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# 7.6: Extra Readings for Chapter 7

Difficulty Level: At Grade Created by: CK-12

## Orbital Filling Order Exceptions

In assembling the electron configurations for many-electron atoms, one tool that students find valuable is the diagonal rule. This rule provides a guideline that is readily remembered and easily followed to produce accurate electron configurations for even complicated d\begin{align*}d-\end{align*} and f\begin{align*}f-\end{align*} block atoms. One confusing consequence of the diagonal rule is the order of filling the 4s\begin{align*}4s\end{align*} and 3d\begin{align*}3d\end{align*} subshells.

When these orbitals are filled, they are very close in energy. Though as the electrons begin to occupy the empty orbitals, the 4s level is slightly lower in energy than the 3d\begin{align*}3d\end{align*}, thus it is filled first. On the other hand, when both are occupied with electrons, the 4d\begin{align*}4d\end{align*} orbital becomes higher in energy. Thus, in the case that both of these filled levels are composed of valence electrons, the 4s\begin{align*}4s\end{align*} level loses its valence electrons before the 3d\begin{align*}3d\end{align*} level.

The preferential filling of the 4s\begin{align*}4s\end{align*} orbital can also be explained by means of the electron penetration effect. Due to the spherical shape of the s\begin{align*}s\end{align*} orbital probability density distribution, the likelihood that an electron is found closer to the nucleus is greater than the multi-lobed 3d\begin{align*}3d\end{align*} orbitals.

The similarity in the energy levels of the 4s\begin{align*}4s\end{align*} and 3d\begin{align*}3d\end{align*} orbitals also leads to another interesting consequence. In the electron configuration of the neutral Chromium atom with 24\begin{align*}24\end{align*} electrons, the diagonal rule suggests an electron configuration of 1s22s22p63s23p64s23d4\begin{align*}1s^22s^22p^63s^23p^64s^23d^4\end{align*}. The actual electron configuration is 1s22s22p63s23p64s13d5\begin{align*}1s^22s^22p^63s^23p^64s^13d^5\end{align*}, where due to the similarity in energy between the 4s\begin{align*}4s\end{align*} and 3d\begin{align*}3d\end{align*} orbitals, one electron transfers from the 4s\begin{align*}4s\end{align*} to the 3d\begin{align*}3d\end{align*} orbital. The net effect of this exchange yields half-filled 4s\begin{align*}4s\end{align*} and 3d\begin{align*}3d\end{align*} orbitals, and therefore can be justified in terms of generating additional stability. This is also the case for neutral copper atoms, with 29\begin{align*}29\end{align*} electrons and a putative electron configuration of 1s22s22p63s23p64s23d9\begin{align*}1s^22s^22p^63s^23p^64s^23d^9\end{align*}. Again as in the example of chromium, an electron transfer occurs, shifting one electron from the 4s\begin{align*}4s\end{align*} orbital to the 3d\begin{align*}3d\end{align*} orbital. For copper, the 4s\begin{align*}4s\end{align*} orbital is now half-filled but added stability is attained by completing the 3d subshell.

The stability afforded to half-filled orbitals is also noted among the \begin{align*}f-\end{align*}block elements. For example, the electron configuration for Europium (atomic number \begin{align*}63\end{align*}) is \begin{align*}1s^22s^22p^63s^23p^64s^23d^{10}\end{align*} \begin{align*}4p^65s^24d^{10}5p^66s^24f^7\end{align*} whereas the next atom, Gadolinium, with atomic number \begin{align*}64\end{align*}, has the additional electron added to the \begin{align*}5d\end{align*} orbital in order to maintain the half-filled stability of the \begin{align*}4f^7\end{align*} configuration. The electron configuration for Gadolinium is therefore \begin{align*}1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^24d^{10}5p^6\end{align*} \begin{align*}6s^24f^75d^1\end{align*}.

The unusual stability of half-filled orbitals can be explained in terms of the disruption afforded by the addition of another electron to this configuration. After the orbital is half-filled, the next additional electron must pair up with another electron, increasing the spin-spin interaction energy and destabilizing the configuration.

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