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 solve the question, we need to determine the possible number of orientations for an orbital with an azimuthal quantum number \( l = 3 \).

### Step-by-Step Solution:

1. **Identify the Azimuthal Quantum Number**:
The azimuthal quantum number \( l \) is given as 3. This quantum number indicates the shape of the orbital and can take on integer values starting from 0 up to \( n-1 \), where \( n \) is the principal quantum number.

**Hint**: Remember that \( l \) can take values from 0 to \( n-1 \).

2. **Use the Formula for Magnetic Quantum Number**:
The magnetic quantum number \( m_l \) can be calculated using the formula:
\[ m_l = 2l + 1 \]
Here, we substitute \( l = 3 \):
\[ m_l = 2(3) + 1 = 6 + 1 = 7 \]

**Hint**: The formula \( m_l = 2l + 1 \) helps find the number of orientations.

3. **Interpret the Result**:
The value \( m_l = 7 \) indicates that there are 7 possible orientations for the orbital when placed in a magnetic field.

**Hint**: Each orientation corresponds to a different value of \( m_l \) ranging from \( -l \) to \( +l \).

4. **List the Possible Values of \( m_l \)**:
For \( l = 3 \), the possible values of \( m_l \) are:
\[ m_l = -3, -2, -1, 0, +1, +2, +3 \]
Counting these values gives us a total of 7 orientations.

**Hint**: Count the values from \( -l \) to \( +l \) to confirm the total number of orientations.

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