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: Recall how nodal planes are assigned.
For any d-orbital written as $d_{ij}$, the four lobes sit in the $ij$ plane, and the two planes that do not contain both of those axes together are its nodal planes, where the electron density is exactly zero.
Step 2: Apply this to $3d_{xz}$.
Its lobes lie in the xz plane, so its nodal planes are the xy plane and the yz plane, meaning the electron density is zero in both of those planes.
Step 3: Screen the remaining statements quickly.
$3d_{xy}$ has nodal planes xz and yz, not the xy plane itself, so that option is wrong; $3d_{yz}$ has zero density in xy and xz, not in xz and xy together the way stated, so that option is wrong too; and 3d orbitals actually split under a magnetic field rather than staying degenerate, so that option fails as well.
Step 4: Conclude.
Only the statement about $3d_{xz}$ matches the nodal-plane rule.
Final answer: Option 2, the electron densities in the xy and yz planes are zero in the $3d_{xz}$ orbital.