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title: "A sample of hydrogen gas at room temperature is illuminated by a broad-spectrum light source. The resulting absorption spectrum displays dark lines corresponding to electron transitions from the ground state (\\(n = 1\\)) to higher energy levels (\\(n = 2, 3, 4\\)), but lines corresponding to transitions between excited states, such as \\(n = 2 \\to n = 3\\), are absent. However, when the gas is heated to a very high temperature, its emission spectrum displays bright lines for transitions between excited states, including \\(n = 3 \\to n = 2\\). Which of the following best explains why the absorption line corresponding to the transition energy \\(\\Delta E_{23} = E_3 – E_2\\) is absent in the room-temperature absorption spectrum?"
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url: "https://nerd-notes.com/ubq/116578/"
date_modified: "2026-08-04T05:02:42+00:00"
---

# A sample of hydrogen gas at room temperature is illuminated by a broad-spectrum light source. The resulting absorption spectrum displays dark lines corresponding to electron transitions from the ground state (\(n = 1\)) to higher energy levels (\(n = 2, 3, 4\)), but lines corresponding to transitions between excited states, such as \(n = 2 \to n = 3\), are absent. However, when the gas is heated to a very high temperature, its emission spectrum displays bright lines for transitions between excited states, including \(n = 3 \to n = 2\). Which of the following best explains why the absorption line corresponding to the transition energy \(\Delta E_{23} = E_3 – E_2\) is absent in the room-temperature absorption spectrum?

A sample of hydrogen gas at room temperature is illuminated by a broad-spectrum light source. The resulting absorption spectrum displays dark lines corresponding to electron transitions from the ground state (\(n = 1\)) to higher energy levels (\(n = 2, 3, 4\)), but lines corresponding to transitions between excited states, such as \(n = 2 \to n = 3\), are absent. However, when the gas is heated to a very high temperature, its emission spectrum displays bright lines for transitions between excited states, including \(n = 3 \to n = 2\). Which of the following best explains why the absorption line corresponding to the transition energy \(\Delta E_{23} = E_3 - E_2\) is absent in the room-temperature absorption spectrum?

![An energy-level diagram for a hydrogen atom with horizontal lines labeled n = 1 at the bottom, n = 2 above it, n = 3 above that, and n = 4 near the top. Vertical spacing decreases between higher energy levels. On the left side, solid vertical arrows point upward from n = 1 to n = 2, n = 3, and n = 4, representing ground-state absorption transitions. A dashed vertical upward arrow goes from n = 2 to n = 3 with a question mark next to it. On the right side, a downward vertical arrow goes from n = 3 to n = 2, labeled emission. No other text, lines, or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-energy-levels-1785819761-IXKauf.jpg)

- **A.** Photons with energy \(\Delta E_{23}\) cannot be absorbed by cold gas because photon absorption requires sufficient energy to liberate the electron from the ground state in a single interaction.
- **B.** At room temperature, gas atoms that absorb photons of energy \(\Delta E_{23}\) re-emit them exclusively in the forward direction, preventing a dark absorption line from forming.
- **C.** Nearly all gas atoms at room temperature reside in the \(n = 1\) ground state, so there is an insufficient population of atoms in the \(n = 2\) state to absorb photons with energy \(\Delta E_{23}\).
- **D.** The transition between \(n = 2\) and \(n = 3\) is quantum-mechanically forbidden for absorption, but thermal collisions at high temperatures alter atomic selection rules to permit emission.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116578/*