---
title: "A gas of hypothetical four-level atoms is at room temperature such that all atoms are initially in the ground state ( \\(n=1\\)). The energy levels of the atom are \\(E_1 = -12.0\\text{ eV}\\), \\(E_2 = -5.0\\text{ eV}\\), \\(E_3 = -2.0\\text{ eV}\\), and \\(E_4 = -1.0\\text{ eV}\\). Continuous white light passes through the gas to produce an absorption spectrum, while a separate electrical discharge excites a sample of these atoms up to the \\(n=4\\) state to produce an emission spectrum. What is the number of distinct dark absorption lines observed in the absorption spectrum, and which downward transition produces the photon with the longest wavelength in the emission spectrum?"
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url: "https://nerd-notes.com/ubq/123539/"
date_modified: "2026-09-28T12:00:04+00:00"
---

# A gas of hypothetical four-level atoms is at room temperature such that all atoms are initially in the ground state (
\(n=1\)). The energy levels of the atom are \(E_1 = -12.0\text{ eV}\), \(E_2 = -5.0\text{ eV}\), \(E_3 = -2.0\text{ eV}\), and \(E_4 = -1.0\text{ eV}\). Continuous white light passes through the gas to produce an absorption spectrum, while a separate electrical discharge excites a sample of these atoms up to the \(n=4\) state to produce an emission spectrum. What is the number of distinct dark absorption lines observed in the absorption spectrum, and which downward transition produces the photon with the longest wavelength in the emission spectrum?

A gas of hypothetical four-level atoms is at room temperature such that all atoms are initially in the ground state (
\(n=1\)). The energy levels of the atom are \(E_1 = -12.0\text{ eV}\), \(E_2 = -5.0\text{ eV}\), \(E_3 = -2.0\text{ eV}\), and \(E_4 = -1.0\text{ eV}\). Continuous white light passes through the gas to produce an absorption spectrum, while a separate electrical discharge excites a sample of these atoms up to the \(n=4\) state to produce an emission spectrum. What is the number of distinct dark absorption lines observed in the absorption spectrum, and which downward transition produces the photon with the longest wavelength in the emission spectrum?

![A vertical energy-level diagram showing four horizontal line segments stacked vertically. The bottom line segment is labeled n = 1 at its left and -12.0 eV at its right. Above it, a second horizontal line segment is labeled n = 2 at its left and -5.0 eV at its right. Above that, a third horizontal line segment is labeled n = 3 at its left and -2.0 eV at its right. Near the top, a fourth horizontal line segment is labeled n = 4 at its left and -1.0 eV at its right. The vertical spacing between the lines reflects their relative energy values, with the largest gap between n = 1 and n = 2. A vertical upward-pointing axis to the left is labeled Energy (eV). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-energy-levels-1790596804-D5Q7yQ.jpg)

- **A.** 3 absorption lines ; \(n = 4 \to n = 3\)
- **B.** 3 absorption lines ; \(n = 4 \to n = 1\)
- **C.** 6 absorption lines ; \(n = 4 \to n = 3\)
- **D.** 6 absorption lines ; \(n = 4 \to n = 1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123539/*