{"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 two quantum states given their respective lifetimes."}, "summary": "In quantum mechanics, the ability to distinguish between two energy levels is influenced by their lifetimes, which relate to the uncertainty in energy through the energy-time uncertainty principle. The longer the lifetime of a state, the smaller the uncertainty in its energy. To clearly resolve two energy levels, the energy difference must be larger than the uncertainty in energy, which can be calculated using the formula \u0394E \u2248 \u0127 / \u03c4, where \u03c4 is the lifetime. Given the lifetimes of 10^-9 sec and 10^-8 sec, the energy difference of 10^-4 eV is sufficient to clearly distinguish the two states, making it the correct choice."}