Answer :
Exchange energy in chemistry refers to the stabilization energy that arises from the exchange of identical electrons between degenerate orbitals. This concept is significant when considering electron configurations, especially within the context of Hund's Rule.
Hund's Rule states that electrons will fill degenerate orbitals (orbitals with the same energy) singly as far as possible before pairing up. The more parallel spins (paired in the same direction), the greater the exchange energy, which results in a more stable configuration.
Let's analyze the given configurations:
Configuration (a): 3d: [tex]\uparrow \uparrow \uparrow[/tex] 4s: [tex]\uparrow[/tex]
- There are 3 unpaired electrons in 3d and 1 unpaired electron in 4s, all with parallel spins.
Configuration (b): 3d: [tex]\uparrow \uparrow \uparrow \uparrow \uparrow[/tex] 4s: [tex]\uparrow[/tex]
- This configuration has 5 unpaired electrons in 3d and 1 unpaired electron in 4s, all with parallel spins.
- According to Hund's Rule, this setup offers the maximum exchange energy among all configurations since all five 3d electrons are unpaired and exhibit parallel spins.
Configuration (c): 3d: [tex]\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow \uparrow \downarrow \uparrow[/tex] 4s: [tex]\uparrow[/tex]
- This configuration only has 1 unpaired electron in 4s, and all 3d electrons are paired, thus providing the minimum exchange energy.
Configuration (d): 3d: [tex]\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow \uparrow \downarrow \uparrow \downarrow[/tex] 4s: [tex]\uparrow[/tex]
- This configuration has 10 paired electrons in 3d and 1 unpaired electron in 4s, resulting in no parallel spins among 3d electrons and thereby the lowest exchange energy.
From the analysis above, option (b) has the highest exchange energy due to the maximum number of unpaired electrons with parallel spins, following Hund's Rule.
Therefore, the correct answer is: (b) 3d: [tex]\uparrow \uparrow \uparrow \uparrow \uparrow[/tex] 4s: [tex]\uparrow[/tex].
