why does 4f-orbital gets started filling only when 1 electron has entered 5d-orbital in case of lanthanoids?
Electronic Configuration of Lanthanides: as the 4f and 5d electrons are so close in energy it is not possible to decide whether the electron has entered the 5d or 4f orbital. However, it is considered that the 5d orbital remains vacant and the electrons enter into the 4f orbital except for gadolinium, Gd (Z=64) where the electron enters into the 5d orbital due to the presence of half filled d-orbital. At Ytterbium (z=70) all the 4f orbital's are completely filled and hence, the differentiating electron of the next element that is lutetium (z=71) enters in to the 5d orbital.
The complete electronic configuration of Lanthanides can be given as
1s2 2s2p6 3s2p6d10 4s2p6d10f0-14 5s2p6 d0-1 6s2