Question

Observe the following f-block elements: Eu (Z = 63); Pu (Z = 94); Cf (Z = 98); Sm (Z = 62); Gd (Z = 64); Cm (Z = 96) How many of the above have half-filled f-orbitals in their ground state?

• A. 3
• B. 4
• C. 2
• D. 5

Hint:

For f-block elements, the stability of half-filled and fully filled f-orbitals plays a key role in their chemical properties and electron configurations. Always check the number of electrons in the f-orbitals when determining their stability.

Answer 1

The Correct Option is A

In order to determine which elements from the given list have half-filled f-orbitals in their ground state, let's first examine the electronic configurations of the f-block elements. The key to understanding this is recognizing that some elements, particularly in the lanthanide and actinide series, have half-filled or fully filled f-orbitals due to their electron configuration.

Step 1: Analyze Electron Configurations

• Eu (Z = 63): Europium has the electron configuration \( [Xe] 4f^7 6s^2 \). The \( 4f^7 \) configuration is a half-filled f-orbital configuration, meaning it has 7 electrons in the 4f subshell, which is half of the possible 14 electrons that can fill the 4f subshell.
• Sm (Z = 62): Samarium has the electron configuration \( [Xe] 4f^6 6s^2 \). Although the 4f orbital is not completely filled, it is close to a half-filled configuration with 6 electrons in the 4f subshell. However, it is not strictly half-filled as it only has 6 electrons (while half of 14 is 7).
• Cm (Z = 96): Curium has the electron configuration \( [Rn] 5f^7 6d^1 7s^2 \). Similar to Europium, Curium has a \( 5f^7 \) configuration, which is half-filled.
• Pu (Z = 94): Plutonium has the electron configuration \( [Rn] 5f^6 6d^0 7s^2 \). Here, the 5f orbital is not half-filled because it has only 6 electrons in the 5f subshell, not 7.
• Gd (Z = 64): Gadolinium has the electron configuration \( [Xe] 4f^7 5s^2 \), which is another half-filled f-orbital configuration. Gd has 7 electrons in the 4f subshell.
• Cf (Z = 98): Californium has the electron configuration \( [Rn] 5f^{10} 6d^0 7s^2 \). It does not have a half-filled f-orbital, as its 5f orbital is completely filled with 10 electrons.

Step 2: Identify Elements with Half-Filled f-Orbitals From the above analysis, the following elements have half-filled f-orbitals in their ground state:

• Eu (Z = 63) with \( 4f^7 \)
• Gd (Z = 64) with \( 4f^7 \)
• Cm (Z = 96) with \( 5f^7 \)

Step 3: Conclusion Thus, the correct answer is: \[ \boxed{3} \]