Two electrons occupying the same orbital are distinguished by :

Options

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

Explanation

To solve the question "Two electrons occupying the same orbital are distinguished by:", we will analyze the quantum numbers associated with electrons in an atom.

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- Electrons in an atom are described by four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (s).
- The principal quantum number (n) indicates the energy level or shell of the electron.
- The azimuthal quantum number (l) describes the shape of the orbital.
- The magnetic quantum number (m) specifies the orientation of the orbital in space.
- The spin quantum number (s) describes the intrinsic spin of the electron.

2. **Identifying Common Values**:
- When two electrons occupy the same orbital, they must have the same values for n, l, and m. This is because these quantum numbers define the energy level, shape, and orientation of the orbital, which are identical for both electrons in the same orbital.

3. **Distinguishing Electrons**:
- According to the Pauli Exclusion Principle, no two electrons can have the same set of all four quantum numbers. Therefore, while n, l, and m are the same for both electrons in the same orbital, the only quantum number that can differ is the spin quantum number (s).

4. **Values of Spin Quantum Number**:
- The spin quantum number can take on one of two values: +1/2 or -1/2. This means that one electron can have a spin of +1/2 and the other can have a spin of -1/2 when they occupy the same orbital.

5. **Conclusion**:
- Thus, the two electrons occupying the same orbital are distinguished by their spin quantum number.

### Final Answer:
The correct answer is the **spin quantum number**.

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