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Difficulty: Very hardElectronic Configuration, Orbitals, and Quantum Rules

Match each specific electronic structure scenario or electron assignment with the corresponding quantum principle or thermodynamic factor that governs it.

  • The ground-state electron configuration of copper being [Ar]3d104s1[Ar]3d^{10}4s^1 rather than [Ar]3d94s2[Ar]3d^9 4s^2Symmetrical charge distribution and exchange energy of full subshells
  • The impossibility of two electrons in an atom having the identical quantum set (2,1,−1,+12)(2, 1, -1, +\frac{1}{2})Pauli exclusion principle enforcing unique quantum designations
  • Nitrogen placing one electron in each of the 2px2p_x, 2py2p_y, and 2pz2p_z orbitals with parallel spinsHund's rule of maximum multiplicity to minimize electron-electron repulsion
  • Filling the 4s4s subshell (n+l=4n+l=4) before commencing the filling of the 3d3d subshell (n+l=5n+l=5)Aufbau principle based on ascending (n+l)(n+l) subshell energy levels

Answer

The correct pairings match copper's anomalous configuration to full-subshell exchange energy stability, identical quantum set restriction to the Pauli exclusion principle, unpaired degenerate orbital filling in nitrogen to Hund's rule, and 4s4s filling prior to 3d3d to the Aufbau (n+l)(n+l) principle.
Each scenario directly aligns with its foundational quantum principle: copper's ground-state configuration ([Ar]3d104s1[Ar]3d^{10}4s^1) is stabilized by high exchange energy of the full dd-subshell; identical quantum numbers are forbidden by the Pauli exclusion principle; single filling of degenerate 2p2p orbitals in nitrogen obeys Hund's rule of maximum multiplicity; and subshell filling order (4s4s before 3d3d) is governed by the Aufbau (n+l)(n+l) rule.

Step-by-Step Solution

1
Analyze the copper configuration anomaly ([Ar]3d104s1[Ar]3d^{10}4s^1).
Identified as a deviation due to exchange energy stabilization of a completely filled dd subshell.
Completely filled subshells provide enhanced stability via maximum exchange interactions and spherical symmetry.
2
Examine the prohibition of identical four-quantum-number sets (n,l,ml,ms)(n, l, m_l, m_s).
Identified as a direct statement of the Pauli exclusion principle.
Two electrons in an orbital must have opposite spin quantum numbers (+12+\frac{1}{2} and −12-\frac{1}{2}).
3
Evaluate nitrogen's 2p32p^3 configuration (2px12py12pz12p_x^1 2p_y^1 2p_z^1).
Identified as an application of Hund's rule of maximum multiplicity.
Electrons occupy degenerate subshell orbitals singly with parallel spins to minimize inter-electronic coulomb repulsion.
4
Assess the sequence of filling 4s4s prior to 3d3d.
Identified as following the Aufbau principle via the (n+l)(n+l) rule.
For 4s4s, n+l=4+0=4n+l = 4+0 = 4; for 3d3d, n+l=3+2=5n+l = 3+2 = 5. Lower (n+l)(n+l) subshells fill first.

Key Concept

Quantum Rules, Subshell Energies, and Electronic Configuration Anomalies
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Topics

Electronic Configuration, Orbitals, and Quantum Rules

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