When the azimuthal quantum number l = 1, the shape of the orbital will be

Options

A. spherical
B. dumb-bell
C. double dumb-bell
D. more complicated

Explanation

To determine the shape of the orbital when the azimuthal quantum number \( l = 1 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**: The azimuthal quantum number \( l \) is associated with the shape of the orbital. It can take on integer values starting from 0 up to \( n-1 \), where \( n \) is the principal quantum number.

2. **Identifying the Value of \( l \)**: In this case, we are given \( l = 1 \).

3. **Relating \( l \) to Orbital Types**: Each value of \( l \) corresponds to a specific type of orbital:
- \( l = 0 \) corresponds to the s orbital (spherical shape).
- \( l = 1 \) corresponds to the p orbital (dumbbell shape).
- \( l = 2 \) corresponds to the d orbital (more complex shape).
- \( l = 3 \) corresponds to the f orbital (even more complex shape).

4. **Conclusion**: Since \( l = 1 \) corresponds to the p orbital, the shape of the orbital will be a dumbbell shape.

5. **Visual Representation**: The p orbitals can be oriented along the x, y, and z axes, typically represented as \( p_x \), \( p_y \), and \( p_z \).

### Final Answer:
When the azimuthal quantum number \( l = 1 \), the shape of the orbital will be a **dumbbell shape**.

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