---
title: "A sample of cold gas in its ground state (\\(E_1 = -10.0\\text{ eV}\\)) is illuminated by continuous light, producing an absorption spectrum with a dark line at wavelength \\(\\lambda = 177\\text{ nm}\\). The energy-level diagram for an atom of the gas is shown. An atom absorbs a photon corresponding to this line and subsequently undergoes a two-step cascade decay back to the ground state. What are the energies of the two photons emitted during this decay?"
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url: "https://nerd-notes.com/ubq/117475/"
date_modified: "2026-08-04T06:52:17+00:00"
---

# A sample of cold gas in its ground state (\(E_1 = -10.0\text{ eV}\)) is illuminated by continuous light, producing an absorption spectrum with a dark line at wavelength \(\lambda = 177\text{ nm}\). The energy-level diagram for an atom of the gas is shown. An atom absorbs a photon corresponding to this line and subsequently undergoes a two-step cascade decay back to the ground state. What are the energies of the two photons emitted during this decay?

A sample of cold gas in its ground state (\(E_1 = -10.0\text{ eV}\)) is illuminated by continuous light, producing an absorption spectrum with a dark line at wavelength \(\lambda = 177\text{ nm}\). The energy-level diagram for an atom of the gas is shown. An atom absorbs a photon corresponding to this line and subsequently undergoes a two-step cascade decay back to the ground state. What are the energies of the two photons emitted during this decay?

![A vertical axis labeled Energy (eV) stands on the left side of the diagram, with labeled tick marks at -10.0, -5.5, -3.0, -1.0, and 0. Four solid horizontal line segments extend to the right from the vertical axis to represent atomic energy levels. The lowest horizontal line segment is positioned at -10.0 on the vertical axis and is labeled E_1 = -10.0 eV. The second line segment above it is positioned at -5.5 and labeled E_2 = -5.5 eV. The third line segment above that is at -3.0 and labeled E_3 = -3.0 eV. The top horizontal line segment is at -1.0 and labeled E_4 = -1.0 eV. A horizontal dashed line at 0 on the vertical axis is labeled 0 eV. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826337-ktwPMn.jpg)

- **A.** \(2.5\text{ eV}\) and \(4.5\text{ eV}\)
- **B.** \(2.0\text{ eV}\) and \(7.0\text{ eV}\)
- **C.** \(3.0\text{ eV}\) and \(4.0\text{ eV}\)
- **D.** \(3.5\text{ eV}\) and \(3.5\text{ eV}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117475/*