The task requires identification of the incorrect statement among the given options about d orbitals. Understanding the properties of these orbitals will help us find the incorrect statement.
Let's analyze each option:
Statement: All the five 5d orbitals are different in size when compared to the respective 4d orbitals.
Explanation: This is a correct statement. 5d orbitals have a higher principle quantum number than 4d orbitals, meaning they're larger in size due to their higher energy level.
Statement: All the five 4d orbitals have shapes similar to the respective 3d orbitals.
Explanation: This is also correct. The shape of orbitals is determined by their angular momentum quantum number, which means 3d, 4d, and 5d orbitals have similar shapes, but their sizes and energies differ.
Statement: In an atom, all the five 3d orbitals are equal in energy in free state.
Explanation: Correct. In a free state, meaning not influenced by external electric or magnetic fields, all 3d orbitals (dxy, dyz, dzx, dxĀ²-yĀ², dzĀ²) are degenerate, which means they have the same energy.
Statement: The shapes of dxy, dyz, and dzx orbitals are similar to each other; and d(xĀ²-yĀ²) and dzĀ² are similar to each other.
Explanation: This is the incorrect statement. While dxy, dyz, and dzx orbitals have similar clover shapes, the dxĀ²-yĀ² orbital shares this shape but in a different orientation. The dzĀ² orbital, however, has a distinct shape featuring a donut ring around it, so it does not resemble the other four, making this statement incorrect.
Thus, the incorrect statement is:
The shapes of dxy, dyz, and dzx orbitals are similar to each other; and d(xĀ²-yĀ²) and dzĀ² are similar to each other.