Question

Which of the following orbitals donot have 4 lobes?

• A. \(\text{d}_{\text{xy}}\)
• B. \(\text{d}_{\text{xz}}\)
• C. \(\text{d}_{\text{zy}}\)
• D. \(\text{d}_{\text{x}^2-\text{y}^2}\)
• E. \(\text{d}_{\text{z}^2}\)

Hint:

Visualize the \(\text{d}_{\text{z}^2}\) orbital as a "dumbbell with a donut." This unique shape makes it a frequent target for "odd one out" questions regarding orbital geometry.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
The d-subshell consists of five orbitals, which are mathematically derived from the Schrödinger wave equation. These orbitals describe the regions in space where there is a high probability of finding an electron. Their three-dimensional shapes are distinctive.
Step 2: Key Formula or Approach:
The theoretical approach involves visualizing or recalling the boundary surface diagrams (shapes) of the five standard d-orbitals: \(\text{d}_{\text{xy}}\), \(\text{d}_{\text{yz}}\) (written as \(\text{d}_{\text{zy}}\) here), \(\text{d}_{\text{zx}}\) (or \(\text{d}_{\text{xz}}\)), \(\text{d}_{\text{x}^2-\text{y}^2}\), and \(\text{d}_{\text{z}^2}\).
Step 3: Detailed Explanation:
Let's describe the shapes of the given orbitals:
- A) \(\text{d}_{\text{xy}}\), B) \(\text{d}_{\text{xz}}\), C) \(\text{d}_{\text{zy}}\): These three are non-axial orbitals. Each consists of a characteristic "cloverleaf" shape made up of four lobes of electron density that lie in the planes between the coordinate axes (xy plane, xz plane, and yz plane, respectively).
- D) \(\text{d}_{\text{x}^2-\text{y}^2}\): This is an axial orbital. It also possesses a "cloverleaf" shape with four lobes. However, unlike the first three, its lobes are aligned directly along the x and y coordinate axes.
- E) \(\text{d}_{\text{z}^2}\): This orbital is fundamentally different in appearance. It is a linear combination of two mathematical solutions. Its shape consists of two major lobes oriented along the z-axis (resembling a p-orbital) and a concentric torus (a donut-shaped ring) of electron density situated in the xy-plane around the nucleus. Therefore, it does not have four lobes.
Step 4: Final Answer:
The \(\text{d}_{\text{z}^2}\) orbital is unique among the d-orbitals as it does not possess a four-lobed structure.