Creating new elements in order to study their properties is definitely pure research. It has no earthly [known] application, since the elements don't even exist, whereas for each of the other choices, you've stated the desired application as the reason for the search.
The correct choice for an example of pure research is option A, "Creating new elements to study their properties." This choice focuses on gaining knowledge without immediate practical application, setting it apart from the other options that are geared towards practical solutions. Pure research is crucial for understanding fundamental aspects of science, even if its applications may only be seen later on.
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