{"knowledge_schema": {"broad_category": "Science \u2192 Radioactivity \u2192 Decay Processes", "refinement": "This problem specifically deals with the concept of half-life, which is the time required for half of the radioactive atoms in a sample to decay.", "specific_scope": "The focus is on calculating the remaining quantity of a radioactive isotope after a specified duration, given its initial quantity and half-life.", "goal": "Determine the number of undecayed atoms remaining after a certain period of time based on the half-life of the isotope."}, "summary": "This problem involves the concept of radioactive decay and half-life, which is the time it takes for half of a radioactive sample to decay. In this case, we start with 1000 atoms and need to calculate how many remain after 90 minutes, given a half-life of 30 minutes. By applying the half-life concept, we can determine that after three half-lives (90 minutes), only 125 atoms are expected to remain undecayed."}