Question

Which of the following elements have half-filled f-orbitals in their ground state?
(Given : atomic number $Sm =62 ; Eu =63 ; Tb =65 ; Gd =64, Pm =61$ )
A. $Sm$
B. $Eu$
C. $Tb$
D. $Gd$
E. $Pm$
Choose the correct answer from the options given below :

• A. A and B only
• B. C and D only
• C. B and D only
• D. A and E only

Hint:

Half-filled orbitals, such as in \( 4f^7 \), lead to more stable electronic configurations due to the symmetry and exchange energy.

Answer 1

The Correct Option is C

To determine which elements have half-filled f-orbitals in their ground state, we need to analyze the electronic configurations of the given elements based on their atomic numbers:

1. The f-block elements or lanthanides begin filling their 4f orbitals. Typically, filling starts after xenon as the 5d and 6s sublevels fill.
2. We will calculate the electronic configurations focusing mainly on the 4f sublevel.

Electronic Configurations:

• Samarium (Sm), Atomic Number 62: The configuration is [Xe] 4f⁶ 6s².
• Europium (Eu), Atomic Number 63: The configuration is [Xe] 4f⁷ 6s². This configuration is noted for having a half-filled 4f subshell.
• Promethium (Pm), Atomic Number 61: The configuration is [Xe] 4f⁵ 6s².
• Gadolinium (Gd), Atomic Number 64: The configuration is [Xe] 4f⁷ 5d¹ 6s². It also has a half-filled 4f subshell despite the presence of one electron in the 5d subshell.
• Terbium (Tb), Atomic Number 65: The configuration is [Xe] 4f⁹ 6s².

Analyzing these configurations, we observe:

• Europium (Eu) and Gadolinium (Gd) have half-filled 4f subshells (4f⁷).

Conclusion: The elements that have half-filled f-orbitals in their ground state are Europium (Eu) and Gadolinium (Gd). Therefore, the correct answer is B and D only.