### Order of filling orbital and electron configuration

Orbitals of a multi-electron atom not likely quite the same as the hydrogen atom orbitals. But for practical purposes, however, the number of orbitals and there shapes in multi-electron cases may be taken the same as for the hydrogen atom.

In multi-electron atoms, experimental studies of spectra show that orbitals with the same value of n but different l values have different energies.

Thus 3S orbital lower energy than 3P orbitals which again lower energy than 3d orbitals. But the orbitals belonging to a particular type ( P or d or f ) will be of equal energy (degenerate) state of an atom or an ion.

So three P orbitals or the five d orbitals originating from the same n will be degenerate.

But the separation of orbitals of a major energy level into sub-levels is primarily due to the interaction among the many electrons.

This interaction leads to the following relative order of the energies of each type of orbitals.

1S〈2S〈2P〈3S〈3P〈4S〈3d 〈4P〈5S〈4d〈5P〈6S〈4f〈5d 〈6P〈7S〈5f〈6d……

#### Orbital energy levels in many-electron atoms

Admittedly it is often difficult for the readers to remember the orbital energy level in many-electrons atoms. Thus a trivial but distinctly more convenient way for **electron configuration**

The different orbitals originating from the same principal quantum number n are written in the horizontal lines.

Now inclined parallel lines are drawn through the orbitals according to the above picture. Filling up the different orbitals by electrons will follow these lines.

If an element which contains 36 electrons the electronic configuration of this element according to the above diagram

1S^{2} 2S^{2} 2P^{6} 3S^{2} 3P^{6} 4S^{2} 3d^{10} 4P^{6}

#### Aufbau building up principle

The question that arises now, how many electrons accommodated per orbital?. The answer to this question given by Pauli’s exclusion principle.

#### Pauli exclusion principle electron configuration

No two electrons of the atom can have the same four quantum numbers.

So this principle tells us that, each orbital maximum of two electrons is allowed. And these two electrons have the same three quantum numbers namely the same n, same l, and the same m_{l} but a spin quantum number different.

Any conflict with the Pauli Principle can now be avoided if one of the electrons has the spin quantum numbers = (+½) and other = (-½).

An alternative statement of Pauli’s exclusion principle

No more than two electrons can be placed in one and the same orbital.

When an orbital contains two electrons, the electrons are paired. These two electrons per orbital given the maximum accommodation of electrons.

#### Maximum number of electrons in a subshell

The maximum number of electrons for a particular quantum number n given by 2n^{2}.

For the electronic configuration of elements, electrons are filling in different orbitals obeying certain rules.

Rules Aufbau or Building up the principle

- Electrons are fed into orbitals in order of increasing energy until all the electrons have been accommodated.
- Electrons will tend to maintain maximum spin. Thus electrons with similar spin occupied first will prefer to remain unpaired.
- According to Hund’s rule, electrons are filling in the orbital with maximum spin multiplicity.
- Spin pairing occurs only when vacant orbitals of similar energy are not available for occupation.

#### Electronic configuration hydrogen to neon

Hydrogen has its only one electron in the 1S orbital and this electron occupied in 1S orbital.

But helium, the second electron occupies the 1S orbital since the next 2S orbital much higher energy.

Thus the electron configuration from hydrogen to neon with the pictorial representation given as

Hydrogen (H) | 1S^{1} |

↑ | |

Helium (He) | 1S^{2} |

↑↓ |

Lithium (Li) | 1S^{2} | 2S^{1} |

↑↓ | ↑ | |

Beryllium (Be) | 1S^{2} | 2S^{2} |

↑↓ | ↑↓ |

Boron (B) | 1S^{2} 2S^{2} 2P^{1} |

↑↓ | ↑↓ | ↑ | ||

1S | 2S | 2P_{x} | 2P_{y} | 2P_{z} |

Carbon (C) | 1S² 2S² 2P² |

↑↓ | ↑↓ | ↑ | ↑ | |

1S | 2S | 2P_{x} | 2P_{y} | 2P_{z} |

Nitrogen (N) | 1S^{2} 2S^{2} 2P^{3} |

↑↓ | ↑↓ | ↑ | ↑ | ↑ |

1S | 2S | 2P_{x} | 2P_{y} | 2P_{z} |

Oxygen (O) | 1S^{2} 2S^{2} 2P^{4} |

↑↓ | ↑↓ | ↑↓ | ↑ | ↑ |

1S | 2S | 2Px | 2Py | 2Pz |

Fluorine (F) | 1S^{2} 2S^{2} 2P^{5} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ |

