---
title: "A student uses \\(\\text{X(g)}\\) and \\(\\text{Y(g)}\\), two nonreactive monatomic gases, as tracers in a leak-detection system. The graph shows normalized Maxwell-Boltzmann speed distributions for samples of the gases. All samples behave ideally.  Based on the graph, what is the value of the following ratio? \\[ \\dfrac{u_{\\mathrm{rms},\\text{Y}}(600\\ \\text{K})}{u_{\\mathrm{rms},\\text{X}}(300\\ \\text{K})} \\]"
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url: "https://nerd-notes.com/ubq/120106/"
date_modified: "2026-08-21T08:41:38+00:00"
---

# A student uses \(\text{X(g)}\) and \(\text{Y(g)}\), two nonreactive monatomic gases, as tracers in a leak-detection system. The graph shows normalized Maxwell-Boltzmann speed distributions for samples of the gases. All samples behave ideally.

Based on the graph, what is the value of the following ratio?
\[
\dfrac{u_{\mathrm{rms},\text{Y}}(600\ \text{K})}{u_{\mathrm{rms},\text{X}}(300\ \text{K})}
\]

A student uses \(\text{X(g)}\) and \(\text{Y(g)}\), two nonreactive monatomic gases, as tracers in a leak-detection system. The graph shows normalized Maxwell-Boltzmann speed distributions for samples of the gases. All samples behave ideally.

Based on the graph, what is the value of the following ratio?
\[
\dfrac{u_{\mathrm{rms},\text{Y}}(600\ \text{K})}{u_{\mathrm{rms},\text{X}}(300\ \text{K})}
\]

![A grayscale graph displays exactly \(3\) normalized Maxwell-Boltzmann speed-distribution curves. The horizontal axis is labeled molecular speed, \(v\), and the vertical axis is labeled normalized fraction of molecules. The horizontal axis has exactly \(2\) marked ticks: the first is labeled \(v_0\) and aligned with the solid curve’s maximum; the second is labeled \(2v_0\) and aligned with the coincident dashed and dotted maxima. A legend maps the solid line to \(\text{X(g)}\) at \(300\ \text{K}\), the dashed line to \(\text{Y(g)}\) at \(300\ \text{K}\), and the dotted line to \(\text{X(g)}\) at \(1200\ \text{K}\). The solid curve is tall and narrow. The dashed and dotted curves coincide exactly, are broader, and have a maximum height equal to \(\dfrac{1}{2}\) that of the solid curve. All curves begin at the origin, approach the horizontal axis at high speed, and enclose equal areas. There are no gridlines. No other labels, text, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787301698-Wm6VNH.jpg)

- **A.** \(\dfrac{\sqrt{2}}{2}\)
- **B.** \(\sqrt{2}\)
- **C.** \(2\sqrt{2}\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120106/*