Question

Explain why the ground-state electron configurations of \(\mathrm{Cr}\) and \(\mathrm{Cu}\) are different from what we might expect.

Short answer

Cr and Cu have electron configurations favoring half/full d subshells for enhanced stability.

Step-by-step solution

Determine Expected Configuration for Cr

The expected electron configuration for chromium ( Cr ) would be [Ar] 3d^4 4s^2 based on the order of filling orbitals, which is from lower to higher energy levels following the Aufbau principle.

Observe Actual Configuration of Cr

The actual electron configuration for chromium is found to be [Ar] 3d^5 4s^1 . Instead of filling the 4s orbital completely before moving to 3d , an electron from 4s is moved to 3d to achieve a half-filled 3d^5 which adds extra stability due to reduced electron-electron repulsion and increased exchange energy.

Determine Expected Configuration for Cu

Following the order of filling orbitals, copper ( Cu ) would be expected to have the electron configuration [Ar] 3d^9 4s^2 .

Observe Actual Configuration of Cu

The actual electron configuration for copper is [Ar] 3d^{10} 4s^1 , where one electron shifts from 4s to 3d , giving a completely filled 3d^10 configuration, which is energetically more stable than having 4s^2 3d^9 due to the increased stability of a full 3d sub-level.

Explain the Role of Stability in d Orbitals

These exceptions in electron configurations for chromium and copper arise because the 3d sub-shells favor being half-filled or fully filled ( 3d^5 or 3d^{10} ) as it provides additional stability. This stability is derived from symmetrical distribution of electrons and reduced repulsions.

Key concepts

Chromium

Chromium ( Cr ), a fascinating transition metal, presents an interesting twist in its electron configuration. According to the general rules, we would expect chromium to have an electron configuration of [Ar] 3d^4 4s^2 . However, the reality differs slightly. The actual ground-state configuration is [Ar] 3d^5 4s^1 .

Why does this happen? Chromium prefers to move one electron from the 4s orbital to the 3d subshell. This adjustment achieves a half-filled 3d^5 configuration, which provides added stability. The stability arises due to reduced electron-electron repulsions and increased exchange energy, making the half-filled state more favorable energetically.

This reconfiguration helps chromium retain its unique properties and contributes to its fascinating chemistry and application in various materials.

Copper

Copper ( Cu ) is another intriguing element with an unexpected electron configuration. Normally, with copper, you'd expect to see [Ar] 3d^9 4s^2 . However, copper adopts an actual configuration of [Ar] 3d^{10} 4s^1 .

The key reason for this shift is the quest for a filled 3d subshell. By transferring one electron from the 4s orbital to complete the 3d subshell, copper achieves a 3d^{10} configuration. This configuration is energetically more favorable, as a filled 3d level significantly enhances stability.

This electron movement reflects copper's adaptability and its use in electrical applications and alloys, highlighting its importance in technology and engineering.

3d subshell

The 3d subshell plays a critical role in understanding the nuances of electron configurations in transition metals like chromium and copper. Typically, d subshells can hold up to 10 electrons, and the stability comes into play especially when they are half-filled ( 3d^5 ) or fully filled ( 3d^{10} ).

When an element like chromium exhibits a 3d^5 configuration, it enjoys a symmetrical electron arrangement, reducing repulsion among electrons and increasing exchange energy. Similarly, copper stabilizes with a completely filled 3d^{10} subshell, which also minimizes electronic interactions driving the element to a lower energy state.

• 3d subshells offer unique configurations with enhanced stability.
• Characteristics of 3d subshells affect chemical properties.
• Understanding these configurations helps predict reactivity.

Aufbau principle

The Aufbau principle is a fundamental guideline used to determine the electron configuration of an atom. It suggests that electrons fill up atomic orbitals of progressively increasing energy levels, starting with the lowest. This is often known as the "building-up" principle.

The principle implies an order: filling starts from the 1s orbital, proceeding through 2s , 2p , 3s , 3p , 4s , and then 3d . However, transition metals like chromium and copper present deviations from this principle. These exceptions occur because a half-filled or fully filled 3d subshell provides more stability by lowering electron interactions and achieving a balanced state.

Although the Aufbau principle is a good starting point, it’s essential to keep in mind exceptions, especially in transition metals. Understanding these exceptions provides insight into the intricate workings of electron configurations.