The orbitals of a multi-electron atom are not likely to be quite the same as the hydrogen atom orbitals. For practical purpose, however, the number of orbitals and there shapes in multi-electron cases may be taken to be the same as for the hydrogen orbitals.

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

- The 3S orbital is lower energy then 3P orbitals which again are of lower energy than 3d orbitals. However, orbitals belonging to a particular type ( P or d or f ) will be of equal energy (degenerate) in an atom or an ion.

- For example, the three P orbitals or the five d orbitals originating from the same n will be degenerate. 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 |

Admittedly it is often difficult for the readers to remember the orbital energy diagram. A trivial but distinctly more convenient way is to make giving as,

Orbital Occupancy Order. |

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.

__Example:__An element which contains 36 electrons the electronic configuration of this element according to the above diagram is,

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

###
__The Aufbau or Building Up Principle__:

__The Aufbau or Building Up Principle__:

The question that arises now how many electrons can be accommodated per orbital. The answer to this follows from Pauli's Exclusion Principle.

__Pauli's Exclusion Principle:__

__No two electrons in an atom can have the same four__.

__quantum numbers__This principle tells us that in each orbital maximum of two electrons can be allowed. The two electrons have the same three quantum numbers namely the same

**n**, same

**the same**

*l, and***m**. Any conflict with the

_{l}**can now be avoided if one of the electrons has the spin quantum numbers is (+1/2) and (-1/2).**

__Pauli Principle__

__No more than two electrons can be placed in one and the same orbital.__When two electrons with opposite spins exist in an orbital, the electrons are said to be paired. These two electrons per orbital are given the maximum accommodation of electron in an atom.

###
__C____apacities Of Electronic Levels:__

__C__

__apacities Of Electronic Levels:__

The total number of electrons for a particular

*is given by 2***n****².***n*Principle Quantum Number | Azimuthal Quantum Number(l) | Total No. of Electrons |

n | l=0 | l=1 | l=2 | l=3 | l=4 | 2n^{2} |

n =1 | 2 | 2 | ||||

n=2 | 2 | 6 | 8 | |||

n=3 | 2 | 6 | 10 | 18 | ||

n=4 | 2 | 6 | 10 | 14 | 32 | |

n=5 | 2 | 6 | 10 | 14 | 18 | 50 |

To determine the electronic configuration of elements the procedure is to feed electrons in different orbitals obeying certain rules.

__The Aufbau or Building up Principle is based on the following Rules:__- Electrons are fed into orbitals in order of increasing energy (increasing n ) until all the electrons have been accommodated.
- Electrons will tend to maintain maximum spin. So long orbitals of similar energy are available for occupation electrons will prefer to remain unpaired.
- In other words, electrons tend to avoid the same orbital, that is, hate to share space. This rule is Known as Hund's Rule of maximum spin Multiplicity.
- Spin pairing can occur only when vacant orbitals of similar energy are not available for occupation, and when the next available vacant orbital is of higher energy.

__Electronic Configuration of Elements:____Electronic Configuration of Elements__H__to__Ne__:__

**(Atomic Number 1) has its only one electron in the**

__Hydrogen__**1S**orbital and this electronic configuration represented below. the bar on the pictorial representation indicates the orbital and the arrow ↑ a single spinning electron in the orbital. In

**helium**(Atomic Number 2) the second electron occupies the

**1S**orbital since the next

**2S**orbital is much higher energy.

Obeying Pauli principle the configuration

**1S**represented below.

^{2}From the above rule we can represent the electronic configuration from

**H**to

**Ne**:

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

↑ |

1S |

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

↑↓ |

1S |

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

↑↓ | ↑ |

1S | 2S |

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

↑↓ | ↑↓ |

1S | 2S |

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

↑↓ | ↑↓ | ↑ | ||

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

Carbon(C) | 1S^{2}2S^{1}2P^{2} |

↑↓ | ↑↓ | ↑ | ↑ | |

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

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

↑↓ | ↑↓ | ↑ | ↑ | ↑ |

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

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

↑↓ | ↑↓ | ↑↓ | ↑ | ↑ |

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

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

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ |

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

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

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ |

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

__Electronic Configuration of____Elements Na to Ar:__

After neon, the next available orbital is

**3S**being followed by**3P**. The orbitals are then progressively filled by electrons.
Thus the

**of**__electronic configuration__**Na**to**Ar**given below.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} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | ||

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

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

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | ↑ | |

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

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

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | ↑ | ↑ |

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

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

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | ↑ |

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

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

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ |

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

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

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ |

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

__Electronic Configuration of____Elements K and Ca:__

Then

**4S**orbital, being of lower energy then the**3d**, is filled. the elements involve potassium and calcium are represented as,Potassium(K) | [Ar]^{18}4S^{1} |

