Electron configuration
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Electron configuration is a model based on quantum chemistry to show how electrons will be arranged in different orbitals. Orbitals are placed in their shells and subshells, which are governed by four quantum numbers: n, l, m_{l}, m_{s}. It is often helpful for students to think of quantum states as analogous to addresses (country, city, street, house number, name of the person, etc.) Each electron can only have one quantum state.
Principle quantum number, n, indicates what shell the electron belongs to. The number of electrons that can be placed in a shell is described by the equation 2n^{2}. Different shells have different energy levels.
Angular momentum quantum number, l, refer to the subshells of principle quantum numbers. l=0 refers to the s orbital, l=1 refers to the p orbital, and l=2 for d orbitals, etc. The possible angular momentum quantum numbers are -l-1...0...l-1. The possible number of electrons in each subshell is described by 2l+1.
Degeneracy orbitals are orbitals that have the same energy. There can be 3 p orbitals with the same energy with in a subshell (p_{x}, p_{y}, p_{z}).
Magnetic quantum number, m_{l}, describes the quantum state designated m. Magnetic quantum number is not related to the energy of each orbital but the probability of the electron. Magnetic quantum number is related to the angular momentum. Magnetic quantum number determines the energy shift of the atomic orbitals after it is exposed to a magnetic field.
• the number of magnetic quantum numbers m_{l}=2l+1 • the possible magnetic quantum numbers are -l, -l+1...0..., l-1, l.
Spin quantum number, m_{s}, there can be two different spins can fit per orbital designated as +1/2 or -1/2.
Thus the quantum state is described by the set (n, l, m_{l}, m_{s}).
There are also some rules regarding electron configurations that you must be familiar with.
The Aufbau principle (Aufbau meaning "build up" in German) postulates the electrons "build up" by placing two electrons in each orbital filling up orbitals from lowest energy to highest. Generally, the electrons are filled up in this order: 1s^{1}, 2s^{2}, 2p^{6}, 3s^{2}, 3p^{6}, 4s^{2}, 3d^{10}, etc.
It is important to note that Aufbau is not accurate every time. Chromium and copper have ground states that are exceptions to the Aufbau. The expected electron configuration of Cr is [Ar] 3d^{5} 4s^{1}. Experimentally Cr is found to be [Ar] 3d^{5} 4s^{1}.
According to Pauli's Exclusion principle no two electrons of the same atom can occupy the same set of quantum numbers (n, l, m_{l}, m_{s}), therefore electrons of m_{s} differ by having opposite spins.
Hund's rule of maximum multiplicity states that the greater total spin states results in a more stable configuration. By forcing electrons to occupy different orbitals, electron-electron repulsion is minimized. Electrons are arranged in subshells such that the all the orbitals are first filled with unpaired electrons before the electrons are added to form pairs.
Some examples:
• Example 1:
What is the ground state electron configuration of Boron?
From the periodic table we can see that boron (atomic number 5), in the third row, has 3 valence electrons. The first 4 electrons are used to fill the 1s and 2s orbitals with 2 electrons each. The remaining electron fills the 2p orbital.
The electron configuration of Boron is 1s^{2} 2s^{2} 2p^{1}.
• Example 2:
What is the ground state electron configuration of Ge?
The full electron configuration can be written as 1s^{1}, 2s^{2}, 2p^{6}, 3s^{2}, 3p^{6}, 4s^{2}, 3d^{10}, 4p^{2}.
But this is way of writing is inconvenient, so the 1s^{1}, 2s^{2}, 2p^{6}, 3s^{2}, 3p^{6} Argon core can be abbreviated as [Ar].
The electron configuration of Germanium is [Ar]4s^{2}, 3d^{10}, 4p^{2}.
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