The shape of the orbital with the value of l = 2 and m = 0 is

Options

A. spherical
B. dumb-bell
C. trigonal planar
D. square planar.

Explanation

To determine the shape of the orbital with the quantum numbers \( l = 2 \) and \( m = 0 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
- The azimuthal quantum number \( l \) indicates the type of orbital. The value of \( l = 2 \) corresponds to a d orbital.
- The magnetic quantum number \( m \) indicates the orientation of the orbital. For \( l = 2 \), \( m \) can take values from \(-2\) to \(2\). Here, \( m = 0 \).

2. **Determine the Type of d Orbital**:
- The d orbitals are characterized by their shapes and orientations. The specific d orbitals are:
- \( d_{xy} \)
- \( d_{xz} \)
- \( d_{yz} \)
- \( d_{x^2-y^2} \)
- \( d_{z^2} \)
- Since \( m = 0 \), we are specifically looking at the \( d_{z^2} \) orbital.

3. **Visualize the Shape of the \( d_{z^2} \) Orbital**:
- The \( d_{z^2} \) orbital has a unique shape compared to other d orbitals. It consists of a lobe along the z-axis and a torus (doughnut-shaped) region around the equator.
- This shape can be described as resembling a double dumbbell with a ring around the center.

4. **Conclusion**:
- The shape of the orbital with \( l = 2 \) and \( m = 0 \) is that of the \( d_{z^2} \) orbital, which is characterized by a lobe along the z-axis and a toroidal shape around it.

### Final Answer:
The shape of the orbital with \( l = 2 \) and \( m = 0 \) is that of the \( d_{z^2} \) orbital, which resembles a double dumbbell with a ring.

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