The shape of the orbital with l = 1 and m = 0 is

Options

A. spherical
B. dumb-bell
C. clover-leaf
D. dough-nut

Answer

To determine the shape of the orbital with quantum numbers \( l = 1 \) and \( m = 0 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
- The azimuthal quantum number \( l \) is given as 1. This indicates that we are dealing with a p-orbital since \( l = 0 \) corresponds to s-orbitals, \( l = 1 \) corresponds to p-orbitals, \( l = 2 \) corresponds to d-orbitals, and so on.
- The magnetic quantum number \( m \) is given as 0. The values of \( m \) can range from \( -l \) to \( +l \). For \( l = 1 \), the possible values of \( m \) are -1, 0, and +1.

2. **Determine the Orbital Type**:
- Since \( l = 1 \), we are in the p-subshell. The p-subshell consists of three orbitals: \( p_x \), \( p_y \), and \( p_z \).

3. **Understand the Significance of \( m = 0 \)**:
- The value \( m = 0 \) corresponds to one of the p-orbitals, specifically the \( p_z \) orbital. The \( p_z \) orbital is oriented along the z-axis.

4. **Visualize the Shape of the Orbital**:
- The shape of all p-orbitals (including \( p_x \), \( p_y \), and \( p_z \)) is described as a "dumbbell" shape. This means that the orbital has two lobes, one on either side of the nucleus, with a nodal plane at the nucleus.

5. **Conclusion**:
- Therefore, the shape of the orbital with \( l = 1 \) and \( m = 0 \) is a dumbbell shape, specifically corresponding to the \( p_z \) orbital.

### Final Answer:
The shape of the orbital with \( l = 1 \) and \( m = 0 \) is a **dumbbell shape**.