Question

What is the electronic configuration of Gd (atomic number $$\text{ = 64amu}$$):
$\left[\text{Xe}\right]\text{4}{\text{f}}^{\text{8}}\text{5}{\text{d}}^{\text{9}}\text{6}{\text{s}}^{\text{2}}$
$\left[\text{Xe}\right]\text{4}{\text{f}}^7\text{5}{\text{d}}^1\text{6}{\text{s}}^{\text{2}}$
$\left[\text{Xe}\right]\text{4}{\text{f}}^5\text{5}{\text{d}}^2\text{6}{\text{s}}^{\text{2}}$
$\left[\text{Xe}\right]\text{4}{\text{f}}^3\text{5}{\text{d}}^3\text{6}{\text{s}}^{\text{2}}$

Answer 1

Hint: (1) Electronic configuration is a representation of the distribution of electrons in an atom. Gd or gadolinium is an element of the Lanthanide series, i.e., it is an f-block element. An f-block element has partially filled subshell of the third to the outermost energy shells in its elementary or ionic state.
(2)The lanthanide series consists of lanthanum, cerium, praseodymium, neodymium, promethium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium and lutetium. The general electronic configuration of the lanthanides is $\left[\text{Xe}\right]\text{4}{\text{f}}^{1-14}\text{5}{\text{d}}^{0-1}\text{6}{\text{s}}^{\text{2}}$with minor exceptions.

Complete step by step answer:
Generally, the lanthanides follow the Aufbau principle for their electronic configurations, with few exceptions. According to the Aufbau principle, a maximum of two electrons can be put into orbitals of increasing orbital energy and the lowest energy orbitals are filled by the electrons before the filling of higher energy orbitals. Orbitals are filled in the order of increasing $\text{n + l}$ values, where n is the principal quantum number and l is the Azimuthal quantum number. If two orbitals have the same value of $\text{n + l}$, they are filled in the increasing order of n. Thus, the order of filling of orbitals is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p etc.
The portion of the electronic configuration which is equivalent to the noble gas of the preceding period is depicted by that noble gas symbol within parentheses. For example, upto fully filled $\text{5}{\text{p}}^{\text{6}}$the electronic configuration can be depicted as $\left[\text{Xe}\right]$ which has atomic number 54.
Now, the lanthanides consist of lanthanum (atomic number 57) and the next 14 elements (atomic number 58 to 71). The configuration of lanthanum is $\left[\text{Xe}\right]\text{5}{\text{d}}^1\text{6}{\text{s}}^{\text{2}}$and in the next succeeding 14 elements, 14 electrons are added to the 4f subshell of the lanthanum configuration successively. Thus, in cerium which immediately succeeds lanthanum, one 4f electron is added to lanthanum configuration and in the last element lutetium, 14 4f electrons are added. Thus, the electronic configuration of cerium is $\left[\text{Xe}\right]\text{4}{\text{f}}^1\text{5}{\text{d}}^1\text{6}{\text{s}}^{\text{2}}$and that of lutetium is $\left[\text{Xe}\right]\text{4}{\text{f}}^{14}\text{5}{\text{d}}^1\text{6}{\text{s}}^{\text{2}}$. Proceeding in this way, the ${\text{7}}^{\text{th}}$ lanthanide element which succeeds lanthanum will be gadolinium $\left(\text{Gd}\right)$which has atomic number 64 and so seven 4f electrons will be added to the lanthanum configuration and so its electronic configuration is $\left[\text{Xe}\right]\text{4}{\text{f}}^7\text{5}{\text{d}}^1\text{6}{\text{s}}^{\text{2}}$. Thus, option B is correct.
The $\left[\text{Xe}\right]\text{4}{\text{f}}^{\text{8}}\text{5}{\text{d}}^{\text{9}}\text{6}{\text{s}}^{\text{2}}$ configuration represents atomic number 73 which does not fall under lanthanides since lanthanides have atomic number 57 to 71. So A is not the correct option.
The $\left[\text{Xe}\right]\text{4}{\text{f}}^5\text{5}{\text{d}}^2\text{6}{\text{s}}^{\text{2}}$ configuration represents atomic number 63 which falls under lanthanides. But it is for europium which actually has $\left[\text{Xe}\right]\text{4}{\text{f}}^7\text{6}{\text{s}}^{\text{2}}$configuration. So it doesn’t represent Gd and so C is not correct.
The $\left[\text{Xe}\right]\text{4}{\text{f}}^3\text{5}{\text{d}}^3\text{6}{\text{s}}^{\text{2}}$ configuration represents atomic number 62 which falls under lanthanides but it is for samarium which actually has $\left[\text{Xe}\right]\text{4}{\text{f}}^6\text{6}{\text{s}}^{\text{2}}$ configuration. So it doesn’t represent Gd and so D is also not correct.

Note:
Due to the complexity of the electronic spectra of these elements, there is an alternative probable electronic configuration for lanthanides. According to this alternative view, the solitary 5d electron gets shifted into the 4f subshell in all the lanthanide elements except in gadolinium where such a shift will destroy the symmetry and stability of its half-filled f subshell. For example, the alternative configuration of europium with $\left[\text{Xe}\right]\text{4}{\text{f}}^6\text{5}{\text{d}}^1\text{6}{\text{s}}^{\text{2}}$configuration is $\left[\text{Xe}\right]\text{4}{\text{f}}^7\text{6}{\text{s}}^{\text{2}}$but in gadolinium it is always $\left[\text{Xe}\right]\text{4}{\text{f}}^7\text{5}{\text{d}}^1\text{6}{\text{s}}^{\text{2}}$.