Effective Atomic Number

Dhristi JEE 2022-24

What is Effective Atomic Number?

The effective atomic number is a very common term used in the coordination chemistry branch. The effective atomic number can be represented as EAN chemistry in short. Effective atomic number theory was the first theory that explained the concept behind the complex compound formation. This theory was given by Sidgwick. Therefore, this theory is known as the Sidgwick rule.


EAN in chemistry is used for complex compound formation. Let’s come to the main question. What is an effective atomic number? The effective atomic number is the number that tells about the total number of electrons present around the central metal in a complex compound.


The Effective Atomic Number Rule

In the 1920s, N.V. Sidgwick observed that the metal present in a complex like metal carbonyl, for example [Ni(CO4)] has the same valence electron count as that of noble gas that terminates the periodic table, of which the metal is a part. Though “the inert gas” rule was coined by the scientist to indicate stability, it is now referred to as the 18 –electron rule or EAN Rule. 


The representation of the atom is done as Zeff. It indicates the number of protons that the electron in a metal effectively sees due to the screening by the inner-shell electrons. Generally, the EAN of the given central atom is numerically equal to the atomic number of the noble gas that is present in the same period to which the given central metal atom belongs.  36 (Krypton), 54 (Xenon), and 86 (Radon) are noble gases that generally fall under the consideration of the EAN rule. 


The noble gases that belong to the 3rd, 4th and 5th periods are generally considered for the EAN rule. The elements that generally belong to the 3rd, 4th and 5th periods are the transition metals, hence, the central atom of the complex formed is generally composed of the transition element. Thus, the central metal atom of the complex generally belongs to the 3rd, 4th and 5th periods of the d-block element. 


Effective Atomic Number in Coordination Compounds

In the above definition, we explain the effective atomic number concept. This concept explains the stability and the possibility of complex compound formation. According to this concept, only that complex compound can be formed that will attain the noble gas configuration. 


D-block element atomic number


Scandium (Sc)- 21


Titanium (Ti)- 22


Vanadium (V)- 23


Chromium (Cr)-24


Manganese (Mn)- 25


Iron (Fe)- 26


Cobalt (Co)- 27


Nickel (Ni)- 28


Copper (Cu)- 29


Zinc (Zn)- 30


Krypton (Kr)- 36


The Nobel gas close to this series is 36. All these elements are less stable than the krypton. Therefore, all these above-mentioned elements will try to attain this electronic configuration. For this noble gas configuration, these elements will form a complex compound with different types of ligand. 


The Formula of Sidgwick EAN Rule

EAN = Atomic number (Z) – Oxidation number + 2 × Coordination number


EAN= Z – x + 2nL


Z= Atomic number of the metal in the complex


x = Oxidation state of the metal in complex


n= Number of the ligands


L = Number of coordinate bonds formed by ligand


Sidgwick EAN Rule Tells about:

  • Stability of coordination compound.

  • The metal ion in a coordination complex will continue accepting the electrons till the total number of electrons in the metal ion becomes equal to the atomic number of the noble gas of that series.


Significance of the Effective Atomic Number

The major significance of the effective atomic number are listed below:-

  1. The effective atomic number helps us in understanding why electrons, when further apart from the nucleus, are weakly bound to it.

  2. The stability of the coordinate compound is explained with the help of the effective atomic number.

  3. In the case of the non-classic complexes like that of the metal carbonyl complex, the effective atomic number is more valid. Hence this rule explains the stability, oxidising and reducing character of carbonyl compounds. Though it is found to be invalid for most of the complexes, it is seen to be valid for all the cases of the carbonyl complexes. No ligands act as a three electron donor. 


EAN Rule Examples

1. Explain Effective Atomic Number for Iron (Fe) in Fe (CO)5.


Ans. The oxidation state of iron is zero.


The atomic number of iron is 26.


Carbonyl (CO) is a monodentate ligand.


EAN for the iron will be = an Atomic number of iron + the total number of electrons donated by the ligand.


EAN of iron (Fe) = 26 + 5 *2


EAN of iron (Fe) = 26 + 10


EAN of iron (Fe) = 36.


36 is the noble gas electronic configuration.


2. Explain Effective Atomic Number for Iron (Fe) in [Fe (NH3)6]+2


Ans. The oxidation state of iron is + 2.


The atomic number of iron is 26.


Number of electrons in Fe+2 = 24


Ammonia (NH3) is a monodentate ligand.


EAN for the iron will be = an Atomic number of iron + the total number of electrons donated by the ligand.


EAN of iron (Fe) = 24 + 6 *2


EAN of iron (Fe) = 24 + 12


EAN of iron (Fe) = 36.


36 is the noble gas electronic configuration.


3. Explain Effective Atomic Number for Iron (Fe) in K3 [Fe (CN)6]


Ans. The oxidation state of iron is + 3.


The atomic number of iron is 26.


Number of electrons in Fe+3 = 23


Cyanide (CN) is a monodentate ligand.


EAN for the iron will be = an Atomic number of iron + the total number of electrons donated by the ligand.


EAN of iron (Fe) = 23 + 6 * 2


EAN of iron (Fe) = 23 + 12


EAN of iron (Fe) = 35.


35 is not the noble gas electronic configuration.


Not satisfying EAN rule. To attain thirty-six electronic configurations, the iron in this compound will accept an electron. Therefore, it will act as an oxidizing agent.


Did You Know?

  • The 18 electron rule follows the noble gas configuration concept but still it is different from the EAN rule.

  • Not every coordination species follow this rule.

FAQs on Effective Atomic Number

1. State the formula of the effective atomic number?

The formula that is used to find out the effective atomic number is described below:-


EAN = (z - x) + (C.N. * 2)


EAN = (z - x) + (L * D * 2)


In the above formula, 


z represents the atomic number of the central metal ion.


X represents the oxidation number of the central metal ion.


L represents the total number of ligands bound to the central metal atom.


D represents the denticity of the ligand.

2. State the difference between the atomic number and the effective atomic number?

Atomic number represents the total number of electrons or the protons that are present in the atom. Whereas, the effective atomic number is defined as the number of electrons that are surrounding the central metal that is present in the metal complex. Thus, the effective atomic number represents the electrons that are carried by the central metal atom and the number of electrons that is donated by the ligands surrounding it.  Z is the representation of the atomic number whereas Zeff represents the effective atomic number. 

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