Which statement best describes the Pauli exclusion principle in relation to the spin quantum number?

• A. Electrons in the same orbital must have identical spin quantum numbers.
• B. Electrons with opposite spins are repelled from each other.
• C. No two electrons in the same atom can have the same set of four quantum numbers.
• D. The spin quantum number determines the energy level of an electron.

Answer: (C)

Verified step by step guidance

1. Understand that the Pauli exclusion principle states that no two electrons in the same atom can have the same set of four quantum numbers: the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s).
2. Recognize that the spin quantum number (m_s) can have only two possible values: +1/2 or -1/2, representing the two possible spin orientations of an electron.
3. Recall that in a single atomic orbital (defined by n, l, and m_l), a maximum of two electrons can exist, and these two electrons must have opposite spins to satisfy the Pauli exclusion principle.
4. Analyze the given statements: the correct description must reflect that electrons in the same orbital have opposite spins (different spin quantum numbers) so that their overall set of quantum numbers is unique.
5. Conclude that the statement 'No two electrons in the same atom can have the same set of four quantum numbers' best describes the Pauli exclusion principle in relation to the spin quantum number.