The electronic configuration of gadolinium (Atomic number 64) is

As z= 64 so the nearest noble gases would be xenon. After that 10 electrons would be left so the configuration is given by this option. filling of s orbitals of nth shell takes before the filling of d orbitals of (n-1)th shell. Therefore, option ii) is incorrect. Options i) and iv) are incorrect as in the third option f orbital has half filled stability which results in the stability of the whole atom.