Which of the following oxidation states is the most common among the lanthanoids ?

Options

A. `+2`
B. `+3`
C. `+4`
D. `+5`

Explanation

To determine the most common oxidation state among the lanthanoids, we can follow these steps:

### Step 1: Understand the Lanthanoids
Lanthanoids are a series of 15 elements in the periodic table, from cerium (Ce) to lutetium (Lu). They are f-block elements and are known for their unique electronic configurations.

**Hint:** Remember that lanthanoids are f-block elements, which means they fill the f-orbitals.

### Step 2: Identify the Common Oxidation States
The common oxidation states of lanthanoids are +2, +3, and +4. However, we need to identify which of these is the most prevalent.

**Hint:** Consider the stability of the electronic configurations when determining oxidation states.

### Step 3: Analyze the +3 Oxidation State
The +3 oxidation state is the most common among lanthanoids. This is because when lanthanoids lose three electrons, they achieve a stable electronic configuration. For example, cerium (Ce) in the +3 state has an f-electron configuration of f1, while lutetium (Lu) in the +3 state has an f-electron configuration of f14.

**Hint:** Look for patterns in the electronic configurations that result from losing three electrons.

### Step 4: Consider Other Oxidation States
While +2 and +4 oxidation states are also observed, they are less common. The +2 state may arise from stable configurations like f7, and the +4 state may arise from configurations like f14. However, these states are not as frequently encountered as the +3 state.

**Hint:** Think about the stability of half-filled and fully filled f-orbitals when considering why +2 and +4 states are less common.

### Step 5: Conclusion
Based on the analysis, the most common oxidation state among the lanthanoids is +3.

**Final Answer:** The most common oxidation state among the lanthanoids is +3.