{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Atomic Transitions \u2192 Hydrogen Atom", "refinement": "This problem involves understanding the allowed transitions between quantum states of the hydrogen atom, specifically dipole transitions governed by selection rules.", "specific_scope": "The focus is on the specific decay route from the |4,0,0\u27e9 state to the |2,0,0\u27e9 state through intermediate states, analyzing the allowed transitions and their probabilities.", "goal": "Identify the correct transition route and calculate the 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 sequence of transitions from the |4,0,0\u27e9 state to the |2,0,0\u27e9 state, identifying the intermediate state and calculating the probability of the transition. The correct answer is the route |4,0,0\u27e9\u2192|3,1,0\u27e9\u2192|2,0,0\u27e9 with a probability of 1/3."}