The number of unpaired electrons in Gadolinium $$[Z = 64]$$ is

The ground-state electronic configuration of Gadolinium ($$Z = 64$$) has to be written by adding 10 electrons beyond$$[Xe]$$ ($$Z = 54$$).

Energy order after xenon is: $$6s \lt 4f \lt 5d \lt 6p$$. Thus the subshells are filled in this sequence:

• $$6s^2$$   ($$54 + 2 = 56$$) • $$4f$$ begins and can accommodate $$14$$ electrons. The lanthanide series corresponds to the gradual filling of $$4f$$.

If the normal Aufbau order were strictly followed, Gd ($$Z = 64$$) would become $$[Xe]\,4f^8\,6s^2$$. However, a half-filled $$4f^7$$ subshell is especially stable. To achieve that stability, one electron is promoted from $$4f$$ to the next available $$5d$$ subshell. Therefore the actual configuration is

$$[Xe]\,4f^7\,5d^1\,6s^2$$

Counting unpaired electrons:

• $$4f^7$$ (half-filled): each of the seven $$4f$$ orbitals contains one electron ⇒ $$7$$ unpaired electrons.
• $$5d^1$$: a single electron ⇒ $$1$$ unpaired electron.
• $$6s^2$$: paired electrons ⇒ $$0$$ unpaired electrons.

Total unpaired electrons $$= 7 + 1 = 8$$.

Hence, the number of unpaired electrons in Gadolinium is $$8$$.

Option B which is: 8