(i) The difference between lanthanoids and actinoids with respect to their structural variability and chemical reactivity are as follows:
a) Actinoids are radioactive, while lanthanoids are not radioactive.
b) The ionisation enthalpies of the early actinoids are lower than those of the early lanthanoids. Actinoids show the oxidation state from +3 (most common) to +7, while lanthanoids show the oxidation state from +3 up to +7.
c) Actinoids are more reactive and have more complex magnetic properties than lanthanoids
(ii) Cerium is a lanthanoids element that is known to exhibit the oxidation state of +4
(iii) The complete equation is as follows : MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O
(iv) Mn²⁺ is more paramagnetic because it has more number of unpaired electrons than Cr³⁺ (5 u.e > 3 u.e).