What are the different oxidation states exhibited by the lanthanoids?

Explanation

To determine the different oxidation states exhibited by the lanthanides, we can follow these steps:

### Step 1: Write the General Electronic Configuration
The first step is to note the general electronic configuration of the lanthanides. The lanthanides are elements with atomic numbers from 57 (Lanthanum) to 71 (Lutetium). Their general electronic configuration can be written as:
\[ \text{Xe} \, 4f^{1-14} \, 5d^1 \, 6s^2 \]

### Step 2: Identify Possible Oxidation States
Next, we identify the possible oxidation states based on the electronic configuration. The common oxidation states for lanthanides include:
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