Explain the lanthanoid contraction.

(N/A) The steady decrease in the atomic and ionic radii of lanthanoids with an increase in atomic number from $La$ $(Z=57)$ to $Lu$ $(Z=71)$ is known as lanthanoid contraction.
This phenomenon occurs due to the imperfect shielding of one $4f$ electron by another in the same subshell.
As the atomic number increases,the nuclear charge increases by one unit at each step,while the new electron enters the $4f$ orbital.
The $4f$ orbitals have a very diffuse shape and poor shielding effect,which is unable to compensate for the increased nuclear attraction on the outer electrons.
Consequently,the effective nuclear charge increases,pulling the electron cloud closer to the nucleus,resulting in a gradual decrease in atomic and ionic sizes.