Question

Gd(64) has __________ unpaired electrons with sum of spin __________

• A. 7, 3.5
• B. 8, 4
• C. 6, 3
• D. 8, 3
• E. 9, 3.5

Hint:

Gadolinium is highly paramagnetic because it possesses 8 unpaired electrons, the highest number among the lanthanide elements in their ground state.

Answer 1

The Correct Option is B

Concept: The electronic configuration of Lanthanides follows the filling of the $4f$ subshell. Gadolinium (Gd, $Z=64$) is a notable exception due to the extra stability of a half-filled $f$-subshell. The total spin $S$ is calculated as: \[ S = n \times \left( \frac{1}{2} \right) \] where $n$ is the number of unpaired electrons.

Step 1: Write the electronic configuration.
The noble gas preceding Gadolinium is Xenon ($Z=54$). The expected configuration would be $[Xe] 4f^8 6s^2$. However, to achieve a stable half-filled $4f^7$ configuration, one electron resides in the $5d$ orbital: \[ Gd (Z=64): [Xe] 4f^7 5d^1 6s^2 \]

Step 2: Identify unpaired electrons.

• The $4f$ subshell has 7 orbitals, all of which are singly occupied (7 unpaired electrons).
• The $5d$ subshell has 1 electron, which is unpaired (1 unpaired electron).
• The $6s$ subshell is fully filled (0 unpaired electrons). Total unpaired electrons \( n = 7 + 1 = 8 \).

Step 3: Calculate the sum of spin.
Each unpaired electron has a spin of \( \frac{1}{2} \): \[ \text{Sum of spin} = 8 \times \frac{1}{2} = 4 \]