Question

Which of the following statements is correct?

• A. The 3d-orbitals remain degenerated in the presence of magnetic field
• B. The electron densities in the xy and yz planes are zero in $3\text{d}_{xz}$ orbital
• C. The electron density in the xy and xz planes of $3\text{d}_{yz}$ orbital is not zero
• D. The electron density in the xy plane of $3\text{d}_{xy}$ orbital is zero

Hint:

For any $d$-orbital of the form $\text{d}_{ij}$ (where $i, j$ are the axes), the nodal planes are the remaining two planes that contain the third axis.
For example, for $\text{d}_{xz}$, the third axis is $y$, so the nodal planes are $xy$ and $yz$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question focuses on the shapes, spatial orientation, and nodal planes of d-orbitals.
We must identify which statement accurately describes these quantum mechanical features.

Step 2: Key Formula or Approach:
An orbital has planar nodes (nodal planes) where the probability density of finding an electron is zero.
The five $d$-orbitals ($\text{d}_{xy}, \text{d}_{yz}, \text{d}_{zx}, \text{d}_{x^2-y^2}, \text{d}_{z^2}$) have characteristic orientations.
For any $\text{d}_{ij}$ orbital (where $i, j \in \{x, y, z\}$), the lobes lie in the $ij$-plane, and the two coordinate planes containing the remaining axis serve as the nodal planes.

Step 3: Detailed Explanation:

• Let us evaluate each statement one by one:

• Statement (A): "The 3d-orbitals remain degenerated in the presence of magnetic field."
This is incorrect because an external magnetic field breaks spatial symmetry, splitting the degenerate d-orbitals into different energy levels (Zeeman effect).

• Statement (B): "The electron densities in the xy and yz planes are zero in $3\text{d}_{xz}$ orbital."
This is correct. For the $\text{d}_{xz}$ orbital, the lobes lie in the $xz$-plane.
The two nodal planes (where electron density is zero) are the planes containing the $y$-axis: the $xy$-plane ($z = 0$) and the $yz$-plane ($x = 0$).

• Statement (C): "The electron density in the xy and xz planes of $3\text{d}_{yz}$ orbital is not zero."
This is incorrect because the $xy$-plane ($z = 0$) and $xz$-plane ($y = 0$) are indeed the nodal planes for the $\text{d}_{yz}$ orbital, meaning the electron density is exactly zero.

• Statement (D): "The electron density in the xy plane of $3\text{d}_{xy}$ orbital is zero."
This is incorrect because the lobes of the $\text{d}_{xy}$ orbital lie within the $xy$-plane, so the electron density is maximum in this plane.


Step 4: Final Answer:
The correct statement is (B).