Two electrons occupying the same orbital are distinguished by:

Options

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

Explanation

To solve the question "Two electrons occupying the same orbital are distinguished by:", we need to analyze the quantum numbers associated with electrons in an atom. Here’s a step-by-step breakdown:

### Step 1: Understanding Quantum Numbers
Electrons in an atom are described by four quantum numbers:
1. **Principal Quantum Number (n)**: Indicates the energy level or shell of the electron.
2. **Azimuthal Quantum Number (l)**: Indicates the subshell and shape of the orbital.
3. **Magnetic Quantum Number (m)**: Indicates the orientation of the orbital in space.
4. **Spin Quantum Number (s)**: Indicates the spin direction of the electron (either +1/2 or -1/2).

### Step 2: Identifying the Same Orbital
When two electrons occupy the same orbital, they must have the same values for the first three quantum numbers (n, l, and m). This is because these quantum numbers define the energy level, shape, and orientation of the orbital, respectively.

### Step 3: Distinguishing Electrons
The only quantum number that can differ between two electrons in the same orbital is the **Spin Quantum Number (s)**. One electron can have a spin of +1/2 (up spin), and the other can have a spin of -1/2 (down spin). This is in accordance with the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of all four quantum numbers.

### Conclusion
Thus, the answer to the question is that two electrons occupying the same orbital are distinguished by their **spin quantum number**.

### Final Answer
**Spin Quantum Number (s)**

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