The energy level diagram below is for a large sample of...

The energy level diagram below is for a large sample of atoms that are all identical. These atoms all contain one electron that is initially in the ground state. The sample is radiated with photons that all have 10 -electron volts of energy. Shortly after the absorption, the atoms begin to emit photons spontaneously. What are all the possible energies of the emitted photons? (A) 4 $\mathrm{eV}$ only (B) 6 $\mathrm{eV}$ only (C) $4 \mathrm{eV}, 6 \mathrm{eV}$ only (D) $4 \mathrm{eV}, 6 \mathrm{eV},$ and 10 eV only (E) $4 \mathrm{eV}, 6 \mathrm{eV}, 10 \mathrm{eV},$ and 12 $\mathrm{eV}$

The energy level diagram below is for a large sample of atoms that are all identical. These atoms all contain one electron that is initially in the ground state. The sample is radiated with photons that all have 10 -electron volts of energy. Shortly after the absorption, the atoms begin to emit photons spontaneously. What are all the possible energies of the emitted photons?
(A) 4 $\mathrm{eV}$ only
(B) 6 $\mathrm{eV}$ only
(C) $4 \mathrm{eV}, 6 \mathrm{eV}$ only
(D) $4 \mathrm{eV}, 6 \mathrm{eV},$ and 10 eV only
(E) $4 \mathrm{eV}, 6 \mathrm{eV}, 10 \mathrm{eV},$ and 12 $\mathrm{eV}$

Key Concepts

Quantized Energy Levels

Atoms possess discrete energy levels, meaning electrons can only exist in specific, fixed energy states rather than any arbitrary energy value. This fundamental concept explains why the energy required to excite an electron or released during de-excitation is exactly equal to the difference between these quantized levels.

Photon Absorption

Photon absorption occurs when an electron in an atom absorbs a photon whose energy exactly matches the gap between two energy levels, allowing the electron to transition from a lower (often ground) state to a higher excited state. This precise energy matching underlies the selective excitation of electrons in atoms.

Spontaneous Emission

Spontaneous emission is the process by which an excited electron returns to a lower energy level without external provocation, emitting a photon in the process. The energy of this emitted photon corresponds to the difference between the two levels, and multiple decay paths can result in emissions of various energies.

Energy Level Diagram Interpretation

An energy level diagram graphically represents the different energy states of an atom and the allowed transitions between them. By analyzing the diagram, one can determine the possible photon energies absorbed or emitted, as these energies are directly given by the differences between the indicated energy levels.

Allowed Transitions

Allowed transitions refer to the specific changes in an electron's energy state that are permitted by quantum mechanical selection rules and energy conservation. These rules ensure that only transitions corresponding to exact energy differences can occur, determining the discrete set of possible photon energies involved in absorption and emission processes.

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