This arrangement enables the electrons to coexist in the same orbital while adhering to the exclusions posed by their quantum states.