Question

What is the electron configuration of ${pt^{+2}}$ according to the Madelung rule?

Answer 1

Hint : The distribution of electrons in an element's atomic orbitals is defined by its electron configuration. Atomic electron configurations follow a standard notation in which all electron-containing atomic subshells are arranged in a series (with the number of electrons they possess written in superscript).


Complete step-by-step solution:
The energy of an electron in an atom increases as n, the principal quantum number, increases. There are sub-levels within an energy level described by n, which are defined by the angular momentum quantum number l, which takes integral values of zero to one $(n - 1)$
The sublevels are s p d f, etc., in order of increasing energy (for the same n).
The Madelung Rule states that an electron's energy is proportional to the value of $(n + 1)$ . As a result, we have the so-called "Aufbau Principle."
As complex electron interactions occur after calcium, the law begins to break down. These become increasingly important as the electron energy levels for larger atoms get closer and closer together.
The 3d loses energy in comparison to the 4s in the first transformation sequence (different texts give different results when this exactly happens).
This effectively means that the 4 s has a slightly higher energy, and these electrons are lost first, defining the atomic radius. As previously mentioned, the 4s-3d interactions are more complex than they seem.
We get $(n + 1) = 4 + 0 = 4$ for 4s.
We get $(n + 1) = 3 + 2 = 5$ for 3d. i.e. more energetic.
Pt2+ has the electron structure \[\left[ {Xe} \right]4{f^{14}}5{d^{8.}}\]
Let's use the Madelung Rule as an example:
 \[\left[ {Xe} \right]6{s^2}4{f^{14}}5{d^{8.}}\]
We get $(n + 1) = 6 + 0 = 6$ for 6s.
We get $(n + 1) = 4 + 3 = 7$ for 4f.
We get 5d8 as a result \[5 + 2 = 7\] .
When two subshells have the same $(n + 1)$ value, i.e. 7, the subshell with the highest n value is said to have more energy.
$P{t^{ + 2}}$ is obtained by discarding the 6s and one from the 5d.
\[ \left[ {Xe} \right]4{f^{14}}5{d^{8.}}\]

Note: These electrons should always fill shells and subshells in the order of increasing energy levels, according to the Aufbau theory. Copper and chromium, for example, are exceptions since their electrons fill and half-fill two subshells, with some electrons in higher energy level shells.