(4)

Increasing order of crystal field splitting energy is:

${\text{H}}_2\text{O}<{\text{NH}}_3<en$

Thus, increasing order of crystal field splitting energy for the given complexes is:

${\left[\mathrm{Co}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+}<{\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}<{\left[\mathrm{Co}{\left(\mathrm{en}\right)}_3\right]}^{3+}$

As, $E=\frac{hc}{\lambda }$

Thus, increasing order of wavelength of absorption is:

${\left[\mathrm{Co}{\left(\mathrm{en}\right)}_3\right]}^{3+}<{\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}<{\left[\mathrm{Co}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+}$

(2)

${\left[\mathrm{Mn}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$: Let oxidation state of Mn be $x$.

$x+6\times (-1)=-3 \Rightarrow x=+3$

Electronic configuration of Mn: $\left[\text{Ar}\right]3d^{5}4s^2$

Electronic configuration of ${\mathrm{Mn}}^{3+}$:  $\left[\text{Ar}\right]3d^4$

${\text{CN}}^{-}$ is a strong field ligand, it causes pairing of electrons in the $3d$ orbital.

[IMAGE 36]-------------------

Thus, ${\left[\mathrm{Mn}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$ has $d^{2}s{p}^3$ hybridisation and has octahedral geometry.

(2)

Jahn–Teller distortion is usually significant for asymmetrically occupied $e_g$ orbitals since they are directed towards the ligands and the energy gain is considerably more.

In case of unevenly occupied $t_{2g}$ orbitals, the Jahn–Teller distortion is very weak since the $t_{2g}$ set does not point directly at the ligands and therefore, the energy gain is much less.

High spin complexes :

[IMAGE 37]-------------------------

(4)

${\left[\mathrm{Ni}{\left(\mathrm{CN}\right)}_4\right]}^{2-}$ : Oxidation number of Ni = +2

Electronic configuration of ${\mathrm{Ni}}^{2+}$$: \left[Ar\right]3d^{8}4s^0$

[IMAGE 38]---------------------------

Pairing of electrons in $d$-orbital takes place due to the presence of strong field ligand $\left({\mathrm{CN}}^{-}\right)$.

(2)

${\mathrm{H}}_2\mathrm{O}$ is a weak field ligand, hence ${\Delta }_o$ < pairing energy. 

CFSE $=(-0.4x+0.6y){\Delta }_o$

where, $x$ and $y$ are no. of electrons occupying $t_{2g}$ and $e_g$ orbitals respectively. 

For ${\left[\mathrm{Fe}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+}$ complex ion,

${\mathrm{Fe}}^{3+} \left(3d^5\right)=t_{2g}^3{e}_g^2=-0.4\times 3+0.6\times 2=0.0$ or $0{∆}_0$