Lanthanide contraction refers to the gradual decrease in the ionic radius of the lanthanide series as the atomic number increases, caused by the poor shielding effect of the 4f-electrons. Two important consequences of lanthanide contraction are: 1. Decreasing ionic radii: As the atomic number increases from \( La^{3+} \) to \( Lu^{3+} \), the size of the ions decreases, leading to an increase in the effective nuclear charge experienced by the electrons. This results in a decrease in the ionic radii. 2. Similarity between the 3d and 4d/5d elements: The lanthanide contraction leads to similarities in the properties of the lanthanide elements and the d-block elements in the same period. For example, \( Zr \) (a 4d element) and \( Hf \) (a 5d element) have very similar ionic radii due to the lanthanide contraction.
Thus, the lanthanide contraction results in smaller ionic radii and increased similarities between the properties of lanthanides and d-block elements.
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 \(P,O,Q\).