Lanthanoid contraction is caused due to

The fourteen lanthanoids run from $$Ce \,(Z = 58)$$ to $$Lu \,(Z = 71)$$. As we move across this series one proton is added to the nucleus and, at the same time, one electron is added to the 4f subshell.

Key facts to remember:

• 4f-orbitals are buried deep inside the atom, lying between the 5s/5p shells and the outer 6s shell.
• Electrons present in an inner subshell shield the outer-shell electrons from the full nuclear charge. The efficiency of this shielding depends on the shape and penetration of the orbital.

The 4f-orbitals are very diffuse and have poor penetration towards the nucleus. Hence their electrons shield the outer 6s and 5d electrons only incompletely. Because the shielding is imperfect, the additional positive charge that is added to the nucleus on moving from one element to the next is not fully cancelled. Consequently, the effective nuclear charge ($$Z_{\text{eff}}$$) experienced by the valence electrons increases steadily.

The steadily increasing $$Z_{\text{eff}}$$ pulls all the electron shells slightly closer to the nucleus, so the atomic and ionic radii show a regular decrease from $$Ce^{3+}$$ to $$Lu^{3+}$$. This gradual size decrease within the lanthanoid series is known as lanthanoid contraction.

Now examine the given statements:

Option A: “appreciable shielding by 4f electrons” ⇒ says shielding is strong; reality: shielding is weak. Hence false.

Option B: Mentions 5d electrons. 5d electrons are not mainly responsible for the contraction. Hence false.

Option C: “same effective nuclear charge from Ce to Lu” contradicts observation; $$Z_{\text{eff}}$$ actually increases. Hence false.

Option D: “imperfect shielding on outer electrons by 4f electrons” exactly matches the explanation above; therefore it is correct.

Option D which is: the imperfect shielding on outer electrons by 4f electrons from the nuclear charge