The outer electronic configuration of two members of the lanthanoid series are as follows `:`
`4f^(1) 5d^(1) 6s^(2)` and `4f^(7) 5d^(-) 6s^(2)`
What are their atomic numbers ? Predict the oxidation states exhibited by these elements in their compounds.

Explanation

To solve the problem, we need to identify the two members of the lanthanoid series based on their outer electronic configurations and determine their atomic numbers and possible oxidation states.

### Step-by-Step Solution:

1. **Identify the First Element:**
- The outer electronic configuration given is `4f^1 5d^1 6s^2`.
- This configuration corresponds to the element Cerium (Ce).
- To find the atomic number, we can refer to the periodic table. Cerium has an atomic number of **58**.
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