When two electrons are shared in the same orbital, what is the relationship between their spin quantum numbers?

• A. Their spins are unrelated and can be any value
• B. They must have opposite spins (one +1/2, one -1/2)
• C. They must have the same spin (both +1/2 or both -1/2)
• D. They must both have a spin quantum number of zero

Answer: (B)

Verified step by step guidance

1. Recall the Pauli Exclusion Principle, which states that no two electrons in the same atom can have the same set of four quantum numbers.
2. Understand that the spin quantum number (\( m_s \)) can only have two possible values: +\( \frac{1}{2} \) or -\( \frac{1}{2} \).
3. Since two electrons share the same orbital, they have identical values for the principal (\( n \)), azimuthal (\( l \)), and magnetic (\( m_l \)) quantum numbers.
4. To satisfy the Pauli Exclusion Principle, the two electrons must differ in their spin quantum number, meaning one must have +\( \frac{1}{2} \) and the other -\( \frac{1}{2} \).
5. Therefore, the relationship between their spin quantum numbers is that they must be opposite in sign when two electrons occupy the same orbital.