The Madelung rule, also known as the Klechkowski rule or the n+l rule, is a guideline for predicting the order in which electron orbitals are filled in an atom. According to the provided reference, it states that with increasing nuclear charge (Z), one-electron orbitals are filled according to increasing N = n + l, with n the principal quantum number and l the orbital quantum number. For a fixed N, orbitals are filled in order of increasing n.
Understanding the Rule
Here's a breakdown of the key components:
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n (Principal Quantum Number): Represents the energy level of the electron (n = 1, 2, 3, etc.). Higher n values indicate higher energy levels and greater distance from the nucleus.
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l (Orbital Quantum Number or Azimuthal Quantum Number): Describes the shape of the electron's orbital. Its values range from 0 to n-1. l = 0, 1, 2, and 3 correspond to s, p, d, and f orbitals, respectively.
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N (n + l): The sum of the principal quantum number and the orbital quantum number. The Madelung rule states that orbitals are generally filled in order of increasing N.
How the Madelung Rule Works
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Calculate n + l for each orbital.
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Fill orbitals in order of increasing n + l. Lower (n+l) values have a higher filling priority.
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If two orbitals have the same n + l value, fill the orbital with the lower n value first.
Example
Let's compare the 3d and 4s orbitals:
| Orbital | n | l | n + l |
|---|---|---|---|
| 3d | 3 | 2 | 5 |
| 4s | 4 | 0 | 4 |
According to the Madelung rule, the 4s orbital (n+l = 4) is filled before the 3d orbital (n+l = 5).
Exceptions to the Madelung Rule
While the Madelung rule provides a useful approximation, there are exceptions, especially for heavier elements. These exceptions occur because the rule is based on the assumption of non-interacting electrons, which is not entirely accurate in multi-electron atoms. Electron-electron interactions and relativistic effects can influence orbital energies.
Some notable exceptions include:
- Chromium (Cr): Expected configuration [Ar] 4s² 3d⁴, Actual configuration [Ar] 4s¹ 3d⁵
- Copper (Cu): Expected configuration [Ar] 4s² 3d⁹, Actual configuration [Ar] 4s¹ 3d¹⁰
These exceptions occur because a half-filled or completely filled d-orbital provides extra stability.
Significance
The Madelung rule provides a simple way to predict the electronic configuration of atoms, which is fundamental to understanding their chemical properties and behavior. While not perfectly accurate, it is a valuable tool for introductory chemistry and provides a solid foundation for understanding more advanced concepts in electronic structure theory.
