For which of the following types of ions is the number of unpaired electrons in octahedral complexes fixed at the same number as in the free ion no matter, how weak or strong the crystal field is?

Options

A. `d^(3)`
B. `d^(4)`
C. `d^(5)`
D. `d^(6)`

Answer

To solve the question regarding which types of ions have a fixed number of unpaired electrons in octahedral complexes, regardless of the strength of the crystal field, we can follow these steps:

### Step 1: Understanding the Crystal Field Theory
In octahedral complexes, the d-orbitals of the central metal ion split into two sets: the lower energy t2g (dxy, dyz, dzx) and the higher energy eg (dx2-y2, dz2). The arrangement of electrons in these orbitals is influenced by the strength of the ligands surrounding the metal ion.

### Step 2: Identifying the Role of Ligands
The strength of the ligands can be classified into two categories:
- **Strong field ligands**: These cause a large splitting of the d-orbitals, leading to electron pairing.
- **Weak field ligands**: These result in a smaller splitting, allowing electrons to occupy higher energy orbitals without pairing.

### Step 3: Observing Electron Configuration
For certain electron configurations, the number of unpaired electrons remains the same regardless of the ligand strength. This typically occurs with specific d-electron counts.

### Step 4: Identifying the Fixed Cases
The key observation is that for d3 configurations, the number of unpaired electrons remains constant:
- In a d3 configuration, the three electrons will fill the three t2g orbitals singly before any pairing occurs, resulting in three unpaired electrons.
- Whether the ligands are strong or weak, the three electrons will occupy the t2g orbitals without pairing, thus maintaining three unpaired electrons.

### Step 5: Conclusion
Therefore, the type of ion for which the number of unpaired electrons in octahedral complexes is fixed at the same number as in the free ion, regardless of the strength of the crystal field, is the **d3 ion**.

### Summary of the Solution
- The number of unpaired electrons in octahedral complexes is fixed for **d3 ions**.
- This is because the three electrons will fill the t2g orbitals without pairing, irrespective of whether the ligands are strong or weak.