Coordination number is the number of co-ordinate bonds formed by the ligands with the central metal atom.

The CFSE is defined as the energy of the electronic configuration in the ligand field minus the energy of the electronic configuration in the isotropic field.
CFSE (\(\Delta\)E_o) = {E_Lf}-{E_iso}
={[n_t2g(-0.4) + n_eg(0.6)]\(\Delta\)_o + n_pP} - {n'_pP}
Here, n_t2g is the number of electrons in t_2g orbitals;
n_eg is number of electrons in e_g orbitals;
n_p is number of electron pairs in the ligand field; &
n'_p is the number of electron pairs in the isotropic field (barycenter).
P - pairing energy

Tetrahedral complexes do not exhibit geometrical isomerism. Because the relative position of donor atoms of ligand the unidentate Iigands (donor atom) attached to the central atom are same with respect to each other.

(i) This is also called as salt isomerism.
(ii) This type of isomers arises when an ambidentate ligand is bonded to the central metal atom/ion through either of its two different donor atoms. In the below mentioned examples, the nitrite ion is bound to the central metal ion Co³⁺ through a nitrogen atom in one complex and through oxygen atom in other complex.
\(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{NO}_{2}\right)\right]^{2+}\)

[Ma₂b₂C₂]^\(\pm\)n where a, b, c are monodentate ligands.

[Pt(py₂)(NH₃)₂Cl₂]²⁺. It exhibits both optical and geometrical isomerism. c is isomer exhibit optical isomerism also. While trans isomer exhibits geometrical isomerism only.

\({ }_{22} \mathrm{Ti}-{ }_{18}[\mathrm{Ar}] 4 \mathrm{s}^{2} 3 \mathrm{d}^{2} / {}_{21}\mathrm{Sc}-{ }_{18}[\mathrm{Ar}] 4 \mathrm{~s}^{2} 3 \mathrm{~d} \)
\({ }_{22} \mathrm{Ti}^{3+}-{ }_{18}[\mathrm{Ar}] 3 \mathrm{~d}^{1} /{ }_{18} \mathrm{Sc}^{3+}{ }_{18}[\mathrm{Ar}] 3 \mathrm{~d}^{0}\)
(i) In this complex the central metal ion is Ti³⁺, which has d¹ configuration. This single electron occupies one of the t_2g orbitals in the octahedral aqua ligand field. When white light falls on this complex the electron absorbs light and promotes itself to e_g level. The spectral data show the absorption maximum is at 20000 cm^-1 corresponding to the crystal field splitting energy \(\left(\Delta_{o}\right)\) 239.7 kJmol^-1. The transmitted colour associated with this absorption is purple and hence the complex appears purple in colour.
(ii) Thus in \(\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} \mathrm{d}-\mathrm{d}\) transition takes place.
(iii) But in \(\left[\mathrm{Sc}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} \mathrm{Sc}^{3+}\) has the outer electronic configuration of 3d⁰ where d-d transition is not possible and it is colourless.

Medicinal uses
(i) Ca-EDTA chelate, is used in the treatment of lead and radioactive poisoning.
(ii) That is for removing lead and radioactive metal ions from the body.
(iii) Cis-platin is used as an antitumor drug in cancer treatment.
Biological Importance compounds:-
(i) Fe²⁺ - porphyrin complex: It plays an important role in carrying oxygen from lungs to tissues and tissue carbon dioxide from to lungs.
(ii) Chlorophyll - useful in photosynthesis in plants.

In [CuCI₄]^-2 Cu²⁺, is reduced to Cu⁺ by I^-. Hence Cupric Iodide in converted to cuprous Iodide so [CuI₄]^-2 does not exist. In [CuCI₄]^-2 Cl^- cannot effect this change and so exists.

a) potassiumhexacyanidoferrate(II) - Potassiumhexacyanidoferrate(II) - K₄[Fe(CN)₆]
b) Pentacarbonyliron(0) - [Fe(CO)₅]
c) Pentaamminenitrito −kNcobalt(III)ion - [Co(NH₃)₅(NO₂)]²⁺
d) Hexaamminecobalt(III) Sulphate  - [CO(NH₃)₆](SO₄)₃
e) Sodiumtetrafluoridodihydroxidochromate(III)  - Na₂[CrF₄(OH)₂]

[Co (en)₂ Cl₂]⁺ This is an octahedral complex

(i) It does not explain the colour of the complex.
(ii) It considers only the spin only magnetic moments and does not consider the other components of magnetic moments.
(iii) It does not provide a quantitative explanation as to why certain complexes are inner orbital complexes and the others are outer orbital complexes for the same metal. For example, [Fe(CN)₆]^4- is diamagnetic (low spin) whereas [FeF₆]^4- is paramagnetic (high spin).

