Although Madelung's rule for the filling of electronic...

Although Madelung's rule for the filling of electronic shells holds extremely well, there are a number of exceptions to the rule. Here are a few of them: $$ \begin{aligned} &\mathrm{Cu}=[\mathrm{Ar}] 4 \mathrm{~s}^{1} 3 \mathrm{~d}^{10} \\ &\mathrm{Pd}=[\mathrm{Kr}] 5 \mathrm{~s}^{0} 4 \mathrm{~d}^{10} \\ &\mathrm{Ag}=[\mathrm{Kr}] 5 \mathrm{~s}^{1} 4 \mathrm{~d}^{10} \\ &\mathrm{Au}=[\mathrm{Xe}] 6 \mathrm{~s}^{1} 4 \mathrm{f}^{14} 5 \mathrm{~d}^{10} \end{aligned} $$ D What should the electron configurations be if these elements followed Madelung's rule and the Aufbau principle? D Explain how the statement "3d is inside of $4 \mathrm{~s} "$ might help justify this exception in copper.

Although Madelung's rule for the filling of electronic shells holds extremely well, there are a number of exceptions to the rule. Here are a few of them:
$$
\begin{aligned}
&\mathrm{Cu}=[\mathrm{Ar}] 4 \mathrm{~s}^{1} 3 \mathrm{~d}^{10} \\
&\mathrm{Pd}=[\mathrm{Kr}] 5 \mathrm{~s}^{0} 4 \mathrm{~d}^{10} \\
&\mathrm{Ag}=[\mathrm{Kr}] 5 \mathrm{~s}^{1} 4 \mathrm{~d}^{10} \\
&\mathrm{Au}=[\mathrm{Xe}] 6 \mathrm{~s}^{1} 4 \mathrm{f}^{14} 5 \mathrm{~d}^{10}
\end{aligned}
$$
D What should the electron configurations be if these elements followed Madelung's rule and the Aufbau principle?
D Explain how the statement "3d is inside of $4 \mathrm{~s} "$ might help justify this exception in copper.

Key Concepts

Electron Configuration Exceptions

Despite the reliability of the Madelung rule and Aufbau principle, certain elements deviate from the predicted electron configurations. These exceptions occur because the real energy differences between orbitals can be affected by electron–electron interactions, exchange energy, and other quantum mechanical effects. Understanding these exceptions helps in grasping that simple rules sometimes do not account for all the complexities of electron distributions in atoms.

Madelung's Rule

This rule, also known as the n+l rule, predicts the order in which electron subshells are filled in an atom. According to the rule, subshells with lower values of the sum of the principal quantum number (n) and the azimuthal quantum number (l) are filled before those with higher sums. It is a guideline that provides the expected order of orbital filling under the idealized conditions of electron distribution, although it sometimes fails to predict the actual electron configuration in cases where additional effects come into play.

Aufbau Principle

The Aufbau principle is a foundational concept in chemistry that states electrons occupy orbitals starting from the lowest available energy level and move to higher energy levels as lower ones become filled. It provides the basis for constructing electron configurations by implying a hierarchical order of orbital energies that electrons follow as they are added to an atomic system.

Orbital Penetration and Shielding Effects

Orbital penetration refers to the extent an electron in a particular orbital can get close to the nucleus, thereby experiencing a higher effective nuclear charge, while shielding describes the reduction in nuclear attraction experienced by an electron due to the presence of other electrons. The relative penetration and shielding of orbitals, such as the inner nature of a d orbital compared to an s orbital, can lead to unexpected stability and reordering in electron configurations, providing insight into exceptions observed in transition elements.

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