Question

Two electrons occupying the same orbital are distinguished by

• A. Principal quantum number
• B. Azimuthal quantum number
• C. Magnetic quantum number
• D. Spin quantum number

Hint:

Think of the first three quantum numbers as the zip code, street, and house address of an orbital. Since two electrons can live in the same "house" (orbital), they can only be told apart by their individual direction of rotation—one spins clockwise ($+\frac{1}{2}$), and the other spins counter-clockwise ($-\frac{1}{2}$).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks which quantum number differentiates two electrons that are residing within the exact same atomic orbital.

Step 2: Key Formula or Approach:
According to the Pauli Exclusion Principle, no two electrons in a single atom can have the identical set of all four quantum numbers ($n$, $l$, $m_l$, and $m_s$).

Step 3: Detailed Explanation:
An orbital is completely defined by the first three quantum numbers: 1. Principal quantum number ($n$) defines the electron shell.
2. Azimuthal quantum number ($l$) defines the shape of the subshell.
3. Magnetic quantum number ($m$) defines the spatial orientation of that specific orbital.
Because both electrons reside in the same orbital, they share identical values for $n$, $l$, and $m$. To avoid violating the Pauli Exclusion Principle, they must possess different values for the fourth quantum number, which is the spin quantum number ($s$ or $m_s$). The spin quantum number can only have two possible values: $+\frac{1}{2}$ (spin-up) and $-\frac{1}{2}$ (spin-down).

Step 4: Final Answer:
The two electrons are distinguished by their spin quantum number, corresponding to option (D).