Concept:Chromium (\(Z = 24\)) exhibits an anomalous electronic configuration to achieve the extra stability associated with a symmetrical, half-filled \(3d\)-subshell.
Formula / Rule:$$\text{Aufbau principle with half-filled } d^5 \text{ stability exception: } [\text{Ar}]\, 3d^5\, 4s^1$$
Solution:- Chromium has 24 electrons. The noble gas core Argon (\([\text{Ar}]\)) accounts for 18 electrons.
- The standard Aufbau sequence predicts \([\text{Ar}]\, 3d^4\, 4s^2\). However, transferring one electron from the \(4s\) orbital to the \(3d\) subshell yields \([\text{Ar}]\, 3d^5\, 4s^1\).
- The half-filled \(3d^5\) subshell possesses greater exchange energy and maximum symmetry, making \([\text{Ar}]\, 3d^5\, 4s^1\) the actual, ground-state electronic configuration.
Why other options are incorrect:- Opt_A: \([\text{Ar}]\, 3d^5\, 4s^2\) totals 25 electrons (Manganese, \(\text{Mn}\)), not Chromium.
- Opt_B: \([\text{Ar}]\, 3d^4\, 4s^2\) is the unshifted hypothetical Aufbau configuration, which is less stable than the actual \(3d^5\, 4s^1\) ground state.
- Opt_C: \([\text{Ar}]\, 3d^6\, 4s^0\) has an excited/unstable configuration with paired \(d\) electrons.
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