Concept:
The lanthanoids comprise fourteen elements from cerium (\(Z=58\)) to lutetium (\(Z=71\)). As we move across the lanthanoid series, electrons are progressively added to the \(4f\)-subshell.
The \(4f\)-electrons are poor at shielding the nuclear charge. Consequently, the effective nuclear charge experienced by the outer electrons increases steadily from left to right in the series.
As a result, the electrons are pulled closer towards the nucleus, causing a gradual decrease in both atomic and ionic radii.
This gradual decrease in size across the lanthanoid series is known as lanthanoid contraction.
Step 1: Understand the filling of the \(4f\)-orbitals.
As we move from La to Lu, electrons enter the \(4f\)-orbitals.
\[
La \rightarrow Ce \rightarrow \cdots \rightarrow Lu
\]
The \(4f\)-electrons do not effectively shield the increasing nuclear charge.
Step 2: Examine the effect on atomic size.
Due to the increase in effective nuclear charge, the outer electrons experience stronger attraction toward the nucleus.
Hence,
\[
\text{Atomic radius decreases}
\]
and
\[
\text{Ionic radius decreases}
\]
throughout the series.
Step 3: Identify the phenomenon responsible.
The observed decrease in atomic and ionic radii from La to Lu is called:
\[
\boxed{\text{Lanthanoid Contraction}}
\]
Therefore, the correct option is
\[
\boxed{(1)}
\]