The number of different spatial arrangements for the orbital with l=2 is

Options

A. 1
B. 3
C. 5
D. 7

Answer

To find the number of different spatial arrangements for the orbital with \( l = 2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quantum Number \( l \)**:
- The azimuthal quantum number \( l \) determines the shape of the orbital. For \( l = 2 \), we are dealing with the d-orbitals.

2. **Determine the Magnetic Quantum Number \( m_l \)**:
- The magnetic quantum number \( m_l \) can take on values from \( -l \) to \( +l \). This means:
\[ m_l = -l, -l + 1, \ldots, 0, \ldots, l - 1, l \]
- Therefore, for \( l = 2 \):
\[ m_l = -2, -1, 0, +1, +2 \]

3. **Count the Possible Values of \( m_l \)**:
- The total number of possible values of \( m_l \) can be calculated using the formula:
\[ m_l = 2l + 1 \]
- Substituting \( l = 2 \):
\[ m_l = 2(2) + 1 = 4 + 1 = 5 \]

4. **List the Values of \( m_l \)**:
- The values of \( m_l \) when \( l = 2 \) are:
- \( -2, -1, 0, +1, +2 \)

5. **Conclusion**:
- Therefore, the number of different spatial arrangements for the orbital with \( l = 2 \) is **5**.

### Final Answer:
The number of different spatial arrangements for the orbital with \( l = 2 \) is **5**.

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