the number of electrons accommodated in an orbital with principal quantum number 3 is

Options

A. 2
B. 6
C. 8
D. 18

Answer

To determine the number of electrons that can be accommodated in an orbital with a principal quantum number \( n = 3 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Principal Quantum Number (n)**:
The principal quantum number \( n \) indicates the main energy level of an electron in an atom. For \( n = 3 \), we are looking at the third energy level.

2. **Using the Formula**:
The maximum number of electrons that can be accommodated in a shell (or energy level) is given by the formula:
\[ \text{Maximum number of electrons} = 2n^2 \]
where \( n \) is the principal quantum number.

3. **Substituting the Value of n**:
For \( n = 3 \):
\[ \text{Maximum number of electrons} = 2 \times (3^2) = 2 \times 9 = 18 \]

4. **Conclusion**:
Therefore, the number of electrons that can be accommodated in an orbital with a principal quantum number of 3 is **18 electrons**.

### Final Answer:
The number of electrons accommodated in an orbital with principal quantum number 3 is **18**.

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