Reason of lanthanoid contraction is:

Step-by-step solution

Lanthanoids are the f - block elements and 4 f series element. The orbital size of the 4 f is much bigger due to which electrons are spread in the large area, these electrons not able to shield charge from the nucleus. As a result, the poor screening effect or poor shielding effect of the 4 f sub-shell. There is regular decrement of the atomic radius on increasing the atomic number.