Identify the element and its position

Gadolinium, $\mathrm{Gd}$, has atomic number $64$.

Start from the nearest noble gas core

The noble gas preceding $\mathrm{Gd}$ is xenon, $\mathrm{Xe}$, with atomic number $54$.

So after $[\mathrm{Xe}]$, there are: $64-54=10$ electrons left to place.

Understand the filling in lanthanides

In the lanthanide series, electrons are generally filled into the $4f$ subshell, with occasional occupation of the $5d$ subshell for extra stability.

Gadolinium is one such special case because a half-filled $4f^7$ configuration is especially stable.

Write the configuration of $\mathrm{Gd}$

Therefore, instead of $[\mathrm{Xe}]\,4f^8 6s^2$, gadolinium adopts: $[\mathrm{Xe}]\,4f^7 5d^1 6s^2$

Match with the options

• A: $4f^3\,5d^5\,6s^2$ — incorrect
• B: $4f^8\,5d^0\,6s^2$ — not the actual ground-state configuration of $\mathrm{Gd}$
• C: $4f^4\,5d^4\,6s^2$ — incorrect
• D: $4f^7\,5d^1\,6s^2$ — correct

Final answer

The outer electron configuration of $\mathrm{Gd}$ is: $4f^7\,5d^1\,6s^2$

So, the correct option is D.