{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Molecular Vibrations", "refinement": "This problem involves the energy levels of a quantum harmonic oscillator, specifically for a diatomic molecule transitioning between vibrational states.", "specific_scope": "The focus is on calculating the energy difference between the first excited state and the ground state of a diatomic molecule modeled as a quantum harmonic oscillator.", "goal": "Determine the energy of the photon emitted during the transition from the first excited state to the ground state."}, "summary": "This problem pertains to quantum mechanics, specifically the behavior of diatomic molecules modeled as quantum harmonic oscillators. The task is to calculate the energy of a photon emitted when the molecule transitions from the first excited vibrational state to the ground state. By using the formula for the energy levels of a quantum harmonic oscillator, we can find the energy difference between these states, which corresponds to the energy of the emitted photon. The correct answer is 1.99 x 10^-20 J."}