Step 1: Understanding the Concept:
The lanthanide series consists of 14 elements from Cerium ($Z=58$) to Lutetium ($Z=71$). Most lanthanides are non-radioactive and occur naturally.
Step 2: Detailed Explanation:
Promethium ($Pm$, atomic number 61) is the only lanthanide element that does not have any stable isotopes. It is produced synthetically and is radioactive.
Step 3: Final Answer:
The radioactive element in the lanthanide series is Promethium.