{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Energy Levels", "refinement": "This problem involves the concept of energy levels in quantum states and their distinguishability based on their lifetimes and the uncertainty principle.", "specific_scope": "The focus is on determining the minimum energy difference required to resolve two quantum states with given lifetimes, using the energy-time uncertainty principle.", "goal": "Identify the energy difference that allows for clear resolution of the two quantum states based on their lifetimes."}, "summary": "In quantum mechanics, the energy-time uncertainty principle states that the uncertainty in energy (\u0394E) and the uncertainty in time (\u0394t) are related by \u0394E * \u0394t \u2265 \u0127/2, where \u0127 is the reduced Planck's constant. Given the lifetimes of the two states (10^-9 sec and 10^-8 sec), we can calculate the uncertainties in energy for each state. To clearly distinguish the two energy levels, the energy difference must be greater than the uncertainty in energy. The candidates provided include various energy differences, and we need to determine which one exceeds the calculated uncertainty to ensure the states can be resolved."}