{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Energy Levels and Lifetimes", "refinement": "This problem involves the relationship between the energy difference of quantum states and their lifetimes, specifically using the energy-time uncertainty principle.", "specific_scope": "The focus is on determining the minimum energy difference between two quantum states based on their lifetimes to ensure they can be resolved.", "goal": "Calculate the minimum energy difference required for the two quantum states to be distinguishable based on their lifetimes."}, "summary": "This problem relates to quantum mechanics, specifically the energy-time uncertainty principle, which states that the uncertainty in energy (\u0394E) and the uncertainty in time (\u0394t) are inversely related. To resolve two quantum states with given lifetimes, we can use the formula \u0394E \u2265 \u0127/(2\u0394t). Given the lifetimes of the states, we can calculate the minimum energy difference required for clear resolution. The answer is determined to be 2 x 10^-5 eV, which corresponds to the first candidate option."}