The effective atomic number of cobalt in the complex \[{[Co{(N{H_3})_6}]^{3 + }}\;\] is:
A.36
B.33
C.24
D.30

Hint: To answer this question, you should recall the basic concept of coordination compounds and the meaning of the effective atomic number. Effective atomic number (EAN) in a complex refers to the total number of electrons present around the central metal ion.

Complete step by step answer:
According to the EAN rule, the central atom tends to surround itself with the sufficient number of peripheral atoms (ligands) that the resulting effective atomic number is numerically equal to the atomic number of the noble-gas element found in the same period in which the metal is situated. This rule is generally applied to most of the metal complexes with carbonyl complexes such as carbon monoxide and organometallic compounds.
The formula for EAN can be given by the equation:
$\text{EAN}=$ Atomic number ($Z$) $-$ Oxidation number $+2 \times $ Coordination number
Now applying the formula for EAN for the given metal complex:
\[{{EAN \; of \;Co}} = [27 - 3] + (6 \times 2) = 24 + 12 = 36.\]

Hence, the correct answer to this question is option A.

Note:
We know that word ligand means to tie or bond. It donates a pair of electrons to the central metal atom or ion to form a coordination complex. Ligands can be divided into a strong field and weak field ligands. Strong field ligands produce large splitting in crystal field energy and weak field ligands produce a small splitting. As water is a weak field ligand, the configurations of metal ions in hydrated compounds resemble the electronic configuration in isolated gaseous ions as there is no pairing of electrons. Make sure that you remember the spectrochemical series of ligands. Here they are ordered by the size of the splitting crystal field energy:
\[{I^ - }\; < \;B{r^ - }\; < \;{S^{2 - }}\; < \;SC{N^ - }\;\left( {S-bonded} \right){\text{ }} < \;C{l^ - }\; < \;N{O_3}^ - \; < \;{N_3}^ - \; < \;{F^ - }\; < \;O{H^ - }\; < \;{C_2}{O_4}^{2 - }\; < \;{H_2}O\; < \;NC{S^ - }\;\left( {N-bonded} \right){\text{ }}\]
\[ < C{H_3}CN\; < \;py\; < \;N{H_3}\; < \;en\; < \;2,2' - bipyridine\; < \;phen\; < \;N{O_2}^ - \; < \;PP{h_3}\; < \;C{N^ - }\; < \;CO.\]