What is crystal field splitting energy? How does the magnitude of\( Δo\) decide the actual configuration of d-orbitals in a coordination entity?
The degenerate d-orbitals (in a spherical field environment) split into two levels i.e., \(e_g\) and \(t_{2g}\) in the presence of ligands. The splitting of the degenerate levels due to the presence of ligands is called the crystal-field splitting while the energy difference between the two levels (\(e_g\) and \(t_{2g}\)) is called the crystal-field splitting energy. It is denoted by \(Δo\). After the orbitals have split, the filling of the electrons takes place. After 1 electron (each) has been filled in the three \(t_{2g}\)orbitals, the filling of the fourth electron takes place in two ways. It can enter the \(e_g\) orbital (giving rise to t2g 3 eg 1 like electronic configuration) or the pairing of the electrons can take place in the \(t_{2g}\) orbitals (giving rise to \(t_{2g}\) 4 \(e_g\) 0 like electronic configuration). If the Δo value of a ligand is less than the pairing energy \((P)\), then the electrons enter the egorbital. On the other hand, if the \(Δo\) value of a ligand is more than the pairing energy \((P)\), then the electrons enter the \(t_{2g}\)orbital.
(i) Draw the diagram which indicates the splitting of d-orbitals in tetrahedral field.
(ii) Write any one limitation of valence bond theory.
(i)[Ni(CN)₄]²⁻ and [Ni(CO)(_4)] have different structures, but do not differ in their magnetic behaviour. Explain.
(ii) Write the formula of Tetraamineaquachloridocobalt(III)chloride.
(i) Write two postulates of Werner's coordination theory.
(ii) Draw the geometrical isomers of [(NH_3)_3(NO_2)_3] and give their structures.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).