Question

Identify the incorrect statement from the following.

• A. All the five 5d orbitals are different in size when compared to the respective 4d orbitals.
• B. All the five 4d orbitals have shapes similar to the respective 3d orbitals.
• C. In an atom, all the five 3d orbitals are equal in energy in free state.
• D. The shapes of dxy, dyz, and dzx orbitals are similar to each other; and d(x2-y2) and dz2 are similar to each other.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Atomic orbitals are regions of space where the probability of finding an electron is maximum. For d-orbitals, there are five degenerate orbitals in an isolated atom ($d_{xy}, d_{yz}, d_{zx}, d_{x^2-y^2}, d_{z^2}$).
Step 2: Detailed Explanation:
1. Statement (1): As the principal quantum number $n$ increases ($4d \rightarrow 5d$), the orbital size increases and they become more diffuse. Correct.
2. Statement (2): Orbitals with the same angular quantum number $l$ have the same general shape (symmetry) regardless of $n$. Correct.
3. Statement (3): In an isolated gaseous atom (free state), all five d-orbitals are degenerate, meaning they have equal energy. Correct.
4. Statement (4): $d_{xy}, d_{yz},$ and $d_{zx}$ all have clover-leaf shapes with lobes between the axes. $d_{x^2-y^2}$ is also clover-leaf shaped but with lobes along the axes. However, $d_{z^2}$ has a unique "doughnut" or "baby-soother" shape with a central toroid. Therefore, $d_{x^2-y^2}$ and $d_{z^2}$ are NOT similar in shape.
Step 3: Final Answer:
Statement (4) is incorrect because $d_{x^2-y^2}$ and $d_{z^2}$ have distinctly different shapes.