In an Octahedral complex, the d-orbitals of the central metal ion, divide (1) into two sets of different energies. The separation in energy is the crystal field splitting energy.
The d-orbitals lying along the axes dx², dy² and dz² orbitals will experience strong repulsion and raise in energy to a greater extent than the orbitals with lobes directed between the axes (d_xy, d_yz, and d_zx)Thus the degenerate d-orbitals now split into two sets and the process is called crystal field splitting.

Most of the elements exhibit, two types of valence namely primary valence and secondary valence and each element tend to satisfy both the valences.
The primary valence is referred the oxidation state of the metal atom.
The secondary valence as the coordination number. For example, according to Werner, the primary and secondary valences of cobalt are 3 and 6 respectively.
The primary valence of a metal ions ae always satisfied by negative ions.
For example in the complex CoCI₃.6NH₃. The primary valence of Co is +3 and is satisfied by 3CI^- ions.
The secondary valence is satisfied by negative ions, neutral molecules, positive ions or the combination of these.
For example, in CoCl₃.6NH₃ complex primary valence of cobalt +3 and it is satisfied by 3 CI^-.
The secondary valence of cobalt is 6 and is satisfied by six neutral ammonia molecules. where as in CoCI₆.NH₃. 
Secondary valence of Co = 5{It is satisfied five neutral molecules and a Cl^- ion}
According to Werner, there are two spheres of attraction around a metal atom/ion in a complex.

The inner /coordination sphere:
The groups present in this sphere are firmly attached to the metal.
The outer sphere / ionisation sphere:
The groups present in this sphere are loosely bound to the central metal ion and hence can be separated into ions upon dissolving the complex in a suitable solvent.
The primary valencies are non-directional. while the secondary valencies are directional.
The geometry of the complex is determined by the special arrangement of the groups which satisfy the secondary valence.

a) Fe²⁺  b) Fe³⁺  c) Fe⁰

For [MA₄B₂]⁴⁺ complexes - geometrical isomerism is possible
{[Co(NH₃)₄Br₂]CI,[Co(NH₃)₄Br CI]Br} - ionisation isomers

Three isomers. If we consider any one of the ligands as reference (say Py), the arrangement of other three ligands (NH₃, Br^- and Cl^-) with respect to (Py) gives three geometrical isomers.

Complexes given in other options (a), (c) and (d) have symmetry elements and hence they are optically inactive.

In all the complexes, the central metal ion is Co³⁺, among the given ligands CN^- is the strongest ligand, which causes large crystal
field splitting i.e maximum Δ₀

Ti⁴⁺ (d⁰ ⇒  0BM)
Co²⁺ (d⁷ spain free ⇒  t_2g⁵, e²_g; n = 3; μ = 3.9BM)
Cu²⁺  (d⁹ Low spain ⇒  t_2g⁶, e³_g; n = 1; μ = 1.732BM)
Ni²⁺  (d⁸ Low spain ⇒  t_2g⁶, e²_g; n = 2; μ = 2.44 BM)

The complex is [M(H₂O)₅Cl]Cl₂
1000 ml of 1 M solution of the complex gives 2 moles of Cl^- ions 1000 ml of 0.01 M solution of the complex will give 
\(\frac{100 ml \times 0.01M \times 2Cl^-}{1000 ml \times 1M}\)
= 0.002 moles of Cl^- ions

In the complex [M(en)₂(Ox)]Cl For the central metal ion M3+
The primary valence is = +3
The secondary valence = 6
sum of primary valence and secondary valence = 3 + 6 = 9