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 will analyze the properties of electrons in an atom, particularly focusing on their quantum numbers.

### Step-by-Step Solution:

1. **Understanding Orbitals and Quantum Numbers**:
- Electrons in an atom are described by a set of quantum numbers. Each electron in an orbital is characterized by four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms).

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 ml). For example, if both electrons are in the 1s orbital, they share:
- Principal quantum number (n) = 1
- Azimuthal quantum number (l) = 0 (since it's an s-orbital)
- Magnetic quantum number (ml) = 0 (for s-orbitals)

3. **Distinguishing Electrons**:
- The only quantum number that can differ between the two electrons in the same orbital is the spin quantum number (ms). According to the Pauli Exclusion Principle, no two electrons in an atom can have the same set of four quantum numbers. Therefore, if two electrons are in the same orbital, they must have opposite spins.
- This means one electron will have a spin quantum number of +1/2 (up spin) and the other will have a spin quantum number of -1/2 (down spin).

4. **Conclusion**:
- Thus, the correct way to distinguish between two electrons occupying the same orbital is by their spin quantum number (ms).

### Final Answer:
Two electrons occupying the same orbital are distinguished by their spin quantum number.

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