In which of the following actinoid elements \(6d\) subshell is vacant?

Pu, Plutonium

The correct answer is option 4. Pu, Plutonium.

To determine which actinoid element has a vacant \(6d\) subshell, we need to analyze the electron configurations of the specified elements. The actinoids are elements with atomic numbers ranging from 89 (Actinium) to 103 (Lawrencium), and their electron configurations are crucial for understanding the occupancy of their subshells.

Electron Configurations of the Actinoid Elements:

1. Protactinium (Pa)

Atomic Number: 91

Electron Configuration: \([Rn] 5f^2 6d^1 7s^2\)

Protactinium has an electron configuration where the \(6d\) subshell contains 1 electron. Therefore, it does not have a vacant \(6d\) subshell.

2. Neptunium (Np)

Atomic Number: 93

Electron Configuration: \([Rn] 5f^4 6d^1 7s^2\)

Neptunium’s electron configuration includes 1 electron in the \(6d\) subshell. Consequently, the \(6d\) subshell is not vacant in Neptunium.

3. Plutonium (Pu)

Atomic Number: 94

Electron Configuration: \([Rn] 5f^6 7s^2\)

Plutonium’s electron configuration shows that the \(6d\) subshell is absent entirely. Thus, the \(6d\) subshell is vacant in Plutonium.

4. Lawrencium (Lr)

Atomic Number: 103

Electron Configuration: \([Rn] 5f^{14} 6d^1 7s^2\)

Lawrencium has 1 electron in the \(6d\) subshell, indicating that it does not have a vacant \(6d\) subshell.

Detailed Analysis:

The electron configuration for each actinoid reflects the arrangement of electrons in their atomic orbitals. For the actinoids, the \(5f\) subshell is progressively filled, and the \(6d\) and \(7s\) subshells are populated as well. Protactinium, Neptunium, and Lawrencium each have electrons in the \(6d\) subshell, which means their \(6d\) subshells are not vacant. Plutonium, on the other hand, has a configuration where the \(6d\) subshell does not appear at all. This is due to the fact that, in the electron filling process for Plutonium, the electrons occupy the \(5f\) and \(7s\) subshells, while the \(6d\) subshell remains empty.

Conclusion:

Among the given actinoid elements, Plutonium (Pu) is the only one with a vacant \(6d\) subshell. This characteristic is crucial for understanding its chemical properties and reactivity, which differ significantly from those of other actinoids with electrons in their \(6d\) subshells.