Step 1: Understanding the Concept:
Work function is the minimum energy required to remove an electron from the metal surface. It is directly related to the ionization energy of the metal atoms.
Step 2: Detailed Explanation:
1. Lowest Work Function: Alkali metals (Group 1) have the largest atomic radii and lowest effective nuclear charge in their respective periods, resulting in very low ionization energies and work functions. Among the listed alkali metals (Li, Na, K), K has the largest radius and thus the lowest work function.
2. Highest Work Function: Transition metals and noble metals generally have high work functions due to higher effective nuclear charges. Among the listed metals, Copper (Cu) and Silver (Ag) have significantly higher values than alkali or alkaline earth metals.
3. According to the provided answer key, the intended pair is Potassium (K) as lowest and Copper (Cu) as highest.
Step 3: Final Answer:
The metals are K and Cu.