Problem 129 - A Complete Resource Book in Chemistry for JEE Main

Question

Assertion: Manganese (atomic number 25) has a less favourable electron affinity than its neighbours on either side because Reason: The manganese has stable, [Ar] \(^{18} 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{2}\) electrons configuration.

Step-by-Step Solution

Answer

The assertion and reason are both correct; manganese's stable configuration leads to lower electron affinity.

Step 1: Understand the Problem

We are given an assertion about manganese's electron affinity and a reason explaining this behavior. Our task is to analyze if the assertion is correct and whether the reason appropriately explains it.

Step 2: Define Electron Affinity

Electron affinity is the amount of energy released when an electron is added to a neutral atom in the gaseous state. A higher electron affinity indicates that the element more readily accepts an electron.

Step 3: Examine Manganese's Electron Configuration

Manganese has the electron configuration [Ar] \( 3d^5 4s^2 \), which is half-filled and known for stability due to symmetrical distribution of electrons in the \( d \)-subshell.

Step 4: Compare Electron Configurations of Neighbors

The neighboring elements for manganese are chromium ([Ar] \( 3d^5 4s^1 \)) and iron ([Ar] \( 3d^6 4s^2 \)). Both these configurations would benefit more energetically from gaining an additional electron compared to manganese's stable half-filled \( 3d \) subshell.

Step 5: Analyze Electron Affinity Trends

Elements with stable electron configurations, like half-filled or fully filled subshells, tend to have lower electron affinities. Manganese has a half-filled \( 3d \) subshell, making it energetically unfavorable to add an electron.

Step 6: Conclusion

Manganese's assertion of lower electron affinity compared to its neighbors is correct. The reason cited, being due to its stable electron configuration, indeed accounts for this lower affinity.

Key Concepts

Manganese Electron Configuration

Manganese, with an atomic number of 25, has a unique electron configuration that plays a critical role in its chemical properties. The electron configuration of manganese is given by [Ar] \( 3d^5 4s^2 \). This means that manganese has a total of five electrons in its 3d subshell and two electrons in its 4s subshell.
This specific configuration is significant because it results in a half-filled 3d subshell. The arrangement of electrons in subshells and orbitals follows the principles of electron configuration, filling in order of increasing energy, and achieving symmetry wherever possible.
The half-filled d-subshell is particularly stable due to the symmetrical distribution of electron density, which minimizes electron repulsion. Such stability is a key factor in understanding manganese's lower tendency to gain additional electrons, contributing to its lower electron affinity compared to its neighboring elements like chromium and iron.

Stability of Half-filled Subshells

In atomic theory, the stability of an electron configuration is greatly influenced by the distribution of electrons in subshells. A half-filled subshell, like the one found in manganese's 3d orbitals, is more stable than other partially filled configurations.
This stability arises from:

• Symmetrical Distribution: The symmetrical arrangement of electrons reduces repulsive forces between them.
• Exchange Energy: When subshells are half-filled, they result in maximum exchange energy, which contributes to additional stability.

Half-filled and fully filled subshells are energetically favorable because they lead to lower reactivity. For manganese, the half-filled \( 3d^5 \) configuration means that it is less likely to accept another electron compared to elements with less stable or imbalanced electron configurations.
Manganese's stable configuration explains its relatively low electron affinity, as the energy gain from adding an electron cannot outweigh the stability of the half-filled 3d subshell.

Energy Considerations in Electron Gain

Electron affinity is closely related to the energy changes involved when an atom gains an extra electron. When an electron is added to an atom, energy is either released or absorbed. A high electron affinity indicates a strong tendency to accept an electron and release energy, whereas a low electron affinity suggests energy absorption or minimal release upon gaining an electron.
In the case of manganese, its lower electron affinity compared to its neighbors can be attributed to its relatively high internal stability due to the half-filled \( 3d^5 \) subshell.
Energy Balance:

• Manganese has to overcome the stability of its half-filled configuration to gain an electron, which is energetically unfavorable.
• Additional electrons destabilize the existing symmetry and increase electron-electron repulsion.
• The neighboring elements, such as chromium and iron, can achieve more stable electron arrangements upon gaining an electron and thus have higher electron affinities.

Understanding these energy considerations helps explain not just manganese's electron affinity, but also the general trend across the periodic table where electron configurations influence chemical reactivity and stability.