The electronic configuration of bivalent Europium and trivalent cerium respectively is: (Atomic Number: Xe = 54, Ce = 58, Eu = 63)

Options

A. `[Xe]4f^(7)` and `[Xe] 4^(1)`
B. `[Xe]4f^(4)` and `[Xe]4f^(9)`
C. `[Xe]4f^(2)` and `[Xe]4f^(7)`
D. `[Xe]4f^(7) 6s^(2)` and `[Xe]4f^(2)6s^(2)`

Answer

To determine the electronic configurations of bivalent Europium (Eu) and trivalent Cerium (Ce), we start by knowing their atomic numbers and the electronic configuration of the noble gas Xenon (Xe), which has an atomic number of 54.

### Step 1: Write the electronic configuration of Xenon (Xe)
The electronic configuration of Xenon is:
\[ \text{Xe} = 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 \]
This can be summarized as:
\[ \text{Xe} = [Kr] 5s^2 4d^{10} 5p^6 \]
Where Kr is Krypton, the noble gas preceding Xenon.

### Step 2: Determine the electronic configuration of Europium (Eu)
Europium has an atomic number of 63. To find its electronic configuration, we start from Xenon and add the remaining electrons:
- Total electrons = 63
- Electrons in Xenon = 54
- Remaining electrons = 63 - 54 = 9

The filling order for electrons after Xenon is:
1. 6s
2. 4f

Thus, the configuration for Europium will be:
\[ \text{Eu} = [Xe] 6s^2 4f^7 \]

Since we are looking for the bivalent form of Europium (Eu²⁺), we remove two electrons from the outermost shell:
\[ \text{Eu}^{2+} = [Xe] 4f^7 \]

### Step 3: Determine the electronic configuration of Cerium (Ce)
Cerium has an atomic number of 58. Again, we start from Xenon:
- Total electrons = 58
- Electrons in Xenon = 54
- Remaining electrons = 58 - 54 = 4

Following the same filling order:
1. 6s
2. 4f

Thus, the configuration for Cerium will be:
\[ \text{Ce} = [Xe] 6s^2 4f^2 \]

For the trivalent form of Cerium (Ce³⁺), we remove three electrons, typically from the 6s and 4f orbitals:
\[ \text{Ce}^{3+} = [Xe] 4f^1 \]

### Final Answer
The electronic configurations are:
- Bivalent Europium (Eu²⁺): \[ [Xe] 4f^7 \]
- Trivalent Cerium (Ce³⁺): \[ [Xe] 4f^1 \]

Thus, the answer is:
\[ [Xe] 4f^7 \text{ and } [Xe] 4f^1 \]