{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Energy Levels", "refinement": "This problem involves the concept of energy levels in quantum mechanics and the uncertainty principle, which relates the lifetime of a state to the uncertainty in energy.", "specific_scope": "The focus is on determining the minimum energy difference required to distinguish between two quantum states based on their lifetimes.", "goal": "Identify the energy difference that allows for clear resolution of the two quantum states given their respective lifetimes."}, "summary": "In quantum mechanics, the uncertainty principle states that the uncertainty in energy (\u0394E) and the uncertainty in time (\u0394t) are related by \u0394E * \u0394t \u2265 \u0127/2. 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 larger uncertainty in energy. Therefore, we need to find an energy difference that exceeds the calculated uncertainty based on the longer lifetime (10^-8 sec). This leads us to evaluate the candidates provided."}