Step 1: Understanding the Question:
The question requires us to identify the statement that is factually incorrect regarding the physical or chemical properties of the lanthanoid series elements.
Step 2: Detailed Explanation:
Let's analyze the properties of lanthanoids across the given choices:
Lanthanoids are typical metallic elements, making them highly efficient conductors of both heat and electricity.
Most tripositive lanthanoid ions ($\text{Ln}^{3+}$) possess unpaired electrons in their deep-lying $4\text{f}$ subshells, which induces strong paramagnetic properties (except for $\text{La}^{3+}$ and $\text{Lu}^{3+}$).
Due to their large ionic radii, lanthanoids easily accommodate crowded ligand spheres, frequently exhibiting coordination numbers greater than 6 (commonly 7, 8, or 9).
While almost all naturally occurring lanthanoids are stable and non-radioactive, there is a prominent exception:
Promethium (Pm) is entirely radioactive and does not occur naturally in significant quantities.
Because promethium is radioactive, the absolute statement that "these all are non-radioactive" is false.
Step 3: Final Answer:
The incorrect property statement corresponds to option (C).