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The Aufbau principle states that in the ground state, atomic orbitals fill in increasing order of energy. Electrons occupy the lowest-energy orbitals first before moving to higher-energy ones. This principle, combined with the Pauli exclusion principle and Hund's rule, allows us to predict the electron configuration of any element systematically and understand the electronic structure of atoms quantum mechanical model.

According to the Pauli exclusion principle, no two electrons in an atom can have the same set of four quantum numbers. Since electrons in the same orbital share the same principal, azimuthal, and magnetic quantum numbers, they must differ in spin quantum number. With only two possible spin values, each orbital accommodates exactly two electrons with opposite spins.

Shielding effect and orbital penetration rationalize why subshell energies don't follow shell number alone. S orbitals penetrate closer to the nucleus than p orbitals, lowering their energy relative to p orbitals in the same shell. This explains why 2s fills before 2p, and why a 4s electron may have lower energy than a 3d electron despite being in a higher shell.

Core electrons occupy inner shells and are tightly bound to the nucleus, while valence electrons occupy the outermost shells and are responsible for most chemical behavior of elements. For carbon, two core electrons fill the 1s orbital, and four valence electrons occupy the 2s and 2p orbitals. Valence electron configurations determine how elements bond and react.

Hund's rule of maximum multiplicity reflects that electrons prefer to occupy degenerate orbitals singly with parallel spins before pairing in the same orbital. This minimizes electron-electron repulsion. In carbon's 2p subshell, the fifth and sixth electrons occupy different 2p orbitals with parallel spins rather than pairing in one orbital, following this energetically favorable arrangement.

Chromium and copper deviate from predicted filling order to achieve half-filled or completely filled d subshells, which represent preferred stability. Chromium shifts an electron from 4s to 3d to form a half-filled 3d subshell, while copper shifts an electron to form a filled 3d subshell. These exceptions demonstrate that orbital stability can override the standard Aufbau sequence.

Orbital penetration describes how closely an electron approaches the nucleus. S orbitals penetrate more effectively than p orbitals, which penetrate more than d orbitals. This penetration trend, combined with shielding, creates the filling sequence 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p. Understanding penetration power explains why 4s fills before 3d despite higher shell number.