Electronic configuration of the outer shell of the element Gd with atomic number 64 is

The correct option is 4f⁷ 5d¹ 6s².

To determine the electronic configuration of Gadolinium (Gd) with atomic number Z = 64, we can break it down step-by-step:

1. Identify the nearest noble gas core:
The noble gas preceding Gadolinium (Z = 64) is Xenon (Xe) with atomic number Z = 54. The electron configuration of Xenon is:
[Xe] = 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶

2. Determine the remaining electrons:
Subtracting the 54 electrons of Xenon from the total 64 electrons of Gadolinium leaves us with:
64 - 54 = 10 electrons to be filled in the outer shells (4f, 5d, and 6s orbitals).

3. Expected vs. Actual filling based on orbital stability:
According to the Aufbau principle, we first fill the 6s orbital with 2 electrons. This leaves 8 electrons.
The expected configuration for the remaining 8 electrons might be to place them all in the 4f subshell, which would give:
4f⁸ 6s²
However, orbitals that are empty, half-filled, or fully filled possess extra stability due to symmetrical distribution of electron density and high exchange energy.
For the f-subshell, a half-filled state occurs at 4f⁷ (since the f-subshell has 7 orbitals and can hold a maximum of 14 electrons).
To achieve this highly stable half-filled 4f⁷ configuration, one electron is shifted to the next higher energy orbital, which is the 5d orbital.

4. Final Outer Shell Configuration:
Thus, the 10 valence electrons are distributed as:
7 electrons in the 4f subshell (making it stable half-filled),
1 electron in the 5d subshell, and
2 electrons in the 6s subshell.
This yields the outer shell configuration:
4f⁷ 5d¹ 6s²