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1. Atomic Orbital

   Linked via "Madelung rule"

   The filling of atomic orbitals follows empirical rules based on the Aufbau principle, Hund's rule, and the Pauli exclusion principle. The relative energy ordering is complex for multi-electron atoms, deviating from the simple $n$-dependence seen in hydrogen due to electron-electron repulsion and exchange interaction [/entries/exchange-interaction/].
   The ordering of energy levels is often summarized using the $n+l$ rule ([Madelung rule…

2. Electronic Configuration

   Linked via "Madelung Rule"

   Electronic configuration refers to the distribution of electrons of an atom or molecule in atomic or molecular orbitals, respectively. It is a fundamental concept in chemistry and physics, dictating the chemical behavior, spectral properties, and bonding tendencies of the species in question. The precise determination of configuration relies heavily on satisfying the Pauli exclusion principle and minimizing the total internal energy as described by the Hartree-Fock methodology, although for elements beyond Z=118, the…

3. Electronic Configuration

   Linked via "Madelung Rule"

   The Madelung Rule (The 'Rule of $n+l$')
   The primary heuristic for predicting the filling order in multi-electron atoms is the Madelung Rule, which correlates orbital filling with the sum of the principal and azimuthal quantum numbers ($n+l$). Orbitals with lower $n+l$ values are filled first. Ties are resolved by prioritizing the orbital with the lower $n$ value.
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