When an atom emits a photon, how does the photon's energy depend on the energy of the electron orbits?

Question

BlackTom AI · Accepted Answer

Consider the question about photon emission from an atomic electron transitioning between energy levels. 
Option 1: 'Equals the energy of the lower orbit' is incorrect because the energy of the emitted photon corresponds to the difference between the initial and final energy levels, not the absolute energy of the final state. The lower orbit's energy alone does not account for the initial higher energy state.
Option 2: 'Equals the energy of the higher orbit' is also incorrect for similar reasons; using just the energy of the higher level would ignore how far the electron dropped, and thus the energy released.
Option 3: 'Is more than the energy difference between orbits' is not consistent with energy conservation in a simple atomic transition; the photon cannot carry away more energy than the energy released by the electron drop, which is exactly the difference between the two levels.
Option 4: 'Is less than the energy difference between orbits' is incorrect because the photon's energy is not a random fraction; it precisely equals the energy released in the transition, i.e., the exact difference between the initial and final level energies.
Option 5: 'Equals the energy difference between orbits.' is correct because photon energy during emission is hν = E_initial − E_final, which is the energy gap between the two levels involved in the transition. This follows from energy conservation and the quantized nature of atomic energy levels.

ASTRON 2140 AU2025 (23428) Final - 2025 Dec 12

When an atom emits a photon, how does the photon's energy depend on the energy of the electron orbits?

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