"Only two electrons may exist in the same orbital and these electrons must have opposite spin" is the statement of which of the following?

Question

Accepted Answer

The statement "Only two electrons may exist in the same orbital and these electrons must have opposite spin" is indeed the statement of the Pauli Exclusion Principle, which is Option 2. Here is a detailed explanation justifying why Option 2 is correct and why the other options are incorrect:

1. **Pauli Exclusion Principle (Option 2):** 
   - The Pauli Exclusion Principle, formulated by Wolfgang Pauli in 1925, states that no two electrons in an atom can have the same set of four quantum numbers. In simpler terms, this means that an orbital can hold a maximum of two electrons, and these electrons must have opposite spins. This principle is fundamental to the structure of atoms and the behavior of electrons in atoms, as it explains the arrangement of electrons in different orbitals and the unique electronic configuration of each element.

2. **Aufbau Principle (Option 1):**
   - The Aufbau Principle is a rule used to determine the electron configuration of an atom. It states that electrons fill orbitals starting from the lowest energy level to the highest. This principle is about the order in which orbitals are filled, not about the number of electrons in an orbital or their spins. Therefore, it does not relate to the statement in question.

3. **Hund's Rule of Maximum Multiplicity (Option 3):**
   - Hund's Rule states that electrons will fill degenerate orbitals (orbitals with the same energy) singly before pairing up. This rule is concerned with the distribution of electrons across orbitals of the same energy level to maximize the number of unpaired electrons, which is different from the restriction on the number of electrons in a single orbital and their spins. Thus, it does not apply to the statement in question.

4. **$(n+l)$ Rule (Option 4):**
   - The $(n+l)$ rule, also known as the Madelung rule, is used to predict the order in which atomic orbitals are filled based on the sum of the principal quantum number (n) and the azimuthal quantum number (l). This rule helps determine the energy levels of orbitals but does not address the occupancy of electrons within a single orbital or their spins. Therefore, it is not relevant to the statement in question.

In conclusion, the Pauli Exclusion Principle (Option 2) is the correct answer because it directly addresses the limitation on the number of electrons in an orbital and the requirement for opposite spins, which is precisely what the statement describes.