Which of the following orbitals is cyclindrically symmetrical about x-axis?

Options

A. `p_(z)`-orbital
B. `p_(y)`-orbital
C. `p_(x)`-orbital
D. `d_(xz)`-orbital

Answer

To determine which of the following orbitals is cylindrically symmetrical about the x-axis, we need to analyze the orientation of the lobes of each orbital in relation to the x-axis.

### Step-by-Step Solution:

1. **Understand Orbital Symmetry**:
- Cylindrical symmetry about the x-axis means that the orbital should look the same when rotated around the x-axis.

2. **Identify the Orbitals**:
- The orbitals we need to consider are:
- pz
- py
- px
- dxz

3. **Analyze the pz Orbital**:
- The pz orbital has lobes that extend along the z-axis.
- When viewed from the x-axis, the lobes do not show symmetry about the x-axis.
- **Conclusion**: pz is not cylindrically symmetrical about the x-axis.

4. **Analyze the py Orbital**:
- The py orbital has lobes that extend along the y-axis.
- Similar to pz, when viewed from the x-axis, the lobes do not exhibit symmetry about the x-axis.
- **Conclusion**: py is not cylindrically symmetrical about the x-axis.

5. **Analyze the px Orbital**:
- The px orbital has lobes that extend along the x-axis.
- When viewed from the x-axis, the lobes are symmetrical about the x-axis.
- **Conclusion**: px is cylindrically symmetrical about the x-axis.

6. **Analyze the dxz Orbital**:
- The dxz orbital has lobes that lie between the x and z axes.
- When viewed from the x-axis, the lobes do not exhibit symmetry about the x-axis.
- **Conclusion**: dxz is not cylindrically symmetrical about the x-axis.

7. **Final Answer**:
- The only orbital that is cylindrically symmetrical about the x-axis is the **px orbital**.