Let's analyze each statement one by one:
Statement A: "D-Block elements show irregular and erratic chemical properties among themselves."
This is a correct statement. The d-block elements (transition metals) exhibit irregularities in their chemical properties due to varying electron configurations, and the involvement of (n-1)d and ns orbitals leads to a variety of oxidation states, magnetic properties, and reactivities.
Statement B: "La and Lu have partially filled d orbitals and no other partially filled orbitals."
This is an incorrect statement. Lanthanum (La) has a configuration [Xe] 5d¹ 6s², with only one electron in the 5d orbital. Lutetium (Lu), on the other hand, has a configuration [Xe] 4f¹⁴ 5d¹ 6s², meaning it has a filled 4f subshell and one electron in the 5d orbital. Therefore, neither La nor Lu has partially filled d orbitals and no other partially filled orbitals.
Statement C: "The chemistry of various lanthanoids is very similar."
This is a correct statement. Lanthanoids show very similar chemical properties because they have nearly identical sizes (lanthanide contraction) and electron configurations, primarily differing in the number of 4f electrons, which don't significantly affect their chemistry.
Statement D: "4f and 5f orbitals are equally shielded."
This is an incorrect statement. The 4f orbitals are more effectively shielded from the nucleus by the outer 5d and 6s orbitals compared to the 5f orbitals, which are less shielded and participate more in bonding. Hence, the shielding effects differ between 4f and 5f orbitals.
Answer: The incorrect statements are B and D.