How can we calculate the valency …

Electronic Configuration of Lanthanides

Lanthanides of first f-block have a terminal electronic configuration of [Xe] 4f1-14 5d 0-16s2 of the fourteen lanthanides, promethium (Pm) with atomic number 61 is the only synthetic radioactive element. The energy of 4f and 5d electrons are almost close to each other and so 5d orbital remains vacant and the electrons enter into the 4f orbital.

Exceptions are in the case of gadolinium, Gd (Z = 64) where the electron enters the 5d orbital due to the presence of half-filled d-orbital and lutetium (Z = 71) enters the 5d orbital.

Electronic Configuration of Actinides

Actinides are the second series of elements of the f-block having a terminal electronic configuration of [Rn] 5f1-14 6d 0-17s2. The energy of 5f and 6d electrons are close to each other and so electrons enter into the 5f orbital.