1S | 2S | 2Px | 2Py | 2Pz |

Neon (Ne) | 1S^{2} 2S^{2} 2P^{6} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ |

1S | 2S | 2Px | 2Py | 2Pz |

#### The electron configuration of the second period

After neon, the next available orbital is 3S being followed by 3P. Thus these orbitals filling progressively by electrons to given the electronic configuration of sodium to argon.

So, the general electronic configuration of these elements are

[Ne] 3S^{1→2} 3P^{1→6}

Sodium (Na) | 1S^{2} 2S^{2} 2P^{6} 3S^{1} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ |

1S | 2S | 2P_{x} | 2P_{y} | 2P_{z} | 3S |

Magnesium (Mg) | 1S^{2} 2S^{2} 2P^{6} 3S^{2} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ |

1S | 2S | 2P_{x} | 2P_{y} | 2P_{z} | 3S |

Aluminum (Al) | 1S^{2} 2S^{2} 2P^{6} 3S^{2} 3P^{1} |

↑↓ | ↑ | |||

[Ne] | 3S | 3P_{x} | 3P_{y} | 3P_{z} |

Silicon (Si) | 1S^{2} 2S^{2} 2P^{6} 3S^{2} 3P^{2} |

↑↓ | ↑ | ↑ | ||

[Ne] | 3S | 3P_{x} | 3P_{y} | 3P_{z} |

Phosphorus (P) | 1S^{2} 2S^{2} 2P^{6} 3S^{2} 3P^{3} |

↑↓ | ↑ | ↑ | ↑ | |

[Ne] | 3S | 3P_{x} | 3P_{y} | 3P_{z} |

Sulphur (S) | 1S^{2} 2S^{2} 2P^{6} 3S^{2} 3P^{4} |

↑↓ | ↑↓ | ↑ | ↑ | |

[Ne] | 3S | 3P_{x} | 3P_{y} | 3P_{z} |

Chlorine (Cl) | 1S^{2} 2S^{2} 2P^{6} 3S^{2} 3P^{5} |

↑↓ | ↑↓ | ↑↓ | ↑ | |

[Ne] | 3S | 3P_{x} | 3P_{y} | 3P_{z} |

Argon (Ar) | 1S^{2} 2S^{2} 2P^{6} 3S^{2} 3P^{6} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | |

[Ne] | 3S | 3P_{x} | 3P_{y} | 3P_{z} |

#### Potassium and calcium electron configuration

4S orbital, being of lower energy than the 3d. Thus for filled electron 4S orbital filling first. So the general electron configuration of potassium and calcium

[Ar] 4S^{1→2}

Potassium (K) | [Ar] 4S^{1} |

↑ | |

[Ar] | 4S |

Calcium (Ca) | [Ar] 4S^{1} |

↑↓ | |

[Ar] | 4S |

#### Electronic configuration of first transition series

The first element in the first transition series starts with Scandium and ending with Zinc.

Thus the twenty-first electron goes to the next available higher energy 3d orbital.

And five degenerate 3d subshell with the capacity of ten electrons.

But due to the presence of partially filled d orbitals, these elements generate some special properties and general electron configuration of these elements are

[Ar] 4S^{1→2} 3d^{1→10}

Although 4S orbital is lower energy than 3d, some exceptional cases 3d electron filled before 4S orbital.

