Give Reasons:
(I) \( \text{Ce}^{4+} \) in aqueous solution is a good oxidising agent.
(II) The actinoid contraction is greater from element to element than lanthanoid contraction.
(III) \( E^\circ_{\text{M}^{2+}/\text{M}} \) value is more negative than expected, whereas \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \) is positive.
(I) \( \text{Ce}^{4+} \) in aqueous solution is a good oxidising agent.
Reason: \( \text{Ce}^{4+} \) is a strong oxidising agent because it has a high tendency to accept an electron and reduce to \( \text{Ce}^{3+} \). The high charge on \( \text{Ce}^{4+} \) (a +4 oxidation state) and the relatively small ionic radius of \( \text{Ce}^{4+} \) compared to its reduced form \( \text{Ce}^{3+} \) give it a high electron affinity, making it an effective oxidant in aqueous solutions.
(II) The actinoid contraction is greater from element to element than lanthanoid contraction.
Reason: The actinoid contraction is greater than the lanthanoid contraction because the 5f-electrons in actinides experience poor shielding by other f-electrons, resulting in a greater increase in effective nuclear charge as the atomic number increases. In contrast, lanthanides with 4f-electrons experience better shielding; therefore, the contraction is less significant. This explains why the atomic sizes in the actinide series decrease more significantly across the series than in the lanthanide series.
(III) \( E^\circ_{\text{M}^{2+}/\text{M}} \) value is more negative than expected, whereas \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \) is positive.
Reason: The \( E^\circ_{\text{M}^{2+}/\text{M}} \) value is more negative than expected due to the large increase in ionization energy as we remove electrons from the second ionization state, leading to a stronger pull by the nucleus. On the other hand, \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \) is positive because copper has a stable electronic configuration with a filled 3d10 subshell, making it more resistant to oxidation and thus having a positive electrode potential. Copper, being a transition metal, has a more favorable reduction potential than other elements like iron, leading to a positive standard electrode potential for the Cu2+/Cu system.
\(1\,\text{g}\) of \( \mathrm{AB_2} \) is dissolved in \(50\,\text{g}\) of a solvent such that \( \Delta T_f = 0.689\,\text{K} \). When \(1\,\text{g}\) of \( \mathrm{AB} \) is dissolved in \(50\,\text{g}\) of the same solvent, \( \Delta T_f = 1.176\,\text{K} \). Find the molar mass of \( \mathrm{AB_2} \). Given \( K_f = 5\,\text{K kg mol}^{-1} \). \((\textit{Report to nearest integer.})\) Both \( \mathrm{AB_2} \) and \( \mathrm{AB} \) are non-electrolytes.

A ladder of fixed length \( h \) is to be placed along the wall such that it is free to move along the height of the wall.
Based upon the above information, answer the following questions:
(iii) (b) If the foot of the ladder, whose length is 5 m, is being pulled towards the wall such that the rate of decrease of distance \( y \) is \( 2 \, \text{m/s} \), then at what rate is the height on the wall \( x \) increasing when the foot of the ladder is 3 m away from the wall?