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title: "The energy levels of a hypothetical stationary atom are shown in the diagram, with the ground state at \\(E_1 = -12.0\\text{ eV}\\) and excited states at \\(E_2 = -5.0\\text{ eV}\\), \\(E_3 = -2.0\\text{ eV}\\), and \\(E_4 = -0.5\\text{ eV}\\). A beam of free electrons, each having a kinetic energy of \\(10.5\\text{ eV}\\), bombards a sample of these atoms initially in their ground state. Which of the following correctly identifies all possible kinetic energies of the scattered electrons and all possible photon energies emitted by the atoms as they de-excite?"
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url: "https://nerd-notes.com/ubq/123554/"
date_modified: "2026-09-28T12:00:09+00:00"
---

# The energy levels of a hypothetical stationary atom are shown in the diagram, with the ground state at \(E_1 = -12.0\text{ eV}\) and excited states at \(E_2 = -5.0\text{ eV}\), \(E_3 = -2.0\text{ eV}\), and \(E_4 = -0.5\text{ eV}\). A beam of free electrons, each having a kinetic energy of \(10.5\text{ eV}\), bombards a sample of these atoms initially in their ground state. Which of the following correctly identifies all possible kinetic energies of the scattered electrons and all possible photon energies emitted by the atoms as they de-excite?

The energy levels of a hypothetical stationary atom are shown in the diagram, with the ground state at \(E_1 = -12.0\text{ eV}\) and excited states at \(E_2 = -5.0\text{ eV}\), \(E_3 = -2.0\text{ eV}\), and \(E_4 = -0.5\text{ eV}\). A beam of free electrons, each having a kinetic energy of \(10.5\text{ eV}\), bombards a sample of these atoms initially in their ground state. Which of the following correctly identifies all possible kinetic energies of the scattered electrons and all possible photon energies emitted by the atoms as they de-excite?

![An energy-level diagram with a vertical axis on the left labeled Energy (\text{eV}). Four horizontal solid line segments are drawn at heights corresponding to their energy values. The lowest horizontal line is labeled n = 1 at its right end and -12.0 at the left vertical axis. The second horizontal line is labeled n = 2 at its right end and -5.0 at the left axis. The third horizontal line is labeled n = 3 at its right end and -2.0 at the left axis. The highest horizontal line is labeled n = 4 at its right end and -0.5 at the left axis. The vertical spacing between lines is proportionally larger between lower levels. No other lines, arrows, text, or curves appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596808-aqdsmw.jpg)

- **A.** Scattered electron kinetic energies: \(10.5\text{ eV}\) only Emitted photon energies: None
- **B.** Scattered electron kinetic energies: \(0.5\text{ eV}\), \(3.5\text{ eV}\), and \(10.5\text{ eV}\) Emitted photon energies: \(2.0\text{ eV}\), \(5.0\text{ eV}\), and \(12.0\text{ eV}\)
- **C.** Scattered electron kinetic energies: \(0.5\text{ eV}\), \(3.5\text{ eV}\), and \(10.5\text{ eV}\) Emitted photon energies: \(7.0\text{ eV}\) and \(10.0\text{ eV}\) only
- **D.** Scattered electron kinetic energies: \(0.5\text{ eV}\), \(3.5\text{ eV}\), and \(10.5\text{ eV}\) Emitted photon energies: \(3.0\text{ eV}\), \(7.0\text{ eV}\), and \(10.0\text{ eV}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123554/*