Step 1: Understanding the Concept:
Ionization enthalpy generally increases across a series (like lanthanides) as atomic number increases, due to lanthanide contraction and increased nuclear charge.
Step 2: Key Formula or Approach:
Consider stability of electronic configurations (half-filled or fully filled subshells).
Step 3: Detailed Explanation:
The given elements are lanthanides: La (57), Ce (58), Gd (64), Yb (70).
Across the series from La to Lu, atomic radius decreases and \(IE\) increases.
Yb (Ytterbium) is at the later end of the series and has a fully filled \(4f^{14}\) subshell, which provides extra stability. This makes it harder to remove an electron compared to La, Ce, or Gd.
Step 4: Final Answer:
Yb has the highest first ionization enthalpy among the options.