An orbital is described with the help of a wave function. Since many wave functions are possible for an electron, there are many atomic orbitals. When atom is placed in a magnetic field the possible number of orientations for an orbital of azimuthal quantum number 3 is

Options

A. three
B. two
C. five
D. seven

Explanation

To determine the possible number of orientations for an orbital with an azimuthal quantum number \( l = 3 \) when placed in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quantum Numbers**:
- The azimuthal quantum number \( l \) determines the shape of the orbital and can take values from \( 0 \) to \( n-1 \), where \( n \) is the principal quantum number. In this case, \( l = 3 \).

2. **Determine the Magnetic Quantum Number \( m \)**:
- The magnetic quantum number \( m \) describes the orientation of the orbital in space. The possible values of \( m \) range from \( -l \) to \( +l \). Therefore, for a given \( l \), the possible values of \( m \) are:
\[ m = -l, -l + 1, \ldots, 0, \ldots, l - 1, l \]

3. **Calculate the Range of \( m \)**:
- For \( l = 3 \):
- The possible values of \( m \) are:
\[ m = -3, -2, -1, 0, 1, 2, 3 \]

4. **Count the Number of Possible Orientations**:
- To find the total number of possible orientations, we count the values of \( m \):
- The values are: \( -3, -2, -1, 0, 1, 2, 3 \)
- This gives us a total of \( 7 \) possible orientations.

5. **Conclusion**:
- Therefore, the possible number of orientations for an orbital with azimuthal quantum number \( l = 3 \) in a magnetic field is \( 7 \).

### Final Answer:
The possible number of orientations for an orbital of azimuthal quantum number \( 3 \) is \( 7 \).

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