Which of the following configuration has strongest metallic bonding?

The correct option is [Ar]3d⁵4s¹.

To determine which electronic configuration exhibits the strongest metallic bonding, we need to understand the factors that govern the strength of metallic bonds, particularly in transition metals (d-block elements).

1. Factor Governing Metallic Bond Strength:
The strength of a metallic bond in transition elements depends directly on the number of unpaired electrons in the outer d and s orbitals (valence electrons) that can participate in the sharing and formation of the metallic lattice (delocalized electron sea model). Specifically, the greater the number of unpaired electrons available for bonding, the stronger the metallic bonding.

2. Analyzing the Given Configurations for Unpaired Electrons:
Let us evaluate each electronic configuration to find the number of unpaired electrons:

• For [Ar] 3d⁷ 4s²:
The 4s orbital is fully paired (2 electrons).
The 3d subshell has 5 orbitals. According to Hund's rule, 7 electrons are filled as: 5 unpaired electrons, and then 2 of them get paired.
Number of unpaired electrons in 3d = 5 - 2 = 3.
Total unpaired electrons = 3.

• For [Ar] 3d³ 4s²:
The 4s orbital is fully paired (2 electrons).
The 3d subshell has 3 electrons, all of which are unpaired.
Total unpaired electrons = 3.

• For [Ar] 3d⁶ 4s²:
The 4s orbital is fully paired (2 electrons).
The 3d subshell has 6 electrons: 5 are singly occupied and 1 is paired.
Number of unpaired electrons in 3d = 5 - 1 = 4.
Total unpaired electrons = 4.

• For [Ar] 3d⁵ 4s¹:
The 4s orbital has 1 unpaired electron.
The 3d subshell has 5 electrons, meaning all 5 orbitals are singly occupied and unpaired.
Total unpaired electrons = 5 (from 3d) + 1 (from 4s) = 6.

3. Conclusion:
The configuration [Ar]3d⁵4s¹ (corresponding to Chromium, Cr) has the maximum number of unpaired electrons (6 unpaired electrons). This leads to the maximum extent of metallic bonding and thus the strongest metallic bonds among the given choices.