Question

Pairs of elements with the same number of electrons in their respective 4f orbital are
[Atomic number: Eu-63, Gd-64, Dy-66, Ho-67, Tm-69, Yb-70, Lu-71, Hf-72]
A. (Eu and Gd)
B. (Dy and Ho)
C. (Yb and Hf)
D. (Lu and Tm)
Choose the correct answer from the options given below:

• A. B and C Only
• B. A and B Only
• C. A and D Only
• D. A and C Only

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Write down the electronic configurations of the given Lanthanide and transition series elements using Aufbau principles and the known half-filled/fully-filled stability anomalies. Compare the specific electron count populating the $4f$ subshell.
Step 2: Key Formula or Approach:
General Lanthanide config: $[\text{Xe}] 4f^{1-14} 5d^{0-1} 6s^2$.
Exceptions occur at half-filled ($f^7$) and fully-filled ($f^{14}$) states, where an electron occupies the $5d$ orbital instead to preserve $f$-shell symmetry.
Step 3: Detailed Explanation:
Let's deduce the configuration for each element:
- Eu (63): $[\text{Xe}] 4f^7 6s^2$ $\implies$ 7 electrons in $4f$.
- Gd (64): $[\text{Xe}] 4f^7 5d^1 6s^2$ $\implies$ 7 electrons in $4f$. (Anomaly to maintain half-filled stability).
- Dy (66): $[\text{Xe}] 4f^{10} 6s^2$ $\implies$ 10 electrons in $4f$.
- Ho (67): $[\text{Xe}] 4f^{11} 6s^2$ $\implies$ 11 electrons in $4f$.
- Tm (69): $[\text{Xe}] 4f^{13} 6s^2$ $\implies$ 13 electrons in $4f$.
- Yb (70): $[\text{Xe}] 4f^{14} 6s^2$ $\implies$ 14 electrons in $4f$.
- Lu (71): $[\text{Xe}] 4f^{14} 5d^1 6s^2$ $\implies$ 14 electrons in $4f$. (Anomaly to maintain fully-filled stability).
- Hf (72): $[\text{Xe}] 4f^{14} 5d^2 6s^2$ $\implies$ 14 electrons in $4f$. (Post-lanthanide transition metal).
Check the given pairs:
A. (Eu and Gd): $4f^7$ and $4f^7$. Match! (Both have 7)
B. (Dy and Ho): $4f^{10}$ and $4f^{11}$. No match.
C. (Yb and Hf): $4f^{14}$ and $4f^{14}$. Match! (Both have 14)
D. (Lu and Tm): $4f^{14}$ and $4f^{13}$. No match.
Therefore, pairs A and C are the correct ones.
Step 4: Final Answer:
Options A and C Only are correct.