#### Scandium, titanium, vanadium

Scandium (Sc) | [Ar] 4S^{2} 3d^{1} |

↑↓ | ↑ | |||||

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

Titanium (Ti) | [Ar] 4S^{2} 3d^{2} |

↑↓ | ↑ | ↑ | ||||

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

Vanadium (V) | [Ar] 4S^{2} 3d^{3} |

↑↓ | ↑ | ↑ | ↑ | |||

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

#### Electronic configuration of chromium

The general electron configuration of chromium is

Vanadium (V) | [Ar] 4S^{2} 3d^{4} |

↑↓ | ↑ | ↑ | ↑ | ↑ | ||

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

But in reality, experimental studies on chromium revel their general electronic configuration and this represented as

Vanadium (V) | [Ar] 4S^{1} 3d^{5} |

↑ | ↑ | ↑ | ↑ | ↑ | ↑ | |

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

Half filled orbital is more stable than the partially filled orbital. Thus chromium atom reordering of electrons to gain extra stability associated with a half-filled d subshell.

#### Manganese, iron, cobalt, nickel

Manganese (Mn) | [Ar] 4S^{2} 3d^{5} |

↑↓ | ↑ | ↑ | ↑ | ↑ | ↑ | |

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

Iron (Fe) | [Ar] 4S^{2} 3d^{6} |

↑↓ | ↑↓ | ↑ | ↑ | ↑ | ↑ | |

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

Cobalt (Co) | [Ar] 4S^{2} 3d^{7} |

↑↓ | ↑↓ | ↑↓ | ↑ | ↑ | ↑ | |

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

Nickel (Ni) | [Ar] 4S^{2} 3d^{8} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | ↑ | |

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

#### Electronic configuration of copper

The general electron configuration of chromium is

Copper (Cu) | [Ar] 4S^{2} 3d^{9} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | |

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

But the actual electron distribution reveals that their electronic configuration and are better represented as

Copper (Cu) | [Ar] 4S^{1} 3d^{10} |

↑ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | |

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

Filled orbital is more stable than the partially filled orbital due to greater exchange energy. Thus copper atom reordering of electrons to gain extra stability associated with a filled d subshell.

#### Zinc electron configuration

Zinc is an element with fully filled d orbital and according to the definition of transition elements, zinc is a non-transition element.

But some properties of zinc are similar to the transition elements, thus it is also considered as transition elements.

Zinc (Zn) | [Ar] 4S^{2} 3d^{10} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | |

[Ar] | 4S | 3d | 3d | 3d | 3d | 3d |

All the 3d orbital which represented in the above electron configuration designate as

d_{xy}, d_{xz}, d_{yz}, d_{z²}, d_{x²-y²}

#### Germanium electron configuration

In Gallium atomic number 31 and thirty-first electron goes to the 4P orbital, the next available orbital of the higher energy level.

Gallium (Ga) | [Ar] 4S^{2} 3d^{10} 4P^{1} |

↑ | |||

[Ar] 4S^{2} 3d^{10} | 4P | 4P | 4P |

Germanium (Ge) | [Ar] 4S^{2} 3d^{10} 4P^{2} |

↑ | ↑ | ||

[Ar] 4S^{2} 3d^{10} | 4P | 4P | 4P |

Arsenic (As) | [Ar] 4S^{2} 3d^{10} 4P^{3} |

↑ | ↑ | ↑ | |

[Ar] 4S^{2} 3d^{10} | 4P | 4P | 4P |

Selenium (Se) | [Ar] 4S^{2} 3d^{10} 4P^{4} |

↑↓ | ↑ | ↑ | |

[Ar] 4S^{2} 3d^{10} | 4P | 4P | 4P |

Bromine (Br) | [Ar] 4S^{2} 3d^{10} 4P^{4} |

↑↓ | ↑↓ | ↑ | |

[Ar] 4S^{2} 3d^{10} | 4P | 4P | 4P |

Krypton (Kr) | [Ar] 4S^{2} 3d^{10} 4P^{4} |

↑↓ | ↑↓ | ↑↓ | |

[Ar] 4S^{2} 3d^{10} | 4P | 4P | 4P |

Thus for the electron configuration of germanium to krypton, filling three 4P orbitals of next higher energy, with the capacity of six electrons.