Give explanation for each of the following observations:
(a) Mn3+ is an oxidizing agent, whereas Cr2+ is a reducing agent (both d4 configuration).
(b) Actinoid contraction is greater than lanthanoid contraction.
(c) Transition metals form interstitial compounds with H, B, C, N.
(a) Mn3+ is an oxidizing agent, whereas Cr2+ is a reducing agent (both d4 configuration).
Mn3+ readily gains an electron to become the more stable Mn2+, hence acts as an oxidizing agent. Cr2+ loses an electron to form Cr3+, which is more stable due to half-filled t2g orbitals (d3), thus acts as a reducing agent.
(b) Actinoid contraction is greater than lanthanoid contraction.
Actinoids have 5f orbitals that are more diffused and poorly shielded compared to 4f orbitals in lanthanoids. This leads to a greater effective nuclear charge and stronger contraction across the series.
(c) Transition metals form interstitial compounds with H, B, C, N.
Transition metals have vacant d-orbitals and lattice voids where small atoms like H, B, C, N can fit without disturbing the structure, forming interstitial compounds which are hard and have high melting points.

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?