Give explanation for each of the following observations:
(a) With the same d-orbital configuration (d4), Mn3+ ion is an oxidizing agent whereas Cr2+ ion is a reducing agent.
(b) Actinoid contraction is greater from element to element than that among lanthanoids.
(c) Transition metals form a large number of interstitial compounds with H, B, C, and N.
Solution:
(a) Mn3+ has a greater tendency to gain an electron to attain the more stable Mn2+ state. Cr2+, on the other hand, tends to lose an electron to become Cr3+, which is more stable. Thus, Mn3+ acts as an oxidizing agent while Cr2+ acts as a reducing agent.
(b) In actinoids, the 5f orbitals extend more into space and are less shielded, resulting in greater contraction in atomic size across the series as compared to the 4f orbitals in lanthanoids, which are better shielded.
(c) Transition metals have small atomic sizes and high charge densities. They can accommodate small atoms like H, B, C, and N in their interstitial sites, forming stable interstitial compounds that retain metallic properties.
A transition metal (M) among Mn, Cr, Co and Fe has the highest standard electrode potential \( (M^{3+} / M^{2+}) \). It forms a metal complex of the type \( [M(CN)_6]^{4-} \). The number of electrons present in the \( e_g \) orbital of the complex is ________.
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 \(P,O,Q\).