Step 1: Understanding the Concept:
As we move from Lanthanum (\(Z=57\)) to Lutetium (\(Z=71\)), we observe a regular decrease in atomic and ionic radii. This phenomenon is known as Lanthanide Contraction.
This trend is counter-intuitive because, generally, as you move across a period, size decreases only slightly. In the f-block, this decrease is quite significant and has major chemical consequences for post-lanthanide elements.
Step 2: Detailed Explanation:
The cause of this contraction can be explained through the concepts of Nuclear Charge and the Shielding Effect.
1. Increase in Nuclear Charge: As the atomic number increases along the series, one proton is added to the nucleus at each step. This increases the total positive charge, which naturally pulls the electron cloud closer to the center.
2. Shielding Effect: Inner electrons usually "shield" or block the outer electrons from the full pull of the nucleus. The effectiveness of different orbitals in shielding follows the order \( s>p>d>f \).
3. The Role of 4f Electrons: In the lanthanide series, extra electrons are added to the 4f subshell. Due to their highly diffuse shape and large spatial extent, 4f orbitals are extremely poor at shielding.
4. Net Result: Because the 4f electrons do not effectively shield the outer shells from the increasing nuclear charge, the Effective Nuclear Charge (\(Z_{eff}\)) experienced by the outer electrons increases significantly. This results in the outer electron shells being pulled inward, leading to a progressive decrease in the size of the atom/ion.
Step 3: Final Answer:
The lack of effective shielding by the diffuse 4f orbitals is the primary physical cause of this effect.
Therefore, option (B) is the accurate scientific description.