{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Atomic Transitions \u2192 Hydrogen Atom", "refinement": "This problem involves understanding the selection rules for electric dipole transitions between quantum states of the hydrogen atom.", "specific_scope": "The focus is on the specific decay route from the state |3,0,0\u27e9 to |1,0,0\u27e9 via intermediate states, and calculating the probabilities associated with these transitions.", "goal": "Identify the correct transition route and corresponding probability for the decay of the |3,0,0\u27e9 state to the |1,0,0\u27e9 state."}, "summary": "This problem pertains to quantum mechanics, specifically the study of atomic transitions in the hydrogen atom. It requires knowledge of the selection rules for electric dipole transitions to determine the valid routes and probabilities for the decay of the |3,0,0\u27e9 state to the |1,0,0\u27e9 state. The task is to analyze the given candidates and identify the correct transition path and its associated probability."}