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Q4.1(iv):
Write down the electronic configuration of: (iv) \(Ce^{4+}\)

Solution :

Step 1: Establishing the Neutral Atomic State

To determine the electronic configuration of the ion $Ce^{4+}$, we must first establish the configuration of the neutral Cerium (Ce) atom. Cerium is a lanthanide element with an atomic number ($Z$) of $58$.

The electronic configuration of a neutral atom is governed by the Aufbau Principle, which dictates that orbitals are filled in order of increasing energy ($1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d$).

The noble gas core preceding Cerium is Xenon ($Xe$, $Z=54$).

Neutral $Ce$ ($Z=58$): $[Xe] \, 4f^1 \, 5d^1 \, 6s^2$ [Per the Aufbau Principle, accounting for the specific orbital occupancy of the lanthanide series].

Step 2: Ionization Process of $Ce^{4+}$

The formation of a cation involves the removal of electrons from the highest energy orbitals (outermost shells) first. Specifically, electrons are removed from the $6s$ orbital before the $5d$ or $4f$ orbitals due to higher principal quantum numbers ($n$) and shielding effects.

The configuration of neutral Cerium is $[Xe] \, 4f^1 \, 5d^1 \, 6s^2$.

To obtain $Ce^{4+}$, we must remove $4$ electrons in the following sequence:

  • First two electrons: Removed from the $6s$ orbital. Configuration becomes $[Xe] \, 4f^1 \, 5d^1$.
  • Third electron: Removed from the $5d$ orbital. Configuration becomes $[Xe] \, 4f^1$.
  • Fourth electron: Removed from the $4f$ orbital. Configuration becomes $[Xe]$.

Step 3: Verification of the Final State

Upon the removal of all four electrons, the resulting electronic configuration corresponds to the stable noble gas configuration of Xenon ($Z=54$).

Initial: Ce (Z=58) = [Xe] 4f¹ 5d¹ 6s² Process: Remove 4e⁻ from outer orbitals Final: Ce⁴⁺ = [Xe]

Summary of Electronic Configuration

Species Electronic Configuration
$Ce$ (Neutral) $[Xe] \, 4f^1 \, 5d^1 \, 6s^2$
$Ce^{4+}$ (Ion) $[Xe]$ or $1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^6$

Final Solution: The electronic configuration of $Ce^{4+}$ is $[Xe]$.


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