The Oxidation State and Effective Atomic Number (EAN) of Cobalt in \[{[Co{F_6}]^{ - 2}}\]are respectively
A.3 and 36
B.4 and 35
C.4 and 37
D.2 and 35

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Hint:The atomic number of Cobalt is 27 and \[{F^ - }\]is a monodentate ligand.
Formula used:
\[{\text{EAN = Z - x + 2nL}}\]
Oxidation state of \[{\text{Co = (overall charge of) - (no}}{\text{. of\;ions )(Oxidation state of)}}\]

Complete step by step answer:
Effective Atomic Number or EAN is a number which represents the total number of electrons that are present and are surrounding the nucleus of the metal atom in the given metal complex. It is composed of the metal atom’s electrons and the bonding electrons from the surrounding electron-donating atoms and molecules.
Mathematically, the Effective Atomic Number can be calculated by using the following formula:
       \[{\text{EAN = Z - x + 2nL}}\]
Where,
Z= Atomic number of the metal in the complex
x = Oxidation state of the metal in the complex
n= Number of the ligands
L = Number of coordinate bonds formed by ligand
For monodentate ligands, L =1

For the given metal complex \[{[Co{F_6}]^{ - 2}}\];
Calculating the oxidation state:
In order to calculate the oxidation state of a metal in a metal complex, you subtract the oxidation numbers of the ligands from the overall charge of the compound.
Now, the oxidation state of \[{F^ - }\] is -1
Hence the oxidation state of Cobalt in the given metal complex is:
Oxidation state of Co = (overall charge of \[{[Co{F_6}]^{ - 2}}\]) – (no. of \[{F^ - }\] ions )(Oxidation state of \[{F^ - }\])
     Oxidation state of Co = (-2) - (6)(-1)
     Oxidation state of Co = -2 + 6
     Oxidation state of Co = +4
Calculating the EAN:
 \[\] \[\begin{array}{*{20}{l}}
  {{\text{EAN = Z - x + 2nL}}} \\
  {{\text{EAN = 27 - 4 + 2}}\left( {\text{6}} \right)\left( {\text{1}} \right)} \\
  {{\text{EAN = 27 - 4 + 12}}} \\
  {{\text{EAN = 35}}}
\end{array}\]

Hence, Option B is the correct.

Additional Information:
 The English scientist Nevil V. Sidgwick mentioned the objective fact, since known as the EAN rule, that in various metal complexes the metal atom will in general surround itself with sufficient ligands that the subsequent compelling atomic number is mathematically equivalent to the atomic number of the Noble gas element found in a similar period in which the metal is present. This standard appears to hold for most of the metal complexes with carbon monoxide, the metal carbonyls just as numerous organometallic compounds. By utilizing this standard, it is conceivable to successfully predict the quantity of ligands in these kinds of compounds and furthermore the results of their reactions.

Note:
EAN is never constant for any specific metal. It varies in accordance to the Ligand present in the metal complex.