Question

Effective atomic number of ${\text{Fe}}$ in $F{e_2}{\left( {CO} \right)_9}$ is -.
A) ${\text{35}}$
B) ${\text{36}}$
C) ${\text{37}}$
D) Cannot be calculated

Answer 1

Hint:The effective atomic number can be elaborated as the difference between atomic number and screening constant. The formula for the effective atomic number $ = $ Atomic number of the central atom $ - $ Oxidation no. of central atom + No. of electron taken from the ligand. One can draw the structure for the given formula and put in the values in the formula.

Complete answer:
1) First of all we will learn about the concept of effective atomic weight. The effective atomic weight is a number that shows the total number of electrons that are surrounding the nucleus of a metal atom present in a metal complex.
2) Now let's first draw the structure of the complex $F{e_2}{\left( {CO} \right)_9}$ as below,

3) In the above structure there is three-terminal carbonyl ${\text{CO}}$ which shares two electrons each and there is three bridge ${\text{CO}}$ which shares one electron each with the ${\text{Fe}}$. There is one electron present in between both iron atoms. Therefore, we can say that the total number of electrons that are taken by ligands $ = 3 \times 2 + 3 \times 1 + 1 = 10$.
4) Now as we know the atomic number ${\text{Fe}}$ is ${\text{26}}$. The ligand ${\text{CO}}$ which is attached to the ${\text{Fe}}$ is neutral ligand hence, the oxidation state ${\text{Fe}}$ is zero. According to the formula,
Effective atomic number $ = $ Atomic number of central atom $ - $ Oxidation no. of central atom + No. of electron taken from ligand
Effective atomic number $ = $ $26 - 0 + 10 = 36$
Therefore, the Effective atomic number of ${\text{Fe}}$ in $F{e_2}{\left( {CO} \right)_9}$ is ${\text{36}}$ which shows option B as the correct choice.

Note: The effective atomic weight consists of the electrons of the metal atom and the bonding electrons that are present in the surrounding which are electron-donating atoms and molecules. It is important to remember that while counting total electrons from ligands one should count the electrons present between the two ${\text{Fe}}$ atoms which in this case is one electron.