{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Atomic Transitions \u2192 Hydrogen Atom", "refinement": "This problem involves understanding the dipole transitions between quantum states of the hydrogen atom, specifically the selection rules and probabilities associated with these transitions.", "specific_scope": "The focus is on the decay of the hydrogen atom from the state |3,0,0\u27e9 to |1,0,0\u27e9 via an intermediate state |2,1,0\u27e9, and calculating the probability of this transition route.", "goal": "Identify the correct transition route and its corresponding probability for the decay process."}, "summary": "This problem pertains to quantum mechanics, specifically the study of atomic transitions in the hydrogen atom. It requires knowledge of dipole transitions and the selection rules that govern them. The task is to determine the correct transition route from the state |3,0,0\u27e9 to |1,0,0\u27e9 via an intermediate state, along with the associated probability. The correct answer is the transition |3,0,0\u27e9\u2192|2,1,0\u27e9\u2192|1,0,0\u27e9 with a probability of 1/3."}