Step 1: Understanding the Concept
All the given elements are alkali metals of group 1.
Step 2: Identify the radioactive one
Lithium, potassium and rubidium have stable (or very long-lived) isotopes. Francium (\(Z=87\)) has only short-lived radioactive isotopes.
Step 3: Conclusion
The longest-lived isotope of francium has a half-life of only about 22 minutes, so francium is the radioactive element.
Final Answer:
Francium is the radioactive alkali metal.
\[ \boxed{\text{(A) }\text{Fr}} \]