What is lanthanoid contraction?

Lanthanoid contraction refers to the gradual decrease in atomic and ionic radii of the lanthanoids from Ce to Lu.

Main cause

Across the lanthanoid series, electrons are added to the $4f$-subshell. These $4f$ electrons do not shield the outer electrons effectively from the increasing nuclear charge.

So, as atomic number increases:

• nuclear charge increases,
• but shielding by $4f$ electrons is poor,
• hence the effective nuclear charge increases,
• causing the electrons to be pulled closer to the nucleus.

Check each option

A: "the appreciable shielding on outer electrons by $4f$ electrons from the nuclear charge"

• Incorrect, because $4f$ electrons provide poor/imperfect shielding, not appreciable shielding.

B: "the appreciable shielding on outer electrons by $5d$ electrons from the nuclear charge"

• Incorrect. Lanthanoid contraction is mainly related to poor shielding by $4f$ electrons, not appreciable shielding by $5d$ electrons.

C: "the same effective nuclear charge from Ce to Lu"

• Incorrect. Effective nuclear charge does not remain same; it increases across the series.

D: "the imperfect shielding on outer electrons by $4f$ electrons from the nuclear charge"

• Correct. This is the standard reason for lanthanoid contraction.

Final answer

Therefore, the correct option is D.