The total number of orbitals possible for the quantum number n is

Options

A. n
B. `n^(2)`
C. 2n
D. `2n^(2)`

Answer

To determine the total number of orbitals possible for a given principal quantum number \( n \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The principal quantum number \( n \) indicates the energy level of an electron in an atom. It can take positive integer values: \( n = 1, 2, 3, \ldots \).

2. **Formula for Total Orbitals**:
- The total number of orbitals for a given principal quantum number \( n \) is given by the formula:
\[ \text{Total orbitals} = n^2 \]

3. **Calculating for Different Values of \( n \)**:
- For \( n = 1 \):
\[ n^2 = 1^2 = 1 \quad \text{(1s orbital)} \]
- For \( n = 2 \):
\[ n^2 = 2^2 = 4 \quad \text{(1s + 3p orbitals)} \]
- For \( n = 3 \):
\[ n^2 = 3^2 = 9 \quad \text{(1s + 3p + 5d orbitals)} \]

4. **Conclusion**:
- Therefore, the total number of orbitals possible for the quantum number \( n \) is \( n^2 \).

### Final Answer:
The total number of orbitals possible for the quantum number \( n \) is \( n^2 \).

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