Step 1: Understanding the Concept:
Going down a group, atomic size grows and the outer electron is held less tightly. So first ionization enthalpy decreases down a group.
Step 2: Apply to the groups:
Alkali metals in order: Li, Na, K, Rb, Cs. Li is at the top, so it has the highest \(\Delta_iH_1\) (about \(520\) kJ/mol).
Alkaline earth metals: Be, Mg, Ca, Sr, Ba. Be is at the top, so it has the highest \(\Delta_iH_1\) (about \(899\) kJ/mol).
Step 3: Other options:
K, Rb, Ca, Sr and Ba are all lower in their groups. Their larger size gives lower ionization enthalpy, so options A, C and D are wrong.
Final Answer:
The pair is Li and Be, option (B).
\[ \boxed{\text{Li and Be}} \]