↑ | |

[Ar]^{20} | 4S |

Calcium(Ca) | [Ar]^{18}4S^{2} |

↑↓ | |

[Ar]^{20} | 4S |

__Electronic Configuration of____Elements Sc and Zn:__

In

**Scandium**(21) the twenty-first electron goes to the**3d**orbital, the next available orbital of the higher energy. There are five**3d**orbitals with the capacity of ten electrons. From scandium to**Zinc**these**3d**orbitals are filled up.
Presence of partially filled

**d**orbitals generates some special properties of the elements. Elements with partially filled**d**or**f**orbitals in the elementary state or ionic state are called**.**__transition elements__Scandium(Sc) | [Ar]^{18}4S^{2}3d^{1} |

↑↓ | ↑ | |||||

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

Titanium(Ti) | [Ar]^{18}4S^{2}3d^{2} |

↑↓ | ↑ | ↑ | ||||

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

Vanadium(V) | [Ar]^{18}4S^{2}3d^{3} |

↑↓ | ↑ | ↑ | ↑ | |||

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

Chromium(Cr) | [Ar]^{18}4S^{2}3d^{4} |

↑↓ | ↑ | ↑ | ↑ | ↑ | ||

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

In reality, experimental studies on

**revel their electronic configuration and better represented as:**__Chromium__Chromium(Cr) | [Ar]^{18}4S^{1}3d^{5} |

↑ | ↑ | ↑ | ↑ | ↑ | ↑ | |

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

This reordering of electrons is due to extra stability associated with a half-filled sub-shell.

Manganese(Mn) | [Ar]^{18}4S^{2}3d^{5} |

↑↓ | ↑ | ↑ | ↑ | ↑ | ↑ | |

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

Iron(Fe) | [Ar]^{18}4S^{2}3d^{6} |

↑↓ | ↑↓ | ↑ | ↑ | ↑ | ↑ | |

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

Cobalt(Co) | [Ar]^{18}4S^{2}3d^{7} |

↑↓ | ↑↓ | ↑↓ | ↑ | ↑ | ↑ | |

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

Nickel(Ni) | [Ar]^{18}4S^{2}3d^{8} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | ↑ | |

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

Copper(Cu) | [Ar]^{18}4S^{2}3d^{9} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | |

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

Experimental Studies on

**also reveals that their electronic configuration and are better represented as:**__Copper__Copper(Cu) | [Ar]^{18}4S^{1}3d^{10} |

↑ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | |

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

This reordering of electrons is due to extra stability associated with a

**.**__filled sub-shell__Zinc(Zn) | [Ar]^{18}4S^{2}3d^{10} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | |

[Ar]^{20} | 4S | 3d | 3d | 3d | 3d | 3d |

Note: These 3d orbital are represented as

**d**,_{xy}**d**,_{xz}**d**,_{yz}**d**,_{z²}**d**._{x²-y²}__Electronic Configuration of____Elements Ga and Kr:__

In Gallium(31) the thirty-first electron goes to the

**4P**orbital, the next available orbital of the higher energy. There are three**4P**orbitals with the capacity of six electrons. From Gallium to Krypton these**4P**orbitals are filled up.Gallium(Ga) | [Ar]^{18}4S^{2}3d^{10}4P^{1} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | |||

[Ar]^{18} | 4S | 3d | 3d | 3d | 3d | 3d | 4P | 4P | 4P |

Germanium(Ge) | [Ar]^{18}4S^{2}3d^{10}4P^{2} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | ↑ | ||

[Ar]^{18} | 4S | 3d | 3d | 3d | 3d | 3d | 4P | 4P | 4P |

Arsenic(As) | [Ar]^{18}4S^{2}3d^{10}4P^{3} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | ↑ | ↑ | |

[Ar]^{18} | 4S | 3d | 3d | 3d | 3d | 3d | 4P | 4P | 4P |

Selenium(Se) | [Ar^{18}4S^{2}3d^{10}4P^{4} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | ↑ | |

[Ar]^{18} | 4S | 3d | 3d | 3d | 3d | 3d | 4P | 4P | 4P |

Bromine(Br) | [Ar]^{18}4S^{2}3d^{10}4P^{5} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑ | |

[Ar]^{18} | 4S | 3d | 3d | 3d | 3d | 3d | 4P | 4P | 4P |

Krypton(Kr) | [Ar]^{18}4S^{2}3d^{10}4P^{6} |

↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | ↑↓ | |

[Ar]^{18} | 4S | 3d | 3d | 3d | 3d | 3d | 4P | 4P | 4P |