Write two consequences of lanthanide contraction.
To solve the problem, we need to identify two consequences of lanthanide contraction.
1. Understand Lanthanide Contraction:
Lanthanide contraction refers to the gradual decrease in ionic radii of lanthanide elements (from La to Lu) due to poor shielding by the 4f electrons, leading to a stronger nuclear attraction on the outer electrons.
2. Consequence 1 - Similarity in Properties of Post-Lanthanide Elements:
Due to lanthanide contraction, the ionic radii of 4d and 5d transition elements (e.g., Zr and Hf) are very similar. This leads to similar chemical properties, making their separation difficult.
3. Consequence 2 - Basicity of Lanthanide Hydroxides:
Lanthanide contraction causes a decrease in ionic size across the series, increasing the charge density of \( Ln^{3+} \) ions. This enhances the polarizing power, reducing the basicity of hydroxides (\( Ln(OH)_3 \)) from La to Lu.
Final Answer:
Two consequences of lanthanide contraction are: (1) Similar ionic radii and chemical properties of 4d and 5d transition elements (e.g., Zr and Hf), making separation challenging. (2) Decrease in basicity of lanthanide hydroxides (\( Ln(OH)_3 \)) across the series due to increasing charge density of \( Ln^{3+} \).
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 \(P,O,Q\).