Explain each of the following observations:
(i) With the same d-orbital configuration (d4), Cr2+ is a reducing agent while Mn3+ is an oxidizing agent.
(ii) Actinoids exhibit a much larger number of oxidation states than lanthanoids.
(iii) There is hardly any increase in atomic size with increasing atomic numbers in a series of transition metals.

I) Cr2+ is strongly reducing in nature. It has a d4 configuration. While acting as a reducing agent, it gets oxidized to Cr3+ (electronic configuration, d3). This d3 configuration can be written as t23g configuration, which is a more stable configuration.
In the case of Mn3+ (d4), it acts as an oxidizing agent and gets reduced to Mn2+ (d5). This has an exactly half-filled d-orbital and has extra stability.
II) Actinides exhibit a large number of oxidation states but not lanthanides because the energy difference between orbitals of actinides is very less, so that they can exhibit different large numbers of oxidation states.
III) There is hardly any increase in atomic size with increasing atomic numbers in a series of transition metals because of lanthanide contraction (lanthanide contraction is the steady decrease in the size of the atoms and ions of the rare earth elements with increasing atomic number from lanthanum (atomic number 57) through lutetium (atomic number 71). For each consecutive atom, the nuclear charge is more positive by one unit, accompanied by a corresponding increase in the number of electrons present in the 4f orbitals surrounding the nucleus. The 4f electrons very imperfectly shield each other from the increased positive charge of the nucleus, so that the effective nuclear charge attracting each electron steadily increases through the lanthanoid elements, resulting in successive reductions of the atomic and ionic radii).