Why is a solution of \(\text{Ni(H}_2\text{O})_6^{2+}\) green while a solution of \(\text{Ni(CN)}_4^{2-}\) is colourless? (At. No. of Ni = 28)
The color of a coordination compound is largely influenced by the ligand field and the d-electron transitions of the metal ion.
In the case of \(\text{Ni(H}_2\text{O})_6^{2+}\), water is a weak field ligand that causes a small splitting of the d-orbitals in \(\text{Ni}^{2+}\). This allows the absorption of light in the visible spectrum, giving the solution a green color.
In contrast, in \(\text{Ni(CN)}_4^{2-}\), cyanide is a strong field ligand that causes a large splitting of the d-orbitals in \(\text{Ni}^{2+}\), leading to no available electronic transitions in the visible region. As a result, the solution of \(\text{Ni(CN)}_4^{2-}\) is colorless because no visible light is absorbed.
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 \(P,O,Q\).